Reorganized Cython modules and updated Radial[T] formula
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cimport numpy as np
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# Cython Types.
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ctypedef np.int64_t INT_T
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ctypedef np.float64_t FLOAT_T
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# Stores initialization functions.
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cdef struct Init:
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IArray (*IArray)(INT_T*, (INT_T, INT_T)) nogil
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FArray (*FArray)(FLOAT_T*, (INT_T, INT_T)) nogil
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#IList (*IList)() nogil
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BitSet (*BitSet)(INT_T) nogil
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Vector2D (*Vector2D)(FLOAT_T, FLOAT_T) nogil
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Matrix2x2 (*Matrix2x2)(FLOAT_T, FLOAT_T, FLOAT_T, FLOAT_T) nogil
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SiteCacheMap (*SiteCacheMap)(INT_T, INT_T, INT_T, INT_T, INT_T) nogil
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EdgeCacheMap (*EdgeCacheMap)(INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T,
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INT_T, INT_T, INT_T, INT_T, INT_T, INT_T) nogil
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VoronoiInfo (*VoronoiInfo)(INT_T [:, ::1], INT_T[:, ::1], FLOAT_T[:, ::1],
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FLOAT_T[:, ::1], FLOAT_T[:, ::1], FLOAT_T[:, ::1],
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EdgeCacheMap*) nogil
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Site (*Site)(INT_T, VoronoiInfo*) nogil
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HalfEdge (*HalfEdge)(INT_T, VoronoiInfo*) nogil
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# Integer Array psuedo-class for continguous arrays.
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cdef struct IArray:
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INT_T* arr
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(INT_T, INT_T) shape
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INT_T (*get)(IArray*, (INT_T, INT_T)) nogil
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void (*set)(IArray*, (INT_T, INT_T), INT_T) nogil
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# Float Array psuedo-class for continguous arrays.
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ctypedef struct FArray:
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FLOAT_T* arr
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(INT_T, INT_T) shape
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FLOAT_T (*get)(FArray*, (INT_T, INT_T)) nogil
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void (*set)(FArray*, (INT_T, INT_T), FLOAT_T) nogil
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# Simple append-only dynamic integer array.
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# ctypedef struct IList:
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# INT_T* data
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# INT_T size, length
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# void (*append)(IList*, INT_T) nogil
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# void (*free)(IList*) nogil
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# Uses an array of bits to determine if value in set.
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ctypedef struct BitSet:
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INT_T* bits
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bint (*add)(BitSet*, INT_T) nogil
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void (*free)(BitSet*) nogil
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# Psuedo-operator definitions.
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ctypedef Vector2D* (*VectorSelfVecOp)(Vector2D*, Vector2D) nogil
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ctypedef Vector2D (*VectorCopyVecOp)(Vector2D*, Vector2D) nogil
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ctypedef Vector2D* (*VectorSelfSclOp)(Vector2D*, FLOAT_T) nogil
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ctypedef Vector2D (*VectorCopySclOp)(Vector2D*, FLOAT_T) nogil
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ctypedef Matrix2x2* (*MatrixSelfMatOp)(Matrix2x2*, Matrix2x2) nogil
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ctypedef Matrix2x2 (*MatrixCopyMatOp)(Matrix2x2*, Matrix2x2) nogil
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ctypedef Matrix2x2* (*MatrixSelfSclOp)(Matrix2x2*, FLOAT_T) nogil
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ctypedef Matrix2x2 (*MatrixCopySclOp)(Matrix2x2*, FLOAT_T) nogil
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ctypedef struct VectorSelfOps:
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Vector2D* (*neg)(Vector2D*) nogil
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VectorSelfVecOp vadd
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VectorSelfVecOp vsub
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VectorSelfVecOp vmul
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VectorSelfVecOp vdiv
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Vector2D* (*matmul)(Vector2D*, Matrix2x2) nogil
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VectorSelfSclOp sadd
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VectorSelfSclOp ssub
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VectorSelfSclOp smul
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VectorSelfSclOp sdiv
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ctypedef struct VectorCopyOps:
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Vector2D (*neg)(Vector2D*) nogil
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VectorCopyVecOp vadd
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VectorCopyVecOp vsub
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VectorCopyVecOp vmul
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VectorCopyVecOp vdiv
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Vector2D (*matmul)(Vector2D*, Matrix2x2) nogil
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VectorCopySclOp sadd
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VectorCopySclOp ssub
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VectorCopySclOp smul
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VectorCopySclOp sdiv
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ctypedef struct MatrixSelfOps:
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Matrix2x2* (*neg)(Matrix2x2*) nogil
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MatrixSelfMatOp madd
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MatrixSelfMatOp msub
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MatrixSelfMatOp mmul
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MatrixSelfMatOp mdiv
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MatrixSelfMatOp matmul
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MatrixSelfSclOp sadd
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MatrixSelfSclOp ssub
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MatrixSelfSclOp smul
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MatrixSelfSclOp sdiv
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ctypedef struct MatrixCopyOps:
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Matrix2x2 (*neg)(Matrix2x2*) nogil
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MatrixCopyMatOp madd
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MatrixCopyMatOp msub
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MatrixCopyMatOp mmul
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MatrixCopyMatOp mdiv
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MatrixCopyMatOp matmul
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MatrixCopySclOp sadd
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MatrixCopySclOp ssub
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MatrixCopySclOp smul
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MatrixCopySclOp sdiv
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# Psuedo-class for a 2-dimensional vector. No orientation.
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ctypedef struct Vector2D:
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FLOAT_T x, y
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VectorSelfOps self
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VectorCopyOps copy
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bint (*equals)(Vector2D*, Vector2D) nogil
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Vector2D (*rot)(Vector2D*) nogil
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FLOAT_T (*dot)(Vector2D*, Vector2D) nogil
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FLOAT_T (*mag)(Vector2D*) nogil
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# Psuedo-class for a 2x2 matrix.
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ctypedef struct Matrix2x2:
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FLOAT_T a, b, c, d
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MatrixSelfOps self
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MatrixCopyOps copy
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bint (*equals)(Matrix2x2*, Matrix2x2) nogil
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Vector2D (*vecmul)(Matrix2x2*, Vector2D) nogil
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# Psuedo-class that handles caching for sites.
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ctypedef struct SiteCacheMap:
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INT_T iarea, iperim, iisoparam, ienergy, iavg_radius
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FLOAT_T (*area)(Site*, FLOAT_T) nogil
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FLOAT_T (*perim)(Site*, FLOAT_T) nogil
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FLOAT_T (*isoparam)(Site*, FLOAT_T) nogil
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FLOAT_T (*energy)(Site*, FLOAT_T) nogil
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FLOAT_T (*avg_radius)(Site*, FLOAT_T) nogil
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# Psuedo-class that handles caching for edges.
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ctypedef struct EdgeCacheMap:
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INT_T iH, ila, ila_mag, ida, ida_mag, ixij, idVdv, iphi, iB, iF, ii2p,\
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ilntan, icsc, size
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Matrix2x2 (*H)(HalfEdge*, Matrix2x2) nogil
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Vector2D (*la)(HalfEdge*, Vector2D) nogil
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Vector2D (*da)(HalfEdge*, Vector2D) nogil
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Vector2D (*xij)(HalfEdge*, Vector2D) nogil
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Vector2D (*dVdv)(HalfEdge*, Vector2D) nogil
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Vector2D (*i2p)(HalfEdge*, Vector2D) nogil
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FLOAT_T (*la_mag)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*da_mag)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*phi)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*B)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*F)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*lntan)(HalfEdge*, FLOAT_T) nogil
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FLOAT_T (*csc)(HalfEdge*, FLOAT_T) nogil
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# Psuedo-class to just contain all pertaining info for sites and edges.
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ctypedef struct VoronoiInfo:
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IArray sites, edges
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FArray points, vertices, site_cache, edge_cache
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EdgeCacheMap* edge_cache_map
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# Psuedo-class for a Site.
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ctypedef struct Site:
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INT_T arr_index
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VoronoiInfo* info
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SiteCacheMap* cache
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INT_T (*index)(Site*) nogil
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Vector2D (*vec)(Site*) nogil
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HalfEdge (*edge)(Site*) nogil
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INT_T (*edge_num)(Site*) nogil
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# Psuedo-class for an HalfEdge.
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ctypedef struct HalfEdge:
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INT_T orig_arr_index, arr_index
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VoronoiInfo* info
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EdgeCacheMap* cache
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INT_T (*origin_index)(HalfEdge*) nogil
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Vector2D (*origin)(HalfEdge*) nogil
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Site (*face)(HalfEdge*) nogil
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HalfEdge (*next)(HalfEdge*) nogil
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HalfEdge (*prev)(HalfEdge*) nogil
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HalfEdge (*twin)(HalfEdge*) nogil
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Matrix2x2 (*get_H)(HalfEdge*, Site) nogil
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cdef class VoronoiContainer:
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cdef readonly INT_T n
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cdef readonly FLOAT_T w, h, r, energy
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cdef FLOAT_T [2] dim
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cdef FLOAT_T [:, ::1] points, vertices, site_cache, edge_cache, grad
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cdef INT_T [:, ::1] sites, edges
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cdef EdgeCacheMap* edge_cache_map
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cdef dict __dict__
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cdef void calculate_voronoi(VoronoiContainer self,
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np.ndarray[FLOAT_T, ndim=2] site_arr) except *
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cdef void generate_dcel(VoronoiContainer self) except *
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cdef void common_cache(VoronoiContainer self) except *
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cdef void precompute(self) except *
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cdef void calc_grad(self) except *
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cdef void get_statistics(VoronoiContainer self) except *
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@staticmethod
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cdef inline Matrix2x2 calc_H(HalfEdge, HalfEdge) nogil
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@staticmethod
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cdef inline bint sign(FLOAT_T [::1], FLOAT_T [::1], FLOAT_T [::1])
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cdef class AreaEnergy(VoronoiContainer):
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cdef readonly FLOAT_T minimum
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cdef void precompute(self) except *
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cdef void calc_grad(self) except *
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cdef class RadialALEnergy(VoronoiContainer):
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cdef void precompute(self) except *
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cdef void calc_grad(self) except *
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cdef class RadialTEnergy(VoronoiContainer):
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cdef void precompute(self) except *
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cdef void calc_grad(self) except *
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cdef class Calc:
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@staticmethod
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cdef inline FLOAT_T phi(HalfEdge) nogil
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@staticmethod
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cdef inline Vector2D I2(HalfEdge, FLOAT_T, FLOAT_T) nogil
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@staticmethod
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cdef Vector2D radialt_edge_grad(HalfEdge, Site, FLOAT_T) nogil
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@ -1,3 +0,0 @@
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include "core.pyx"
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include "voronoi_dcel.pyx"
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include "energy.pyx"
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@ -1,385 +0,0 @@
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import array, scipy.spatial, numpy as np
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from cython.parallel import parallel, prange
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cimport numpy as np
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from cpython cimport array
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from libc.stdlib cimport malloc, realloc, calloc, free
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from libc.math cimport isnan, NAN, pi as PI, M_PI_2 as PI_2, \
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sqrt, log, sin, cos, tan, acos, fabs
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from _squish cimport INT_T, FLOAT_T, Init, IArray, FArray, BitSet, Vector2D, Matrix2x2, \
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VectorSelfOps, VectorCopyOps, MatrixSelfOps, MatrixCopyOps, \
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SiteCacheMap, EdgeCacheMap, VoronoiInfo, Site, HalfEdge
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#### Constants ####
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INT = np.int64
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FLOAT = np.float64
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cdef FLOAT_T TAU = 2*PI
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# In most cases, the amount of edges relevant to a gradient will
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# not exceed this number. However, we assign a growth rate of 8 edges,
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# when dynamically allocating.
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cdef INT_T EDGE_ARR_SIZE = 32
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cdef Init init
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init.IArray, init.FArray, init.BitSet, init.Vector2D, init.Matrix2x2 = \
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init_iarray, init_farray, init_bitset, init_vector2d, init_matrix2x2
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cdef VectorSelfOps VSO
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cdef VectorCopyOps VCO
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cdef MatrixSelfOps MSO
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cdef MatrixCopyOps MCO
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VSO.neg, VSO.vadd, VSO.vsub, VSO.vmul, VSO.vdiv, VSO.sadd, VSO.ssub, VSO.smul, VSO.sdiv = \
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v_neg_s, v_vadd_s, v_vsub_s, v_vmul_s, v_vdiv_s, v_sadd_s, v_ssub_s, v_smul_s, v_sdiv_s
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VSO.matmul = v_matmul_s
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VCO.neg, VCO.vadd, VCO.vsub, VCO.vmul, VCO.vdiv, VCO.sadd, VCO.ssub, VCO.smul, VCO.sdiv = \
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v_neg_c, v_vadd_c, v_vsub_c, v_vmul_c, v_vdiv_c, v_sadd_c, v_ssub_c, v_smul_c, v_sdiv_c
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VCO.matmul = v_matmul_c
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MSO.neg, MSO.madd, MSO.msub, MSO.mmul, MSO.mdiv, MSO.sadd, MSO.ssub, MSO.smul, MSO.sdiv = \
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m_neg_s, m_madd_s, m_msub_s, m_mmul_s, m_mdiv_s, m_sadd_s, m_ssub_s, m_smul_s, m_sdiv_s
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MSO.matmul = m_matmul_s
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MCO.neg, MCO.madd, MCO.msub, MCO.mmul, MCO.mdiv, MCO.sadd, MCO.ssub, MCO.smul, MCO.sdiv = \
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m_neg_c, m_madd_c, m_msub_c, m_mmul_c, m_mdiv_c, m_sadd_c, m_ssub_c, m_smul_c, m_sdiv_c
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MCO.matmul = m_matmul_c
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cdef Vector2D NAN_VECTOR = init.Vector2D(NAN, NAN)
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cdef Matrix2x2 NAN_MATRIX = init.Matrix2x2(NAN, NAN, NAN, NAN)
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cdef FLOAT_T[18] SYMM = [0,0, 1,0, 1,1, 0,1, -1,1, -1,0, -1,-1, 0,-1, 1,-1]
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cdef Matrix2x2 R = init.Matrix2x2(0, -1, 1, 0)
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"""
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If bound checking is desired, uncomment out ..._valid_indices functions.
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"""
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#### IArray Methods ####
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cdef inline IArray init_iarray(INT_T* arr, (INT_T, INT_T) shape) nogil:
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cdef IArray iarray
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iarray.arr, iarray.shape = arr, shape
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iarray.get = iarray_get
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iarray.set = iarray_set
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return iarray
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cdef inline bint iarray_valid_indices(IArray* self, (INT_T, INT_T) index) nogil:
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if index[0] > self.shape[0] or index[1] > self.shape[1]:
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with gil:
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raise IndexError(f"Index out of range for IArray with shape {self.shape}")
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cdef inline INT_T iarray_get(IArray* self, (INT_T, INT_T) index) nogil:
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#iarray_valid_indices(&self, index)
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return self.arr[index[0]*self.shape[1] + index[1]]
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cdef inline void iarray_set(IArray* self, (INT_T, INT_T) index, INT_T val) nogil:
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#iarray_valid_indices(&self, index)
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self.arr[index[0]*self.shape[1] + index[1]] = val
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#### FArray Methods ####
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cdef inline FArray init_farray(FLOAT_T* arr, (INT_T, INT_T) shape) nogil:
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|
||||||
cdef FArray farray
|
|
||||||
farray.arr, farray.shape = arr, shape
|
|
||||||
|
|
||||||
farray.get = farray_get
|
|
||||||
farray.set = farray_set
|
|
||||||
return farray
|
|
||||||
|
|
||||||
cdef inline bint farray_valid_indices(FArray* self, (INT_T, INT_T) index) nogil:
|
|
||||||
if index[0] > self.shape[0] or index[1] > self.shape[1]:
|
|
||||||
with gil:
|
|
||||||
raise IndexError(f"Index out of range for FArray with shape {self.shape}")
|
|
||||||
|
|
||||||
cdef inline FLOAT_T farray_get(FArray* self, (INT_T, INT_T) index) nogil:
|
|
||||||
#iarray_valid_indices(&self, index)
|
|
||||||
return self.arr[index[0]*self.shape[1] + index[1]]
|
|
||||||
|
|
||||||
cdef inline void farray_set(FArray* self, (INT_T, INT_T) index, FLOAT_T val) nogil:
|
|
||||||
#iarray_valid_indices(&self, index)
|
|
||||||
self.arr[index[0]*self.shape[1] + index[1]] = val
|
|
||||||
|
|
||||||
|
|
||||||
#### IList Methods ####
|
|
||||||
|
|
||||||
# cdef inline IList init_ilist() nogil:
|
|
||||||
# cdef IList ilist
|
|
||||||
# ilist.size = EDGE_ARR_SIZE
|
|
||||||
# ilist.length = 0
|
|
||||||
# ilist.data = <INT_T*> malloc(self.size * sizeof(INT_T))
|
|
||||||
|
|
||||||
# ilist.append, ilist.free = ilist_append, ilist_free
|
|
||||||
|
|
||||||
# return ilist
|
|
||||||
|
|
||||||
# cdef inline void ilist_append(IList* self, INT_T) nogil:
|
|
||||||
# if self.size == self.length:
|
|
||||||
# ilist.data = <INT_T*> realloc((self.size+8) * sizeof(INT_T))
|
|
||||||
# self.size += 8
|
|
||||||
|
|
||||||
# self.data[self.length] == INT_T
|
|
||||||
# self.length += 1
|
|
||||||
|
|
||||||
# cdef inline void ilist_free(IList* self) nogil:
|
|
||||||
# free(self.data)
|
|
||||||
|
|
||||||
#### BitSet Methods ####
|
|
||||||
|
|
||||||
cdef inline BitSet init_bitset(INT_T elements) nogil:
|
|
||||||
cdef BitSet bitset
|
|
||||||
bitset.bits = <INT_T*> calloc(((elements/sizeof(INT_T))+1), sizeof(INT_T))
|
|
||||||
|
|
||||||
bitset.add, bitset.free = bitset_add, bitset_free
|
|
||||||
return bitset
|
|
||||||
|
|
||||||
cdef inline bint bitset_add(BitSet* self, INT_T val) nogil:
|
|
||||||
cdef INT_T index, rel_index, old
|
|
||||||
index = val/sizeof(INT_T)
|
|
||||||
old = self.bits[index]
|
|
||||||
rel_index = val - index*sizeof(INT_T)
|
|
||||||
|
|
||||||
self.bits[index] = (1 << rel_index) | old # New value.
|
|
||||||
|
|
||||||
return old == self.bits[index] # Means 1 was already there.
|
|
||||||
|
|
||||||
cdef inline void bitset_free(BitSet* self) nogil:
|
|
||||||
free(self.bits)
|
|
||||||
|
|
||||||
#### Vector2D Methods ####
|
|
||||||
"""
|
|
||||||
Prefix 'v' stands for vector, element by element operation.
|
|
||||||
Prefix 's' stands for scalar, broadcasted operation.
|
|
||||||
Suffix 'w' stands for write, overwriting current value.
|
|
||||||
Suffix 'n' stands for new, copying to a new location.
|
|
||||||
|
|
||||||
While it's possible to chain 'new' operations, when possible,
|
|
||||||
avoid this, so fewer objects are needed.
|
|
||||||
"""
|
|
||||||
|
|
||||||
cdef inline Vector2D init_vector2d(FLOAT_T x, FLOAT_T y) nogil:
|
|
||||||
cdef Vector2D vec
|
|
||||||
vec.x, vec.y = x, y
|
|
||||||
vec.self, vec.copy = VSO, VCO
|
|
||||||
|
|
||||||
vec.equals, vec.rot, vec.dot, vec.mag = v_equals, rot, dot, mag
|
|
||||||
|
|
||||||
return vec
|
|
||||||
|
|
||||||
|
|
||||||
cdef inline bint v_equals(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return ((self.x == w.x) and (self.y == w.y))
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_neg_s(Vector2D* self) nogil:
|
|
||||||
self.x = -self.x
|
|
||||||
self.y = -self.y
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_vadd_s(Vector2D* self, Vector2D w) nogil:
|
|
||||||
self.x += w.x
|
|
||||||
self.y += w.y
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_vsub_s(Vector2D* self, Vector2D w) nogil:
|
|
||||||
self.x -= w.x
|
|
||||||
self.y -= w.y
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_vmul_s(Vector2D* self, Vector2D w) nogil:
|
|
||||||
self.x *= w.x
|
|
||||||
self.y *= w.y
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_vdiv_s(Vector2D* self, Vector2D w) nogil:
|
|
||||||
self.x /= w.x
|
|
||||||
self.y /= w.y
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_sadd_s(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
self.x += s
|
|
||||||
self.y += s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_ssub_s(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
self.x -= s
|
|
||||||
self.y -= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_smul_s(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
self.x *= s
|
|
||||||
self.y *= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_sdiv_s(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
self.x /= s
|
|
||||||
self.y /= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D* v_matmul_s(Vector2D* self, Matrix2x2 m) nogil:
|
|
||||||
self.x, self.y = self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Vector2D v_neg_c(Vector2D* self) nogil:
|
|
||||||
return init.Vector2D(-self.x, -self.y)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_vadd_c(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return init.Vector2D(self.x + w.x, self.y + w.y)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_vsub_c(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return init.Vector2D(self.x - w.x, self.y - w.y)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_vmul_c(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return init.Vector2D(self.x * w.x, self.y * w.y)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_vdiv_c(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return init.Vector2D(self.x / w.x, self.y / w.y)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_sadd_c(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
return init.Vector2D(self.x + s, self.y + s)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_ssub_c(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
return init.Vector2D(self.x + s, self.y + s)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_smul_c(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
return init.Vector2D(self.x * s, self.y * s)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_sdiv_c(Vector2D* self, FLOAT_T s) nogil:
|
|
||||||
return init.Vector2D(self.x / s, self.y / s)
|
|
||||||
|
|
||||||
cdef inline Vector2D v_matmul_c(Vector2D* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Vector2D(
|
|
||||||
self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline Vector2D rot(Vector2D* self) nogil:
|
|
||||||
return init.Vector2D(-self.y, self.x)
|
|
||||||
|
|
||||||
cdef inline FLOAT_T dot(Vector2D* self, Vector2D w) nogil:
|
|
||||||
return self.x*w.x + self.y*w.y
|
|
||||||
|
|
||||||
cdef inline FLOAT_T mag(Vector2D* self) nogil:
|
|
||||||
return <FLOAT_T>sqrt(<double>(self.x*self.x + self.y*self.y))
|
|
||||||
|
|
||||||
|
|
||||||
#### Matrix2x2 Methods ####
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 init_matrix2x2(FLOAT_T a, FLOAT_T b, FLOAT_T c, FLOAT_T d) nogil:
|
|
||||||
cdef Matrix2x2 matrix
|
|
||||||
matrix.a, matrix.b, matrix.c, matrix.d = a, b, c, d
|
|
||||||
matrix.self, matrix.copy = MSO, MCO
|
|
||||||
|
|
||||||
matrix.equals, matrix.vecmul = m_equals, m_vecmul
|
|
||||||
|
|
||||||
return matrix
|
|
||||||
|
|
||||||
cdef inline bint m_equals(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return (
|
|
||||||
(self.a == m.a) and (self.b == m.b) and (self.c == m.c) and (self.d == m.d)
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline Vector2D m_vecmul(Matrix2x2* self, Vector2D v) nogil:
|
|
||||||
return init.Vector2D(
|
|
||||||
self.a*v.x + self.b*v.y, self.c*v.x + self.d*v.y
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_neg_s(Matrix2x2* self) nogil:
|
|
||||||
self.a, self.b, self.c, self.d = -self.a, -self.b, -self.c, -self.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_madd_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
self.a += m.a
|
|
||||||
self.b += m.b
|
|
||||||
self.c += m.c
|
|
||||||
self.d += m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_msub_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
self.a -= m.a
|
|
||||||
self.b -= m.b
|
|
||||||
self.c -= m.c
|
|
||||||
self.d -= m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_mmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
self.a *= m.a
|
|
||||||
self.b *= m.b
|
|
||||||
self.c *= m.c
|
|
||||||
self.d *= m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_mdiv_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
self.a /= m.a
|
|
||||||
self.b /= m.b
|
|
||||||
self.c /= m.c
|
|
||||||
self.d /= m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_sadd_s(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
self.a += s
|
|
||||||
self.b += s
|
|
||||||
self.c += s
|
|
||||||
self.d += s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_ssub_s(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
self.a -= s
|
|
||||||
self.b -= s
|
|
||||||
self.c -= s
|
|
||||||
self.d -= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_smul_s(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
self.a *= s
|
|
||||||
self.b *= s
|
|
||||||
self.c *= s
|
|
||||||
self.d *= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_sdiv_s(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
self.a /= s
|
|
||||||
self.b /= s
|
|
||||||
self.c /= s
|
|
||||||
self.d /= s
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2* m_matmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
self.a, self.b, self.c, self.d = \
|
|
||||||
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d, \
|
|
||||||
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
|
|
||||||
return self
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_neg_c(Matrix2x2* self) nogil:
|
|
||||||
return init.Matrix2x2(-self.a, -self.b, -self.c, -self.d)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_madd_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Matrix2x2(self.a+m.a, self.b+m.b, self.c+m.c, self.d+m.d)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_msub_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Matrix2x2(self.a-m.a, self.b-m.b, self.c-m.c, self.d-m.d)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_mmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Matrix2x2(self.a*m.a, self.b*m.b, self.c*m.c, self.d*m.d)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_mdiv_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Matrix2x2(self.a/m.a, self.b/m.b, self.c/m.c, self.d/m.d)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_sadd_c(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
return init.Matrix2x2(self.a+s, self.b+s, self.c+s, self.d+s)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_ssub_c(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
return init.Matrix2x2(self.a-s, self.b-s, self.c-s, self.d-s)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_smul_c(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
return init.Matrix2x2(self.a*s, self.b*s, self.c*s, self.d*s)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_sdiv_c(Matrix2x2* self, FLOAT_T s) nogil:
|
|
||||||
return init.Matrix2x2(self.a/s, self.b/s, self.c/s, self.d/s)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 m_matmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
|
||||||
return init.Matrix2x2(
|
|
||||||
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d,
|
|
||||||
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
|
|
||||||
)
|
|
||||||
@ -1,338 +0,0 @@
|
|||||||
cdef class AreaEnergy(VoronoiContainer):
|
|
||||||
"""
|
|
||||||
Class for formulas relevant to the Area energy.
|
|
||||||
:param n: [int] how many sites to generate.
|
|
||||||
:param w: [float] width of the bounding domain.
|
|
||||||
:param h: [float] height of the bounding domain.
|
|
||||||
:param r: [float] radius of zero energy circle.
|
|
||||||
:param sites: [np.ndarray] collection of sites.
|
|
||||||
"""
|
|
||||||
|
|
||||||
attr_str = "area"
|
|
||||||
title_str = "Area"
|
|
||||||
|
|
||||||
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
|
||||||
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
|
||||||
self.edge_cache_map = &AREA_EDGE_CACHE_MAP
|
|
||||||
self.energy = 0.0
|
|
||||||
|
|
||||||
super().__init__(n, w, h, r, site_arr)
|
|
||||||
self.minimum = (<FLOAT_T>n)*(w*h/(<FLOAT_T>n)-PI*r**2)**2
|
|
||||||
|
|
||||||
|
|
||||||
cdef void precompute(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
cdef Site xi
|
|
||||||
cdef HalfEdge em, e, ep
|
|
||||||
cdef Vector2D vdiff
|
|
||||||
cdef FLOAT_T A = PI*self.r**2
|
|
||||||
cdef FLOAT_T energy = 0
|
|
||||||
|
|
||||||
cdef INT_T i, j
|
|
||||||
for i in prange(self.sites.shape[0], nogil=True):
|
|
||||||
xi = init.Site(i, &info)
|
|
||||||
e = xi.edge(&xi)
|
|
||||||
xi.cache.energy(&xi,
|
|
||||||
(xi.cache.area(&xi, NAN) - A)**2
|
|
||||||
)
|
|
||||||
if i < self.n:
|
|
||||||
energy += xi.cache.energy(&xi, NAN)
|
|
||||||
|
|
||||||
for j in range(xi.edge_num(&xi)):
|
|
||||||
em, ep = e.prev(&e), e.next(&e)
|
|
||||||
vdiff = em.origin(&em)
|
|
||||||
vdiff.self.vsub(&vdiff, ep.origin(&ep))
|
|
||||||
e.cache.dVdv(&e, R.vecmul(&R, vdiff))
|
|
||||||
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
|
|
||||||
|
|
||||||
e = e.next(&e)
|
|
||||||
|
|
||||||
self.energy = energy
|
|
||||||
|
|
||||||
|
|
||||||
cdef void calc_grad(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
cdef Site xi, xf
|
|
||||||
cdef HalfEdge e, f
|
|
||||||
cdef Vector2D dedxi_p
|
|
||||||
cdef BitSet edge_set
|
|
||||||
|
|
||||||
cdef INT_T num_edges = self.edges.shape[0]
|
|
||||||
cdef FLOAT_T A = PI*self.r**2
|
|
||||||
|
|
||||||
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
|
|
||||||
|
|
||||||
cdef INT_T i, j
|
|
||||||
for i in prange(self.n, nogil=True):
|
|
||||||
xi = init.Site(i, &info)
|
|
||||||
e = xi.edge(&xi)
|
|
||||||
edge_set = init.BitSet(num_edges)
|
|
||||||
for j in range(xi.edge_num(&xi)): # Looping through site edges.
|
|
||||||
f = e
|
|
||||||
while True: # Circling this vertex.
|
|
||||||
if not edge_set.add(&edge_set, f.arr_index):
|
|
||||||
xf = f.face(&f)
|
|
||||||
dedxi_p = f.cache.dVdv(&f, NAN_VECTOR) #dVdv
|
|
||||||
dedxi_p.self.smul(&dedxi_p, xf.cache.area(&xf, NAN) - A)
|
|
||||||
dedxi_p.self.matmul(&dedxi_p, e.cache.H(&e, NAN_MATRIX))
|
|
||||||
dedx[i][0] -= dedxi_p.x
|
|
||||||
dedx[i][1] -= dedxi_p.y
|
|
||||||
|
|
||||||
f = f.twin(&f)
|
|
||||||
f = f.next(&f)
|
|
||||||
if f.arr_index == e.arr_index:
|
|
||||||
break
|
|
||||||
|
|
||||||
e = e.next(&e)
|
|
||||||
edge_set.free(&edge_set)
|
|
||||||
self.grad = dedx
|
|
||||||
|
|
||||||
|
|
||||||
cdef class RadialALEnergy(VoronoiContainer):
|
|
||||||
"""
|
|
||||||
Class for formulas relevant to the Area energy.
|
|
||||||
:param n: [int] how many sites to generate.
|
|
||||||
:param w: [float] width of the bounding domain.
|
|
||||||
:param h: [float] height of the bounding domain.
|
|
||||||
:param r: [float] radius of zero energy circle.
|
|
||||||
:param sites: [np.ndarray] collection of sites.
|
|
||||||
"""
|
|
||||||
|
|
||||||
attr_str = "radial-al"
|
|
||||||
title_str = "Radial[AL]"
|
|
||||||
|
|
||||||
|
|
||||||
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
|
||||||
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
|
||||||
#self.edge_cache_map = &AREA_EDGE_CACHE_MAP
|
|
||||||
self.energy = 0.0
|
|
||||||
|
|
||||||
super().__init__(n, w, h, r, site_arr)
|
|
||||||
|
|
||||||
|
|
||||||
cdef void precompute(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
pass
|
|
||||||
|
|
||||||
|
|
||||||
cdef void calc_grad(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
pass
|
|
||||||
|
|
||||||
|
|
||||||
cdef class RadialTEnergy(VoronoiContainer):
|
|
||||||
"""
|
|
||||||
Class for formulas relevant to the Area energy.
|
|
||||||
:param n: [int] how many sites to generate.
|
|
||||||
:param w: [float] width of the bounding domain.
|
|
||||||
:param h: [float] height of the bounding domain.
|
|
||||||
:param r: [float] radius of zero energy circle.
|
|
||||||
:param sites: [np.ndarray] collection of sites.
|
|
||||||
"""
|
|
||||||
|
|
||||||
attr_str = "radial-t"
|
|
||||||
title_str = "Radial[T]"
|
|
||||||
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
|
||||||
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
|
||||||
self.edge_cache_map = &RADIALT_EDGE_CACHE_MAP
|
|
||||||
self.energy = 0.0
|
|
||||||
|
|
||||||
super().__init__(n, w, h, r, site_arr)
|
|
||||||
|
|
||||||
|
|
||||||
cdef void precompute(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
cdef Site xi
|
|
||||||
cdef HalfEdge em, e
|
|
||||||
cdef Vector2D Rnla
|
|
||||||
|
|
||||||
# All energy has a 2pir_0 term.
|
|
||||||
cdef FLOAT_T [:] site_energy = np.full(self.sites.shape[0], TAU*self.r**2)
|
|
||||||
cdef FLOAT_T [:] avg_radii = np.zeros(self.sites.shape[0])
|
|
||||||
cdef FLOAT_T energy, r0, t, tp, B, lntan, csc
|
|
||||||
energy, r0 = 0, self.r
|
|
||||||
|
|
||||||
cdef INT_T i, j
|
|
||||||
for i in prange(self.sites.shape[0], nogil=True):
|
|
||||||
xi = init.Site(i, &info)
|
|
||||||
e = xi.edge(&xi)
|
|
||||||
for j in range(xi.edge_num(&xi)):
|
|
||||||
em = e.prev(&e)
|
|
||||||
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
|
|
||||||
t = Calc.phi(e)
|
|
||||||
|
|
||||||
e.cache.phi(&e, t)
|
|
||||||
Rnla = e.cache.la(&e, NAN_VECTOR)
|
|
||||||
Rnla.self.neg(&Rnla)
|
|
||||||
Rnla = Rnla.rot(&Rnla)
|
|
||||||
|
|
||||||
if Rnla.x < 0:
|
|
||||||
e.cache.B(&e, -<FLOAT_T>acos(<double>(Rnla.y/e.cache.la_mag(&e, NAN))))
|
|
||||||
else:
|
|
||||||
e.cache.B(&e, <FLOAT_T>acos(<double>(Rnla.y/e.cache.la_mag(&e, NAN))))
|
|
||||||
|
|
||||||
e.cache.i2p(&e, Calc.I2(e, r0, t))
|
|
||||||
e = e.next(&e)
|
|
||||||
|
|
||||||
# For looping again to calculate integrals.
|
|
||||||
em = xi.edge(&xi)
|
|
||||||
for j in range(xi.edge_num(&xi)):
|
|
||||||
e = em.next(&em)
|
|
||||||
B = em.cache.B(&em, NAN)
|
|
||||||
t, tp = em.cache.phi(&em, NAN), e.cache.phi(&e, NAN)
|
|
||||||
|
|
||||||
lntan = <FLOAT_T>(log(fabs(tan(<double>((tp+B)/2))))) - \
|
|
||||||
<FLOAT_T>(log(fabs(tan(<double>((t+B)/2)))))
|
|
||||||
|
|
||||||
csc = 1/(<FLOAT_T>(sin(<double>(tp+B)))) - \
|
|
||||||
1/(<FLOAT_T>(sin(<double>(t+B))))
|
|
||||||
|
|
||||||
em.cache.lntan(&em, lntan)
|
|
||||||
em.cache.csc(&em, csc)
|
|
||||||
|
|
||||||
avg_radii[i] += (em.cache.F(&em, NAN)/em.cache.la_mag(&em, NAN))*lntan
|
|
||||||
|
|
||||||
em = em.next(&em)
|
|
||||||
|
|
||||||
site_energy[i] += 2*(xi.cache.area(&xi, NAN) - r0*avg_radii[i])
|
|
||||||
|
|
||||||
xi.cache.avg_radius(&xi, avg_radii[i]/TAU)
|
|
||||||
xi.cache.energy(&xi, site_energy[i])
|
|
||||||
if i < self.n:
|
|
||||||
energy += site_energy[i]
|
|
||||||
|
|
||||||
self.energy = energy
|
|
||||||
|
|
||||||
|
|
||||||
cdef void calc_grad(self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
cdef Site xi
|
|
||||||
cdef HalfEdge e, fm, f
|
|
||||||
cdef Vector2D dedxi_p
|
|
||||||
cdef BitSet edge_set
|
|
||||||
|
|
||||||
cdef INT_T num_edges = self.edges.shape[0]
|
|
||||||
cdef FLOAT_T r0 = self.r
|
|
||||||
|
|
||||||
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
|
|
||||||
|
|
||||||
cdef INT_T i, j
|
|
||||||
for i in prange(self.n, nogil=True):
|
|
||||||
xi = init.Site(i, &info)
|
|
||||||
e = xi.edge(&xi)
|
|
||||||
edge_set = init.BitSet(num_edges)
|
|
||||||
|
|
||||||
for j in range(xi.edge_num(&xi)): # Looping through site edges.
|
|
||||||
f = e
|
|
||||||
while True: # Circling this vertex.
|
|
||||||
fm = f.prev(&f)
|
|
||||||
if not edge_set.add(&edge_set, f.arr_index):
|
|
||||||
dedxi_p = Calc.radialt_edge_grad(f, xi, r0)
|
|
||||||
dedx[i][0] -= dedxi_p.x
|
|
||||||
dedx[i][1] -= dedxi_p.y
|
|
||||||
|
|
||||||
if not edge_set.add(&edge_set, fm.arr_index):
|
|
||||||
dedxi_p = Calc.radialt_edge_grad(fm, xi, r0)
|
|
||||||
dedx[i][0] -= dedxi_p.x
|
|
||||||
dedx[i][1] -= dedxi_p.y
|
|
||||||
|
|
||||||
|
|
||||||
f = f.twin(&f)
|
|
||||||
f = f.next(&f)
|
|
||||||
|
|
||||||
if f.arr_index == e.arr_index:
|
|
||||||
break
|
|
||||||
|
|
||||||
e = e.next(&e)
|
|
||||||
edge_set.free(&edge_set)
|
|
||||||
self.grad = dedx
|
|
||||||
|
|
||||||
|
|
||||||
cdef class Calc:
|
|
||||||
@staticmethod
|
|
||||||
cdef inline FLOAT_T phi(HalfEdge e) nogil:
|
|
||||||
cdef Vector2D da = e.cache.da(&e, NAN_VECTOR)
|
|
||||||
cdef FLOAT_T angle = <FLOAT_T>acos(<double>(da.x/e.cache.da_mag(&e, NAN)))
|
|
||||||
return angle if da.y >= 0 else TAU - angle
|
|
||||||
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
cdef inline Vector2D I2(HalfEdge e, FLOAT_T r0, FLOAT_T t) nogil:
|
|
||||||
cdef Vector2D Rda = e.cache.da(&e, NAN_VECTOR)
|
|
||||||
Rda = Rda.rot(&Rda)
|
|
||||||
Rda.self.sdiv(&Rda, e.cache.da_mag(&e, NAN))
|
|
||||||
|
|
||||||
return Rda
|
|
||||||
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
cdef Vector2D radialt_edge_grad(HalfEdge e, Site xi, FLOAT_T r0) nogil:
|
|
||||||
cdef Site xe
|
|
||||||
cdef HalfEdge ep
|
|
||||||
cdef Vector2D Rda, i2ps, fp, gterms, q
|
|
||||||
cdef Matrix2x2 ha, hap, hdiff
|
|
||||||
|
|
||||||
cdef FLOAT_T t1, t2, lntan, csc, sinB, cosB, sinBp, cosBp, F, A, B
|
|
||||||
|
|
||||||
xe = e.face(&e)
|
|
||||||
ep = e.next(&e)
|
|
||||||
F, A, B = e.cache.F(&e, NAN), e.cache.la_mag(&e, NAN), e.cache.B(&e, NAN)
|
|
||||||
t1, t2 = e.cache.phi(&e, NAN), ep.cache.phi(&ep, NAN)
|
|
||||||
|
|
||||||
lntan, csc = e.cache.lntan(&e, NAN), e.cache.csc(&e, NAN)
|
|
||||||
|
|
||||||
sinB, cosB = <FLOAT_T>(sin(<double>(B))), <FLOAT_T>(cos(<double>(B)))
|
|
||||||
sinBp, cosBp = <FLOAT_T>(sin(<double>(B-PI_2))), \
|
|
||||||
<FLOAT_T>(cos(<double>(B-PI_2)))
|
|
||||||
|
|
||||||
|
|
||||||
ha, hap = e.get_H(&e, xi), ep.get_H(&ep, xi)
|
|
||||||
hdiff = hap.copy.msub(&hap, ha)
|
|
||||||
# If edge is part of differentiated site.
|
|
||||||
if xe.index(&xe) == xi.index(&xi):
|
|
||||||
ha.self.msub(&ha, init.Matrix2x2(1.0, 0.0, 0.0, 1.0))
|
|
||||||
hap.self.msub(&hap, init.Matrix2x2(1.0, 0.0, 0.0, 1.0))
|
|
||||||
|
|
||||||
i2ps = ep.cache.i2p(&ep, NAN_VECTOR)
|
|
||||||
i2ps.self.matmul(&i2ps, hap)
|
|
||||||
|
|
||||||
q = e.cache.i2p(&e, NAN_VECTOR)
|
|
||||||
q.self.matmul(&q, ha)
|
|
||||||
|
|
||||||
i2ps.self.vsub(&i2ps, q)
|
|
||||||
|
|
||||||
Rda = e.cache.da(&e, NAN_VECTOR)
|
|
||||||
Rda = Rda.rot(&Rda)
|
|
||||||
|
|
||||||
fp = e.cache.la(&e, NAN_VECTOR)
|
|
||||||
fp.self.matmul(&fp, R.copy.matmul(&R, ha))
|
|
||||||
fp.self.vadd(&fp, Rda.copy.matmul(&Rda, hdiff))
|
|
||||||
fp.self.smul(&fp, lntan/A)
|
|
||||||
|
|
||||||
gterms = init.Vector2D(
|
|
||||||
cosBp*lntan + sinBp*csc,
|
|
||||||
cosB*lntan + sinB*csc
|
|
||||||
)
|
|
||||||
gterms.self.smul(>erms, -F/A**2)
|
|
||||||
|
|
||||||
gterms = gterms.rot(>erms)
|
|
||||||
gterms.self.matmul(>erms, hdiff)
|
|
||||||
|
|
||||||
fp.self.vadd(&fp, gterms)
|
|
||||||
|
|
||||||
i2ps.self.vadd(&i2ps, fp)
|
|
||||||
i2ps.self.smul(&i2ps, -2*r0)
|
|
||||||
|
|
||||||
return i2ps
|
|
||||||
@ -1,689 +0,0 @@
|
|||||||
from _squish cimport SiteCacheMap, EdgeCacheMap, VoronoiInfo, Site, HalfEdge
|
|
||||||
|
|
||||||
#### Constants ####
|
|
||||||
|
|
||||||
init.SiteCacheMap, init.EdgeCacheMap, init.VoronoiInfo, init.Site, init.HalfEdge = \
|
|
||||||
init_sitecachemap, init_edgecachemap, init_voronoiinfo, init_site, init_halfedge
|
|
||||||
|
|
||||||
cdef SiteCacheMap SITE_CACHE_MAP = init.SiteCacheMap(0, 1, 2, 3, 4)
|
|
||||||
|
|
||||||
cdef EdgeCacheMap AREA_EDGE_CACHE_MAP = init.EdgeCacheMap(0, 4, 6, 8, 10, -1, 12, 13,
|
|
||||||
-1, -1, -1, -1, -1, 14)
|
|
||||||
cdef EdgeCacheMap RADIALT_EDGE_CACHE_MAP = init.EdgeCacheMap(0, 4, 6, 8, -1, 10, 12, 13,
|
|
||||||
14, 15, 16, 17, 18, 19)
|
|
||||||
|
|
||||||
#### SiteCacheMap Methods ####
|
|
||||||
|
|
||||||
cdef inline SiteCacheMap init_sitecachemap(INT_T iarea, INT_T iperim, INT_T iisoparam,
|
|
||||||
INT_T ienergy, INT_T iavg_radius) nogil:
|
|
||||||
cdef SiteCacheMap sc
|
|
||||||
sc.iarea, sc.iperim, sc.iisoparam, sc.ienergy, sc.iavg_radius = \
|
|
||||||
iarea, iperim, iisoparam, ienergy, iavg_radius
|
|
||||||
|
|
||||||
sc.area, sc.perim, sc.isoparam, sc.energy, sc.avg_radius = \
|
|
||||||
area, perim, isoparam, energy, avg_radius
|
|
||||||
|
|
||||||
return sc
|
|
||||||
|
|
||||||
|
|
||||||
cdef inline FLOAT_T area(Site* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.site_cache.get(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iarea)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.site_cache.set(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iarea), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T perim(Site* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.site_cache.get(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iperim)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.site_cache.set(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iperim), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T isoparam(Site* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.site_cache.get(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iisoparam)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.site_cache.set(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iisoparam), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T energy(Site* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.site_cache.get(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.ienergy)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.site_cache.set(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.ienergy), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T avg_radius(Site* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.site_cache.get(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iavg_radius)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.site_cache.set(&self.info.site_cache,
|
|
||||||
(self.arr_index, self.cache.iavg_radius), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
|
|
||||||
#### EdgeCacheMap Methods ####
|
|
||||||
|
|
||||||
cdef inline EdgeCacheMap init_edgecachemap(INT_T iH, INT_T ila, INT_T ida, INT_T ixij,
|
|
||||||
INT_T idVdv, INT_T ii2p, INT_T ila_mag, INT_T ida_mag, INT_T iphi, INT_T iB,
|
|
||||||
INT_T iF, INT_T ilntan, INT_T icsc, INT_T size) nogil:
|
|
||||||
cdef EdgeCacheMap ec
|
|
||||||
ec.iH, ec.ila, ec.ida, ec.ixij, ec.idVdv, ec.ii2p, ec.ila_mag, ec.ida_mag, ec.iphi, \
|
|
||||||
ec.iB, ec.iF, ec.ilntan, ec.icsc = iH, ila, ida, ixij, idVdv, ii2p, \
|
|
||||||
ila_mag, ida_mag, iphi, iB, iF, ilntan, icsc
|
|
||||||
ec.size = size
|
|
||||||
|
|
||||||
ec.H, ec.la, ec.da, ec.xij, ec.dVdv, ec.i2p, ec.la_mag, ec.da_mag, ec.phi, ec.B, ec.F, \
|
|
||||||
ec.lntan, ec.csc = H, la, da, xij, dVdv, i2p, la_mag, da_mag, phi, B, F, lntan, csc
|
|
||||||
|
|
||||||
return ec
|
|
||||||
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 H(HalfEdge* self, Matrix2x2 val) nogil:
|
|
||||||
if isnan(<double>val.a):
|
|
||||||
return init.Matrix2x2(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+1)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+2)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+3)
|
|
||||||
),
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH), val.a)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+1), val.b)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+2), val.c)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iH+3), val.d)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline Vector2D la(HalfEdge* self, Vector2D val) nogil:
|
|
||||||
if isnan(<double>val.x):
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila+1)
|
|
||||||
)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila), val.x)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila+1), val.y)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline Vector2D da(HalfEdge* self, Vector2D val) nogil:
|
|
||||||
if isnan(<double>val.x):
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida+1)
|
|
||||||
)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida), val.x)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida+1), val.y)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline Vector2D xij(HalfEdge* self, Vector2D val) nogil:
|
|
||||||
if isnan(<double>val.x):
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ixij)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ixij+1)
|
|
||||||
)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ixij), val.x)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ixij+1), val.y)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline Vector2D dVdv(HalfEdge* self, Vector2D val) nogil:
|
|
||||||
if isnan(<double>val.x):
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.idVdv)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.idVdv+1)
|
|
||||||
)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.idVdv), val.x)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.idVdv+1), val.y)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline Vector2D i2p(HalfEdge* self, Vector2D val) nogil:
|
|
||||||
if isnan(<double>val.x):
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ii2p)
|
|
||||||
),
|
|
||||||
self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ii2p+1)
|
|
||||||
)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ii2p), val.x)
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ii2p+1), val.y)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T la_mag(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila_mag)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ila_mag), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T da_mag(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida_mag)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ida_mag), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T phi(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iphi)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iphi), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T B(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iB)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iB), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T F(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iF)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.iF), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T lntan(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ilntan)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.ilntan), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
cdef inline FLOAT_T csc(HalfEdge* self, FLOAT_T val) nogil:
|
|
||||||
if isnan(<double>val):
|
|
||||||
return self.info.edge_cache.get(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.icsc)
|
|
||||||
)
|
|
||||||
else:
|
|
||||||
self.info.edge_cache.set(&self.info.edge_cache,
|
|
||||||
(self.arr_index, self.cache.icsc), val)
|
|
||||||
return val
|
|
||||||
|
|
||||||
|
|
||||||
#### VoronoiInfo Methods ####
|
|
||||||
|
|
||||||
cdef inline VoronoiInfo init_voronoiinfo(INT_T [:, ::1] sites, INT_T [:, ::1] edges,
|
|
||||||
FLOAT_T [:, ::1] points, FLOAT_T [:, ::1] vertices,
|
|
||||||
FLOAT_T [:, ::1] site_cache, FLOAT_T [:, ::1] edge_cache,
|
|
||||||
EdgeCacheMap* edge_cache_map) nogil:
|
|
||||||
cdef VoronoiInfo info
|
|
||||||
info.sites = init_iarray(&sites[0,0], (<INT_T>sites.shape[0], <INT_T>sites.shape[1]))
|
|
||||||
info.edges = init_iarray(&edges[0,0], (<INT_T>edges.shape[0], <INT_T>edges.shape[1]))
|
|
||||||
info.points = init_farray(&points[0,0], (<INT_T>points.shape[0], <INT_T>points.shape[1]))
|
|
||||||
info.vertices = init_farray(&vertices[0,0],
|
|
||||||
(<INT_T>vertices.shape[0], <INT_T>vertices.shape[1])
|
|
||||||
)
|
|
||||||
info.site_cache = init_farray(&site_cache[0,0],
|
|
||||||
(<INT_T>site_cache.shape[0], <INT_T>site_cache.shape[1])
|
|
||||||
)
|
|
||||||
info.edge_cache = init_farray(&edge_cache[0,0],
|
|
||||||
(<INT_T>edge_cache.shape[0], <INT_T>edge_cache.shape[1])
|
|
||||||
)
|
|
||||||
info.edge_cache_map = edge_cache_map
|
|
||||||
|
|
||||||
return info
|
|
||||||
|
|
||||||
|
|
||||||
#### Site Methods ####
|
|
||||||
|
|
||||||
cdef inline Site init_site(INT_T arr_index, VoronoiInfo* info) nogil:
|
|
||||||
cdef Site site
|
|
||||||
site.arr_index, site.info, site.cache = arr_index, info, &SITE_CACHE_MAP
|
|
||||||
|
|
||||||
site.index, site.vec, site.edge, site.edge_num = index, vec, edge, edge_num
|
|
||||||
|
|
||||||
return site
|
|
||||||
|
|
||||||
|
|
||||||
cdef inline INT_T index(Site* self) nogil:
|
|
||||||
return self.info.sites.get(&self.info.sites, (self.arr_index, 0))
|
|
||||||
|
|
||||||
cdef inline Vector2D vec(Site* self) nogil:
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.points.get(&self.info.points, (self.index(self), 0)),
|
|
||||||
self.info.points.get(&self.info.points, (self.index(self), 1))
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline HalfEdge edge(Site* self) nogil:
|
|
||||||
return init.HalfEdge(
|
|
||||||
self.info.sites.get(&self.info.sites, (self.arr_index, 1)), self.info
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline INT_T edge_num(Site* self) nogil:
|
|
||||||
return self.info.sites.get(&self.info.sites, (self.arr_index, 2))
|
|
||||||
|
|
||||||
|
|
||||||
#### HalfEdge Methods ####
|
|
||||||
|
|
||||||
cdef inline HalfEdge init_halfedge(INT_T arr_index, VoronoiInfo* info) nogil:
|
|
||||||
cdef HalfEdge edge
|
|
||||||
edge.arr_index, edge.info, edge.cache = arr_index, info, info.edge_cache_map
|
|
||||||
edge.orig_arr_index = arr_index
|
|
||||||
|
|
||||||
edge.origin_index, edge.origin, edge.face, edge.next, edge.prev, edge.twin, edge.get_H = \
|
|
||||||
origin_index, origin, face, edge_next, prev, twin, get_H
|
|
||||||
|
|
||||||
return edge
|
|
||||||
|
|
||||||
|
|
||||||
cdef inline INT_T origin_index(HalfEdge* self) nogil:
|
|
||||||
return self.info.edges.get(&self.info.edges, (self.arr_index, 0))
|
|
||||||
|
|
||||||
cdef inline Vector2D origin(HalfEdge* self) nogil:
|
|
||||||
return init.Vector2D(
|
|
||||||
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 0)),
|
|
||||||
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 1))
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline Site face(HalfEdge* self) nogil:
|
|
||||||
return init.Site(
|
|
||||||
self.info.edges.get(&self.info.edges, (self.arr_index, 1)), self.info
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline HalfEdge edge_next(HalfEdge* self) nogil:
|
|
||||||
|
|
||||||
return init.HalfEdge(
|
|
||||||
self.info.edges.get(&self.info.edges, (self.arr_index, 2)), self.info
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline HalfEdge prev(HalfEdge* self) nogil:
|
|
||||||
return init.HalfEdge(
|
|
||||||
self.info.edges.get(&self.info.edges, (self.arr_index, 3)), self.info
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline HalfEdge twin(HalfEdge* self) nogil:
|
|
||||||
return init.HalfEdge(
|
|
||||||
self.info.edges.get(&self.info.edges, (self.arr_index, 4)), self.info
|
|
||||||
)
|
|
||||||
|
|
||||||
cdef inline Matrix2x2 get_H(HalfEdge* self, Site xi) nogil:
|
|
||||||
cdef INT_T this_e = self.origin_index(self)
|
|
||||||
cdef HalfEdge s_e = xi.edge(&xi)
|
|
||||||
cdef INT_T i
|
|
||||||
|
|
||||||
for i in range(xi.edge_num(&xi)):
|
|
||||||
if s_e.origin_index(&s_e) == this_e:
|
|
||||||
return s_e.cache.H(&s_e, NAN_MATRIX)
|
|
||||||
s_e = s_e.next(&s_e)
|
|
||||||
return init.Matrix2x2(0.0, 0.0, 0.0, 0.0)
|
|
||||||
|
|
||||||
|
|
||||||
cdef class VoronoiContainer:
|
|
||||||
"""
|
|
||||||
Class for Voronoi diagrams, stored in a modified DCEL.
|
|
||||||
:param n: [int] how many sites to generate.
|
|
||||||
:param w: [float] width of the bounding domain.
|
|
||||||
:param h: [float] height of the bounding domain.
|
|
||||||
:param r: [float] radius of zero energy circle.
|
|
||||||
:param sites: np.ndarray collection of sites.
|
|
||||||
"""
|
|
||||||
|
|
||||||
def __init__(VoronoiContainer self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r, object site_arr):
|
|
||||||
self.n, self.w, self.h, self.r = n, w, h, r
|
|
||||||
self.dim = [w, h]
|
|
||||||
|
|
||||||
self.calculate_voronoi(site_arr.astype(FLOAT))
|
|
||||||
self.generate_dcel()
|
|
||||||
|
|
||||||
self.common_cache()
|
|
||||||
self.precompute()
|
|
||||||
self.calc_grad()
|
|
||||||
self.get_statistics()
|
|
||||||
|
|
||||||
|
|
||||||
cdef void calculate_voronoi(VoronoiContainer self,
|
|
||||||
np.ndarray[FLOAT_T, ndim=2] site_arr) except *:
|
|
||||||
"""
|
|
||||||
Does all necessary computation and caching once points are set.
|
|
||||||
:param site_arr: initial points for this container.
|
|
||||||
"""
|
|
||||||
global SYMM
|
|
||||||
cdef np.ndarray[FLOAT_T, ndim=2] symm = np.asarray(SYMM).reshape(9,2)
|
|
||||||
cdef np.ndarray[FLOAT_T, ndim=1] dim = np.asarray(self.dim)
|
|
||||||
cdef np.ndarray[FLOAT_T, ndim=2] full_site_arr = np.empty((self.n*9+8, 2), dtype=FLOAT)
|
|
||||||
|
|
||||||
# Generate periodic sites and sites that bound periodic sites.
|
|
||||||
cdef INT_T i
|
|
||||||
for i in range(9):
|
|
||||||
full_site_arr[self.n*i:self.n*(i+1)] = site_arr + symm[i]*dim
|
|
||||||
if i > 0:
|
|
||||||
full_site_arr[9*self.n+i-1] = dim/2 + 2*dim*symm[i]
|
|
||||||
|
|
||||||
# Use SciPy to compute the Voronoi set.
|
|
||||||
self.scipy_vor = scipy.spatial.Voronoi(full_site_arr)
|
|
||||||
self.points = self.scipy_vor.points
|
|
||||||
self.vertices = self.scipy_vor.vertices
|
|
||||||
|
|
||||||
|
|
||||||
cdef void generate_dcel(VoronoiContainer self) except *:
|
|
||||||
cdef INT_T npoints = self.n*9+8
|
|
||||||
cdef array.array int_tmplt = array.array('q', [])
|
|
||||||
|
|
||||||
cdef np.ndarray[INT_T, ndim=1] offsets = np.zeros(self.n*9+1, dtype=INT)
|
|
||||||
cdef array.array vert_indices = array.clone(int_tmplt, 0, False)
|
|
||||||
|
|
||||||
# Flatten regions into array, so it can be used later.
|
|
||||||
cdef INT_T i
|
|
||||||
for i in range(self.n*9):
|
|
||||||
verts = self.scipy_vor.regions[self.scipy_vor.point_region[i]]
|
|
||||||
offsets[i+1] = offsets[i] + len(verts) # Build offsets.
|
|
||||||
vert_indices.extend(array.array('q', verts)) # Flatten
|
|
||||||
|
|
||||||
# Get vertices of original N sites.
|
|
||||||
cdef np.ndarray[INT_T, ndim=1] vert_indices_np = np.asarray(vert_indices)
|
|
||||||
cdef np.ndarray[INT_T, ndim=1] border_sites = np.unique(np.searchsorted(
|
|
||||||
np.asarray(offsets), # Check indices where below matches would be inserted
|
|
||||||
np.nonzero(np.isin( # Indices of other verts being in bound verts.
|
|
||||||
vert_indices_np[offsets[self.n]:], # Rest of the verts to check.
|
|
||||||
np.unique(vert_indices_np[:offsets[self.n]]) # Bound verts
|
|
||||||
))[0] + offsets[self.n],
|
|
||||||
side='right' # If on index == offset_number, should be part of the next site.
|
|
||||||
) - 1) # Subtract by one to get actual site number.
|
|
||||||
|
|
||||||
cdef INT_T border_num = len(border_sites)
|
|
||||||
|
|
||||||
# Build sites array.
|
|
||||||
# [Site Index, Edge Index/Offset, Edge Count]
|
|
||||||
self.sites = np.empty((self.n+border_num, 3), dtype=INT)
|
|
||||||
self.sites.base[:self.n, 0] = np.arange(self.n, dtype=INT)
|
|
||||||
self.sites.base[self.n:, 0] = border_sites
|
|
||||||
self.sites.base[:self.n+1, 1] = offsets[:self.n+1]
|
|
||||||
for i in range(self.n):
|
|
||||||
self.sites[i, 2] = self.sites[i+1, 1] - self.sites[i, 1]
|
|
||||||
|
|
||||||
cdef INT_T edge_count = offsets[self.n]
|
|
||||||
cdef INT_T diff
|
|
||||||
for i in range(border_num):
|
|
||||||
diff = offsets[border_sites[i]+1] - offsets[border_sites[i]]
|
|
||||||
edge_count += diff
|
|
||||||
self.sites[self.n+i, 2] = diff
|
|
||||||
if i < border_num - 1:
|
|
||||||
self.sites[self.n+i+1, 1] = self.sites[self.n+i, 1] + diff
|
|
||||||
|
|
||||||
# Build edges array
|
|
||||||
# [Origin Index, Site Index, Next Index, Prev Index, Twin Index]
|
|
||||||
self.edges = np.empty((edge_count, 5), dtype=INT)
|
|
||||||
cdef np.ndarray[INT_T, ndim=1] site_verts
|
|
||||||
cdef INT_T j, site_i, edge_i, edge_offset, vert_num, twin_index, prev_res
|
|
||||||
|
|
||||||
edge_indices = dict()
|
|
||||||
|
|
||||||
for i in range(self.n + border_num):
|
|
||||||
site_i = self.sites[i, 0]
|
|
||||||
edge_offset = self.sites[i, 1]
|
|
||||||
site_verts = vert_indices_np[offsets[site_i]:offsets[site_i+1]]
|
|
||||||
|
|
||||||
# Scipy outputs sorted vertices, but reverse if not counterclockwise.
|
|
||||||
if not VoronoiContainer.sign(self.points[site_i],
|
|
||||||
self.vertices[site_verts[0]], self.vertices[site_verts[1]]):
|
|
||||||
site_verts = np.flip(site_verts)
|
|
||||||
|
|
||||||
vert_num = offsets[site_i+1] - offsets[site_i]
|
|
||||||
|
|
||||||
for j in range(vert_num):
|
|
||||||
edge_i = edge_offset+j
|
|
||||||
self.edges[edge_i, 0] = site_verts[j]
|
|
||||||
self.edges[edge_i, 1] = i
|
|
||||||
# Add vert_num because of C modulo to get always positive.
|
|
||||||
self.edges[edge_i, 2] = (j+vert_num+1) % vert_num + edge_offset
|
|
||||||
self.edges[edge_i, 3] = (j+vert_num-1) % vert_num + edge_offset
|
|
||||||
|
|
||||||
# Get reversed tuple to theck for twin.
|
|
||||||
twin_index = edge_indices.get(
|
|
||||||
(site_verts[(j+1) % vert_num], site_verts[j]
|
|
||||||
), -1)
|
|
||||||
|
|
||||||
self.edges[edge_i, 4] = twin_index
|
|
||||||
if twin_index == -1:
|
|
||||||
edge_indices[(site_verts[j], site_verts[(j+1) % vert_num])] = \
|
|
||||||
j + edge_offset
|
|
||||||
else:
|
|
||||||
self.edges[twin_index, 4] = j + edge_offset
|
|
||||||
|
|
||||||
self.site_cache = np.empty((self.n + border_num, 5), dtype=FLOAT)
|
|
||||||
self.edge_cache = np.empty((edge_count, self.edge_cache_map.size), dtype=FLOAT)
|
|
||||||
|
|
||||||
|
|
||||||
cdef void common_cache(VoronoiContainer self) except *:
|
|
||||||
cdef VoronoiInfo info = init.VoronoiInfo(self.sites, self.edges, self.points,
|
|
||||||
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
|
||||||
|
|
||||||
cdef Site xi
|
|
||||||
cdef HalfEdge em, ep
|
|
||||||
cdef Vector2D p, q, la, da, Rla
|
|
||||||
|
|
||||||
cdef FLOAT_T [:] area = np.zeros(self.sites.shape[0], dtype=FLOAT)
|
|
||||||
cdef FLOAT_T [:] perim = np.zeros(self.sites.shape[0], dtype=FLOAT)
|
|
||||||
|
|
||||||
cdef INT_T i, j
|
|
||||||
cdef FLOAT_T e_area, la_mag
|
|
||||||
for i in prange(self.sites.shape[0], nogil=True):
|
|
||||||
xi = init.Site(i, &info)
|
|
||||||
em = xi.edge(&xi)
|
|
||||||
for j in range(xi.edge_num(&xi)):
|
|
||||||
ep = em.next(&em)
|
|
||||||
p, q = em.origin(&em), ep.origin(&ep)
|
|
||||||
la, da = q.copy.vsub(&q, p), p.copy.vsub(&p, xi.vec(&xi)) # vp - vm, vm - xi
|
|
||||||
|
|
||||||
la_mag = la.mag(&la)
|
|
||||||
e_area = la.dot(&la, da.rot(&da))
|
|
||||||
Rla = la.rot(&la)
|
|
||||||
|
|
||||||
em.cache.la(&em, la)
|
|
||||||
em.cache.la_mag(&em, la_mag)
|
|
||||||
em.cache.da(&em, da)
|
|
||||||
em.cache.da_mag(&em, da.mag(&da))
|
|
||||||
em.cache.xij(&em, Rla.copy.smul(&Rla, -e_area/la.dot(&la, la)))
|
|
||||||
|
|
||||||
if info.edge_cache_map.iF != -1:
|
|
||||||
em.cache.F(&em, e_area)
|
|
||||||
|
|
||||||
area[i] += e_area
|
|
||||||
perim[i] += la_mag
|
|
||||||
|
|
||||||
em = em.next(&em)
|
|
||||||
|
|
||||||
xi.cache.area(&xi, area[i]/2)
|
|
||||||
xi.cache.perim(&xi, perim[i])
|
|
||||||
xi.cache.isoparam(&xi, 2*PI*area[i]/(perim[i]*perim[i]))
|
|
||||||
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
cdef inline Matrix2x2 calc_H(HalfEdge em, HalfEdge ep) nogil:
|
|
||||||
cdef Vector2D xmv, xpv, im, mp, right, Rpm, Rim, f
|
|
||||||
cdef Matrix2x2 h
|
|
||||||
cdef FLOAT_T im2, mp2
|
|
||||||
|
|
||||||
# Vectors from xi to xm and xp.
|
|
||||||
xmv, xpv = em.cache.xij(&em, NAN_VECTOR), ep.cache.xij(&ep, NAN_VECTOR)
|
|
||||||
im, mp = xmv.copy.neg(&xmv), xmv.copy.vsub(&xmv, xpv) # -xmv, xmv - xpv
|
|
||||||
im2, mp2 = -(xmv.dot(&xmv, xmv)), xmv.dot(&xmv, xmv) - xpv.dot(&xpv, xpv)
|
|
||||||
# (-xmv*xmv, xmv*xmv - xpv*xpv)
|
|
||||||
right = init.Vector2D(im2, mp2)
|
|
||||||
Rpm, Rim = R.vecmul(&R, mp.copy.neg(&mp)), im.rot(&im) # R*-mp, R*im
|
|
||||||
|
|
||||||
h = init.Matrix2x2(Rpm.x, Rim.x, Rpm.y, Rim.y) # [Rpm | Rim], h is temporary.
|
|
||||||
f = h.vecmul(&h, right) # [Rpm | Rim]*right
|
|
||||||
h = R.copy.smul(&R, mp2*(2*mp.dot(&mp, Rim))) # fp*g, g is a scalar.
|
|
||||||
# (fp*g - f*gp)/(g**2). f is a column vector, gp = 2*Rpm is a row vector.
|
|
||||||
h.self.msub(&h, init.Matrix2x2(
|
|
||||||
f.x*2*Rpm.x, f.x*2*Rpm.y, f.y*2*Rpm.x, f.y*2*Rpm.y
|
|
||||||
))
|
|
||||||
h.self.sdiv(&h, (2*mp.dot(&mp, Rim))**2)
|
|
||||||
|
|
||||||
return h
|
|
||||||
|
|
||||||
|
|
||||||
@staticmethod
|
|
||||||
cdef inline bint sign(FLOAT_T [::1] ref, FLOAT_T [::1] p, FLOAT_T [::1] q):
|
|
||||||
"""
|
|
||||||
Outputs if p2 - self is counterclockwise of p1 - self.
|
|
||||||
:param p1: [List[float]] first vector
|
|
||||||
:param p2: [List[float]] second vector
|
|
||||||
:return: [bool] returns if counterclockwise.
|
|
||||||
"""
|
|
||||||
return ((q[0] - ref[0])*-(p[1] - ref[1]) + \
|
|
||||||
(q[1] - ref[1])*(p[0] - ref[0])) >= 0
|
|
||||||
|
|
||||||
# global ROT
|
|
||||||
# cdef np.ndarray[FLOAT_T, ndim=2] rot = np.asarray(ROT).reshape(2,2)
|
|
||||||
# return (q - ref).dot(rot.dot(p - ref)) >= 0
|
|
||||||
|
|
||||||
cdef void precompute(self) except *:
|
|
||||||
pass
|
|
||||||
|
|
||||||
cdef void calc_grad(self) except *:
|
|
||||||
pass
|
|
||||||
|
|
||||||
cdef void get_statistics(self) except *:
|
|
||||||
self.stats = {}
|
|
||||||
cache = self.site_cache[:self.n, :]
|
|
||||||
|
|
||||||
self.stats["site_areas"] = np.asarray(cache[:, SITE_CACHE_MAP.iarea])
|
|
||||||
self.stats["site_edge_count"] = np.asarray(self.sites[:self.n, 2])
|
|
||||||
|
|
||||||
self.stats["site_isos"] = np.asarray(cache[:, SITE_CACHE_MAP.iisoparam])
|
|
||||||
self.stats["site_energies"] = np.asarray(cache[:, SITE_CACHE_MAP.ienergy])
|
|
||||||
self.stats["avg_radius"] = np.asarray(cache[:, SITE_CACHE_MAP.iavg_radius])
|
|
||||||
|
|
||||||
self.stats["isoparam_avg"] = self.stats["site_areas"] / \
|
|
||||||
(PI*self.stats["avg_radius"]**2)
|
|
||||||
|
|
||||||
edges = np.asarray(self.edges)
|
|
||||||
|
|
||||||
mask = np.nonzero(edges[:, 0] != -1)[0]
|
|
||||||
all_edges = mask[(mask % 2 == 0)]
|
|
||||||
caches = edges[all_edges, 4]
|
|
||||||
|
|
||||||
edge_cache = np.asarray(self.edge_cache)
|
|
||||||
|
|
||||||
self.stats["edge_lengths"] = edge_cache[caches, self.edge_cache_map.ila_mag]
|
|
||||||
|
|
||||||
@property
|
|
||||||
def site_arr(self):
|
|
||||||
return np.asarray(self.points[:self.n], dtype=FLOAT)
|
|
||||||
|
|
||||||
@property
|
|
||||||
def vor_data(self):
|
|
||||||
return self.scipy_vor
|
|
||||||
|
|
||||||
@property
|
|
||||||
def gradient(self):
|
|
||||||
return np.asarray(self.grad, dtype=FLOAT)
|
|
||||||
|
|
||||||
def add_sites(self, add):
|
|
||||||
return (self.site_arr + add) % np.asarray(self.dim, dtype=FLOAT)
|
|
||||||
|
|
||||||
def iterate(self, FLOAT_T step):
|
|
||||||
k1 = self.gradient
|
|
||||||
k2 = self.__class__(self.n, self.w, self.h, self.r,
|
|
||||||
self.add_sites(step*k1)
|
|
||||||
).gradient
|
|
||||||
|
|
||||||
return (step/2)*(k1+k2), k1
|
|
||||||
|
|
||||||
|
|
||||||
def hessian(self, d: float) -> np.ndarray:
|
|
||||||
"""
|
|
||||||
Obtains the approximate Hessian.
|
|
||||||
:param d: [float] small d for approximation.
|
|
||||||
:return: 2Nx2N array that represents Hessian.
|
|
||||||
"""
|
|
||||||
HE = np.zeros((2*self.n, 2*self.n))
|
|
||||||
new_sites = np.copy(self.site_arr) # Maintain one copy for speed.
|
|
||||||
for i in range(self.n):
|
|
||||||
for j in range(2):
|
|
||||||
mod = self.w if j == 0 else self.h
|
|
||||||
new_sites[i][j] = (new_sites[i][j] + d) % mod
|
|
||||||
Ep = self.__class__(self.n, self.w, self.h, self.r, new_sites)
|
|
||||||
new_sites[i][j] = (new_sites[i][j] - 2*d) % mod
|
|
||||||
Em = self.__class__(self.n, self.w, self.h, self.r, new_sites)
|
|
||||||
new_sites[i][j] = (new_sites[i][j] + d) % mod
|
|
||||||
|
|
||||||
HE[:, 2*i+j] = ((Ep.gradient - Em.gradient)/(2*d)).flatten()
|
|
||||||
|
|
||||||
# Average out discrepencies, since it should be symmetric.
|
|
||||||
for i in range(2*self.n):
|
|
||||||
for j in range(i, 2*self.n):
|
|
||||||
HE[i][j] = (HE[i][j] + HE[j][i])/2
|
|
||||||
HE[j][i] = HE[i][j]
|
|
||||||
|
|
||||||
return HE
|
|
||||||
|
|
||||||
@ -3,7 +3,8 @@ from typing import List, Tuple, Union, Optional, Iterator, Generator
|
|||||||
import pickle, numpy as np
|
import pickle, numpy as np
|
||||||
from math import gcd
|
from math import gcd
|
||||||
from pathlib import Path
|
from pathlib import Path
|
||||||
from ._squish import VoronoiContainer, AreaEnergy, RadialALEnergy, RadialTEnergy
|
from squish.voronoi import VoronoiContainer
|
||||||
|
from squish.energy import AreaEnergy, RadialALEnergy, RadialTEnergy
|
||||||
|
|
||||||
OUTPUT_DIR = Path("squish_output")
|
OUTPUT_DIR = Path("squish_output")
|
||||||
|
|
||||||
|
|||||||
8834
squish/core.c
Normal file
8834
squish/core.c
Normal file
File diff suppressed because it is too large
Load Diff
135
squish/core.pxd
Normal file
135
squish/core.pxd
Normal file
@ -0,0 +1,135 @@
|
|||||||
|
cimport numpy as np
|
||||||
|
|
||||||
|
# Cython Types.
|
||||||
|
ctypedef np.int64_t INT_T
|
||||||
|
ctypedef np.float64_t FLOAT_T
|
||||||
|
|
||||||
|
ctypedef (INT_T, INT_T) Pair
|
||||||
|
|
||||||
|
# Integer Array psuedo-class for continguous arrays.
|
||||||
|
cdef struct IArray:
|
||||||
|
INT_T* arr
|
||||||
|
Pair shape
|
||||||
|
|
||||||
|
INT_T (*get)(IArray*, Pair) nogil
|
||||||
|
void (*set)(IArray*, Pair, INT_T) nogil
|
||||||
|
|
||||||
|
# Float Array psuedo-class for continguous arrays.
|
||||||
|
ctypedef struct FArray:
|
||||||
|
FLOAT_T* arr
|
||||||
|
Pair shape
|
||||||
|
|
||||||
|
FLOAT_T (*get)(FArray*, Pair) nogil
|
||||||
|
void (*set)(FArray*, Pair, FLOAT_T) nogil
|
||||||
|
|
||||||
|
# Simple append-only dynamic integer array.
|
||||||
|
# ctypedef struct IList:
|
||||||
|
# INT_T* data
|
||||||
|
# INT_T size, length
|
||||||
|
|
||||||
|
# void (*append)(IList*, INT_T) nogil
|
||||||
|
# void (*free)(IList*) nogil
|
||||||
|
|
||||||
|
# Uses an array of bits to determine if value in set.
|
||||||
|
ctypedef struct BitSet:
|
||||||
|
INT_T* bits
|
||||||
|
|
||||||
|
bint (*add)(BitSet*, INT_T) nogil
|
||||||
|
void (*free)(BitSet*) nogil
|
||||||
|
|
||||||
|
# Psuedo-operator definitions.
|
||||||
|
ctypedef Vector2D* (*VectorSelfVecOp)(Vector2D*, Vector2D) nogil
|
||||||
|
ctypedef Vector2D (*VectorCopyVecOp)(Vector2D*, Vector2D) nogil
|
||||||
|
ctypedef Vector2D* (*VectorSelfSclOp)(Vector2D*, FLOAT_T) nogil
|
||||||
|
ctypedef Vector2D (*VectorCopySclOp)(Vector2D*, FLOAT_T) nogil
|
||||||
|
|
||||||
|
ctypedef Matrix2x2* (*MatrixSelfMatOp)(Matrix2x2*, Matrix2x2) nogil
|
||||||
|
ctypedef Matrix2x2 (*MatrixCopyMatOp)(Matrix2x2*, Matrix2x2) nogil
|
||||||
|
ctypedef Matrix2x2* (*MatrixSelfSclOp)(Matrix2x2*, FLOAT_T) nogil
|
||||||
|
ctypedef Matrix2x2 (*MatrixCopySclOp)(Matrix2x2*, FLOAT_T) nogil
|
||||||
|
|
||||||
|
|
||||||
|
ctypedef struct VectorSelfOps:
|
||||||
|
Vector2D* (*neg)(Vector2D*) nogil
|
||||||
|
|
||||||
|
VectorSelfVecOp vadd
|
||||||
|
VectorSelfVecOp vsub
|
||||||
|
VectorSelfVecOp vmul
|
||||||
|
VectorSelfVecOp vdiv
|
||||||
|
Vector2D* (*matmul)(Vector2D*, Matrix2x2) nogil
|
||||||
|
|
||||||
|
VectorSelfSclOp sadd
|
||||||
|
VectorSelfSclOp ssub
|
||||||
|
VectorSelfSclOp smul
|
||||||
|
VectorSelfSclOp sdiv
|
||||||
|
|
||||||
|
|
||||||
|
ctypedef struct VectorCopyOps:
|
||||||
|
Vector2D (*neg)(Vector2D*) nogil
|
||||||
|
|
||||||
|
VectorCopyVecOp vadd
|
||||||
|
VectorCopyVecOp vsub
|
||||||
|
VectorCopyVecOp vmul
|
||||||
|
VectorCopyVecOp vdiv
|
||||||
|
Vector2D (*matmul)(Vector2D*, Matrix2x2) nogil
|
||||||
|
|
||||||
|
VectorCopySclOp sadd
|
||||||
|
VectorCopySclOp ssub
|
||||||
|
VectorCopySclOp smul
|
||||||
|
VectorCopySclOp sdiv
|
||||||
|
|
||||||
|
|
||||||
|
ctypedef struct MatrixSelfOps:
|
||||||
|
Matrix2x2* (*neg)(Matrix2x2*) nogil
|
||||||
|
|
||||||
|
MatrixSelfMatOp madd
|
||||||
|
MatrixSelfMatOp msub
|
||||||
|
MatrixSelfMatOp mmul
|
||||||
|
MatrixSelfMatOp mdiv
|
||||||
|
MatrixSelfMatOp matmul
|
||||||
|
|
||||||
|
MatrixSelfSclOp sadd
|
||||||
|
MatrixSelfSclOp ssub
|
||||||
|
MatrixSelfSclOp smul
|
||||||
|
MatrixSelfSclOp sdiv
|
||||||
|
|
||||||
|
|
||||||
|
ctypedef struct MatrixCopyOps:
|
||||||
|
Matrix2x2 (*neg)(Matrix2x2*) nogil
|
||||||
|
|
||||||
|
MatrixCopyMatOp madd
|
||||||
|
MatrixCopyMatOp msub
|
||||||
|
MatrixCopyMatOp mmul
|
||||||
|
MatrixCopyMatOp mdiv
|
||||||
|
MatrixCopyMatOp matmul
|
||||||
|
|
||||||
|
MatrixCopySclOp sadd
|
||||||
|
MatrixCopySclOp ssub
|
||||||
|
MatrixCopySclOp smul
|
||||||
|
MatrixCopySclOp sdiv
|
||||||
|
|
||||||
|
# Psuedo-class for a 2-dimensional vector. No orientation.
|
||||||
|
ctypedef struct Vector2D:
|
||||||
|
FLOAT_T x, y
|
||||||
|
VectorSelfOps self
|
||||||
|
VectorCopyOps copy
|
||||||
|
|
||||||
|
bint (*equals)(Vector2D*, Vector2D) nogil
|
||||||
|
Vector2D (*rot)(Vector2D*) nogil
|
||||||
|
FLOAT_T (*dot)(Vector2D*, Vector2D) nogil
|
||||||
|
FLOAT_T (*mag)(Vector2D*) nogil
|
||||||
|
|
||||||
|
# Psuedo-class for a 2x2 matrix.
|
||||||
|
ctypedef struct Matrix2x2:
|
||||||
|
FLOAT_T a, b, c, d
|
||||||
|
MatrixSelfOps self
|
||||||
|
MatrixCopyOps copy
|
||||||
|
|
||||||
|
bint (*equals)(Matrix2x2*, Matrix2x2) nogil
|
||||||
|
Vector2D (*vecmul)(Matrix2x2*, Vector2D) nogil
|
||||||
|
|
||||||
|
cdef IArray _IArray(INT_T*, Pair) nogil
|
||||||
|
cdef FArray _FArray(FLOAT_T*, Pair) nogil
|
||||||
|
cdef BitSet _BitSet(INT_T) nogil
|
||||||
|
cdef Vector2D _Vector2D(FLOAT_T, FLOAT_T) nogil
|
||||||
|
cdef Matrix2x2 _Matrix2x2(FLOAT_T, FLOAT_T, FLOAT_T, FLOAT_T) nogil
|
||||||
363
squish/core.pyx
Normal file
363
squish/core.pyx
Normal file
@ -0,0 +1,363 @@
|
|||||||
|
from libc.stdlib cimport calloc, free
|
||||||
|
from libc.math cimport sqrt
|
||||||
|
from squish.core cimport INT_T, FLOAT_T, Pair, \
|
||||||
|
IArray, FArray, BitSet, Vector2D, Matrix2x2, \
|
||||||
|
VectorSelfOps, VectorCopyOps, MatrixSelfOps, MatrixCopyOps
|
||||||
|
|
||||||
|
#### Constants ####
|
||||||
|
|
||||||
|
# In most cases, the amount of edges relevant to a gradient will
|
||||||
|
# not exceed this number. However, we assign a growth rate of 8 edges,
|
||||||
|
# when dynamically allocating.
|
||||||
|
cdef INT_T EDGE_ARR_SIZE = 32
|
||||||
|
|
||||||
|
cdef VectorSelfOps VSO
|
||||||
|
cdef VectorCopyOps VCO
|
||||||
|
cdef MatrixSelfOps MSO
|
||||||
|
cdef MatrixCopyOps MCO
|
||||||
|
|
||||||
|
VSO.neg, VSO.vadd, VSO.vsub, VSO.vmul, VSO.vdiv, VSO.sadd, VSO.ssub, VSO.smul, VSO.sdiv = \
|
||||||
|
v_neg_s, v_vadd_s, v_vsub_s, v_vmul_s, v_vdiv_s, v_sadd_s, v_ssub_s, v_smul_s, v_sdiv_s
|
||||||
|
VSO.matmul = v_matmul_s
|
||||||
|
|
||||||
|
VCO.neg, VCO.vadd, VCO.vsub, VCO.vmul, VCO.vdiv, VCO.sadd, VCO.ssub, VCO.smul, VCO.sdiv = \
|
||||||
|
v_neg_c, v_vadd_c, v_vsub_c, v_vmul_c, v_vdiv_c, v_sadd_c, v_ssub_c, v_smul_c, v_sdiv_c
|
||||||
|
VCO.matmul = v_matmul_c
|
||||||
|
|
||||||
|
MSO.neg, MSO.madd, MSO.msub, MSO.mmul, MSO.mdiv, MSO.sadd, MSO.ssub, MSO.smul, MSO.sdiv = \
|
||||||
|
m_neg_s, m_madd_s, m_msub_s, m_mmul_s, m_mdiv_s, m_sadd_s, m_ssub_s, m_smul_s, m_sdiv_s
|
||||||
|
MSO.matmul = m_matmul_s
|
||||||
|
|
||||||
|
MCO.neg, MCO.madd, MCO.msub, MCO.mmul, MCO.mdiv, MCO.sadd, MCO.ssub, MCO.smul, MCO.sdiv = \
|
||||||
|
m_neg_c, m_madd_c, m_msub_c, m_mmul_c, m_mdiv_c, m_sadd_c, m_ssub_c, m_smul_c, m_sdiv_c
|
||||||
|
MCO.matmul = m_matmul_c
|
||||||
|
|
||||||
|
"""
|
||||||
|
If bound checking is desired, uncomment out ..._valid_indices functions.
|
||||||
|
"""
|
||||||
|
|
||||||
|
#### IArray Methods ####
|
||||||
|
|
||||||
|
cdef inline IArray _IArray(INT_T* arr, Pair shape) nogil:
|
||||||
|
cdef IArray iarray
|
||||||
|
iarray.arr, iarray.shape = arr, shape
|
||||||
|
|
||||||
|
iarray.get, iarray.set = &iarray_get, &iarray_set
|
||||||
|
return iarray
|
||||||
|
|
||||||
|
cdef inline bint iarray_valid_indices(IArray* self, Pair index) nogil:
|
||||||
|
if index[0] > self.shape[0] or index[1] > self.shape[1]:
|
||||||
|
with gil:
|
||||||
|
raise IndexError(f"Index out of range for IArray with shape {self.shape}")
|
||||||
|
|
||||||
|
cdef inline INT_T iarray_get(IArray* self, Pair index) nogil:
|
||||||
|
#iarray_valid_indices(&self, index)
|
||||||
|
return self.arr[index[0]*self.shape[1] + index[1]]
|
||||||
|
|
||||||
|
cdef inline void iarray_set(IArray* self, Pair index, INT_T val) nogil:
|
||||||
|
#iarray_valid_indices(&self, index)
|
||||||
|
self.arr[index[0]*self.shape[1] + index[1]] = val
|
||||||
|
|
||||||
|
|
||||||
|
#### FArray Methods ####
|
||||||
|
|
||||||
|
cdef inline FArray _FArray(FLOAT_T* arr, Pair shape) nogil:
|
||||||
|
cdef FArray farray
|
||||||
|
farray.arr, farray.shape = arr, shape
|
||||||
|
|
||||||
|
farray.get, farray.set = &farray_get, &farray_set
|
||||||
|
return farray
|
||||||
|
|
||||||
|
cdef inline bint farray_valid_indices(FArray* self, Pair index) nogil:
|
||||||
|
if index[0] > self.shape[0] or index[1] > self.shape[1]:
|
||||||
|
with gil:
|
||||||
|
raise IndexError(f"Index out of range for FArray with shape {self.shape}")
|
||||||
|
|
||||||
|
cdef inline FLOAT_T farray_get(FArray* self, Pair index) nogil:
|
||||||
|
#iarray_valid_indices(&self, index)
|
||||||
|
return self.arr[index[0]*self.shape[1] + index[1]]
|
||||||
|
|
||||||
|
cdef inline void farray_set(FArray* self, Pair index, FLOAT_T val) nogil:
|
||||||
|
#iarray_valid_indices(&self, index)
|
||||||
|
self.arr[index[0]*self.shape[1] + index[1]] = val
|
||||||
|
|
||||||
|
|
||||||
|
#### IList Methods ####
|
||||||
|
|
||||||
|
# cdef inline IList init_ilist() nogil:
|
||||||
|
# cdef IList ilist
|
||||||
|
# ilist.size = EDGE_ARR_SIZE
|
||||||
|
# ilist.length = 0
|
||||||
|
# ilist.data = <INT_T*> malloc(self.size * sizeof(INT_T))
|
||||||
|
|
||||||
|
# ilist.append, ilist.free = ilist_append, ilist_free
|
||||||
|
|
||||||
|
# return ilist
|
||||||
|
|
||||||
|
# cdef inline void ilist_append(IList* self, INT_T) nogil:
|
||||||
|
# if self.size == self.length:
|
||||||
|
# ilist.data = <INT_T*> realloc((self.size+8) * sizeof(INT_T))
|
||||||
|
# self.size += 8
|
||||||
|
|
||||||
|
# self.data[self.length] == INT_T
|
||||||
|
# self.length += 1
|
||||||
|
|
||||||
|
# cdef inline void ilist_free(IList* self) nogil:
|
||||||
|
# free(self.data)
|
||||||
|
|
||||||
|
#### BitSet Methods ####
|
||||||
|
|
||||||
|
cdef inline BitSet _BitSet(INT_T elements) nogil:
|
||||||
|
cdef BitSet bitset
|
||||||
|
bitset.bits = <INT_T*> calloc(((elements/sizeof(INT_T))+1), sizeof(INT_T))
|
||||||
|
|
||||||
|
bitset.add, bitset.free = &bitset_add, &bitset_free
|
||||||
|
return bitset
|
||||||
|
|
||||||
|
cdef inline bint bitset_add(BitSet* self, INT_T val) nogil:
|
||||||
|
cdef INT_T index, rel_index, old
|
||||||
|
index = val/sizeof(INT_T)
|
||||||
|
old = self.bits[index]
|
||||||
|
rel_index = val - index*sizeof(INT_T)
|
||||||
|
|
||||||
|
self.bits[index] = (1 << rel_index) | old # New value.
|
||||||
|
|
||||||
|
return old == self.bits[index] # Means 1 was already there.
|
||||||
|
|
||||||
|
cdef inline void bitset_free(BitSet* self) nogil:
|
||||||
|
free(self.bits)
|
||||||
|
|
||||||
|
#### Vector2D Methods ####
|
||||||
|
"""
|
||||||
|
Prefix 'v' stands for vector, element by element operation.
|
||||||
|
Prefix 's' stands for scalar, broadcasted operation.
|
||||||
|
Suffix 'w' stands for write, overwriting current value.
|
||||||
|
Suffix 'n' stands for new, copying to a new location.
|
||||||
|
|
||||||
|
While it's possible to chain 'new' operations, when possible,
|
||||||
|
avoid this, so fewer objects are needed.
|
||||||
|
"""
|
||||||
|
|
||||||
|
cdef inline Vector2D _Vector2D(FLOAT_T x, FLOAT_T y) nogil:
|
||||||
|
cdef Vector2D vec
|
||||||
|
vec.x, vec.y = x, y
|
||||||
|
vec.self, vec.copy = VSO, VCO
|
||||||
|
|
||||||
|
vec.equals, vec.rot, vec.dot, vec.mag = &v_equals, &rot, &dot, &mag
|
||||||
|
|
||||||
|
return vec
|
||||||
|
|
||||||
|
|
||||||
|
cdef inline bint v_equals(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return ((self.x == w.x) and (self.y == w.y))
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_neg_s(Vector2D* self) nogil:
|
||||||
|
self.x = -self.x
|
||||||
|
self.y = -self.y
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_vadd_s(Vector2D* self, Vector2D w) nogil:
|
||||||
|
self.x += w.x
|
||||||
|
self.y += w.y
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_vsub_s(Vector2D* self, Vector2D w) nogil:
|
||||||
|
self.x -= w.x
|
||||||
|
self.y -= w.y
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_vmul_s(Vector2D* self, Vector2D w) nogil:
|
||||||
|
self.x *= w.x
|
||||||
|
self.y *= w.y
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_vdiv_s(Vector2D* self, Vector2D w) nogil:
|
||||||
|
self.x /= w.x
|
||||||
|
self.y /= w.y
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_sadd_s(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
self.x += s
|
||||||
|
self.y += s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_ssub_s(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
self.x -= s
|
||||||
|
self.y -= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_smul_s(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
self.x *= s
|
||||||
|
self.y *= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_sdiv_s(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
self.x /= s
|
||||||
|
self.y /= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D* v_matmul_s(Vector2D* self, Matrix2x2 m) nogil:
|
||||||
|
self.x, self.y = self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Vector2D v_neg_c(Vector2D* self) nogil:
|
||||||
|
return _Vector2D(-self.x, -self.y)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_vadd_c(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return _Vector2D(self.x + w.x, self.y + w.y)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_vsub_c(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return _Vector2D(self.x - w.x, self.y - w.y)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_vmul_c(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return _Vector2D(self.x * w.x, self.y * w.y)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_vdiv_c(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return _Vector2D(self.x / w.x, self.y / w.y)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_sadd_c(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
return _Vector2D(self.x + s, self.y + s)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_ssub_c(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
return _Vector2D(self.x + s, self.y + s)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_smul_c(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
return _Vector2D(self.x * s, self.y * s)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_sdiv_c(Vector2D* self, FLOAT_T s) nogil:
|
||||||
|
return _Vector2D(self.x / s, self.y / s)
|
||||||
|
|
||||||
|
cdef inline Vector2D v_matmul_c(Vector2D* self, Matrix2x2 m) nogil:
|
||||||
|
return _Vector2D(
|
||||||
|
self.x*m.a + self.y*m.c, self.x*m.b + self.y*m.d
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline Vector2D rot(Vector2D* self) nogil:
|
||||||
|
return _Vector2D(-self.y, self.x)
|
||||||
|
|
||||||
|
cdef inline FLOAT_T dot(Vector2D* self, Vector2D w) nogil:
|
||||||
|
return self.x*w.x + self.y*w.y
|
||||||
|
|
||||||
|
cdef inline FLOAT_T mag(Vector2D* self) nogil:
|
||||||
|
return <FLOAT_T>sqrt(<double>(self.x*self.x + self.y*self.y))
|
||||||
|
|
||||||
|
|
||||||
|
#### Matrix2x2 Methods ####
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 _Matrix2x2(FLOAT_T a, FLOAT_T b, FLOAT_T c, FLOAT_T d) nogil:
|
||||||
|
cdef Matrix2x2 matrix
|
||||||
|
matrix.a, matrix.b, matrix.c, matrix.d = a, b, c, d
|
||||||
|
matrix.self, matrix.copy = MSO, MCO
|
||||||
|
|
||||||
|
matrix.equals, matrix.vecmul = &m_equals, &m_vecmul
|
||||||
|
|
||||||
|
return matrix
|
||||||
|
|
||||||
|
cdef inline bint m_equals(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return (
|
||||||
|
(self.a == m.a) and (self.b == m.b) and (self.c == m.c) and (self.d == m.d)
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline Vector2D m_vecmul(Matrix2x2* self, Vector2D v) nogil:
|
||||||
|
return _Vector2D(
|
||||||
|
self.a*v.x + self.b*v.y, self.c*v.x + self.d*v.y
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_neg_s(Matrix2x2* self) nogil:
|
||||||
|
self.a, self.b, self.c, self.d = -self.a, -self.b, -self.c, -self.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_madd_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
self.a += m.a
|
||||||
|
self.b += m.b
|
||||||
|
self.c += m.c
|
||||||
|
self.d += m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_msub_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
self.a -= m.a
|
||||||
|
self.b -= m.b
|
||||||
|
self.c -= m.c
|
||||||
|
self.d -= m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_mmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
self.a *= m.a
|
||||||
|
self.b *= m.b
|
||||||
|
self.c *= m.c
|
||||||
|
self.d *= m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_mdiv_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
self.a /= m.a
|
||||||
|
self.b /= m.b
|
||||||
|
self.c /= m.c
|
||||||
|
self.d /= m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_sadd_s(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
self.a += s
|
||||||
|
self.b += s
|
||||||
|
self.c += s
|
||||||
|
self.d += s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_ssub_s(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
self.a -= s
|
||||||
|
self.b -= s
|
||||||
|
self.c -= s
|
||||||
|
self.d -= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_smul_s(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
self.a *= s
|
||||||
|
self.b *= s
|
||||||
|
self.c *= s
|
||||||
|
self.d *= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_sdiv_s(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
self.a /= s
|
||||||
|
self.b /= s
|
||||||
|
self.c /= s
|
||||||
|
self.d /= s
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2* m_matmul_s(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
self.a, self.b, self.c, self.d = \
|
||||||
|
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d, \
|
||||||
|
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
|
||||||
|
return self
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_neg_c(Matrix2x2* self) nogil:
|
||||||
|
return _Matrix2x2(-self.a, -self.b, -self.c, -self.d)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_madd_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return _Matrix2x2(self.a+m.a, self.b+m.b, self.c+m.c, self.d+m.d)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_msub_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return _Matrix2x2(self.a-m.a, self.b-m.b, self.c-m.c, self.d-m.d)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_mmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return _Matrix2x2(self.a*m.a, self.b*m.b, self.c*m.c, self.d*m.d)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_mdiv_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return _Matrix2x2(self.a/m.a, self.b/m.b, self.c/m.c, self.d/m.d)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_sadd_c(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
return _Matrix2x2(self.a+s, self.b+s, self.c+s, self.d+s)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_ssub_c(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
return _Matrix2x2(self.a-s, self.b-s, self.c-s, self.d-s)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_smul_c(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
return _Matrix2x2(self.a*s, self.b*s, self.c*s, self.d*s)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_sdiv_c(Matrix2x2* self, FLOAT_T s) nogil:
|
||||||
|
return _Matrix2x2(self.a/s, self.b/s, self.c/s, self.d/s)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 m_matmul_c(Matrix2x2* self, Matrix2x2 m) nogil:
|
||||||
|
return _Matrix2x2(
|
||||||
|
self.a*m.a + self.b*m.c, self.a*m.b + self.b*m.d,
|
||||||
|
self.c*m.a + self.d*m.c, self.c*m.b + self.d*m.d
|
||||||
|
)
|
||||||
@ -183,8 +183,8 @@ class Diagram:
|
|||||||
defects[7]["x"].append(vec[0])
|
defects[7]["x"].append(vec[0])
|
||||||
defects[7]["y"].append(vec[1])
|
defects[7]["y"].append(vec[1])
|
||||||
|
|
||||||
ax.scatter(defects[5]["x"], defects[5]["y"], marker="p", color="red")
|
ax.scatter(defects[5]["x"], defects[5]["y"], marker="p", color="C0")
|
||||||
ax.scatter(defects[7]["x"], defects[7]["y"], marker="*", color="red")
|
ax.scatter(defects[7]["x"], defects[7]["y"], marker="*", color="C0")
|
||||||
|
|
||||||
ax.text(
|
ax.text(
|
||||||
0.05,
|
0.05,
|
||||||
|
|||||||
27737
squish/energy.c
Normal file
27737
squish/energy.c
Normal file
File diff suppressed because it is too large
Load Diff
302
squish/energy.pyx
Normal file
302
squish/energy.pyx
Normal file
@ -0,0 +1,302 @@
|
|||||||
|
import numpy as np
|
||||||
|
from cython.parallel import parallel, prange
|
||||||
|
|
||||||
|
cimport numpy as np
|
||||||
|
from libc.math cimport NAN, pi as PI, atanh
|
||||||
|
from squish.core cimport INT_T, FLOAT_T, Vector2D, Matrix2x2, BitSet, \
|
||||||
|
_Vector2D, _Matrix2x2, _BitSet
|
||||||
|
from squish.voronoi cimport Site, HalfEdge, EdgeCacheMap, VoronoiInfo, \
|
||||||
|
_Site, _HalfEdge, _EdgeCacheMap, _VoronoiInfo, VoronoiContainer, \
|
||||||
|
R, NAN_MATRIX, NAN_VECTOR
|
||||||
|
|
||||||
|
#### Constants ####
|
||||||
|
|
||||||
|
INT = np.int64
|
||||||
|
FLOAT = np.float64
|
||||||
|
|
||||||
|
cdef EdgeCacheMap AREA_ECM = _EdgeCacheMap(0, 4, 6, 8, 10, 12, 13, -1, -1, 14)
|
||||||
|
cdef EdgeCacheMap RADIALT_ECM = _EdgeCacheMap(0, 4, 6, 8, -1, 10, 11, 12, 13, 14)
|
||||||
|
|
||||||
|
cdef class AreaEnergy(VoronoiContainer):
|
||||||
|
"""
|
||||||
|
Class for formulas relevant to the Area energy.
|
||||||
|
:param n: [int] how many sites to generate.
|
||||||
|
:param w: [float] width of the bounding domain.
|
||||||
|
:param h: [float] height of the bounding domain.
|
||||||
|
:param r: [float] radius of zero energy circle.
|
||||||
|
:param sites: [np.ndarray] collection of sites.
|
||||||
|
"""
|
||||||
|
|
||||||
|
attr_str = "area"
|
||||||
|
title_str = "Area"
|
||||||
|
|
||||||
|
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
||||||
|
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
||||||
|
self.edge_cache_map = &AREA_ECM
|
||||||
|
self.energy = 0.0
|
||||||
|
|
||||||
|
super().__init__(n, w, h, r, site_arr)
|
||||||
|
self.minimum = (<FLOAT_T>n)*(w*h/(<FLOAT_T>n)-PI*r**2)**2
|
||||||
|
|
||||||
|
|
||||||
|
cdef void precompute(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef Site xi
|
||||||
|
cdef HalfEdge em, e, ep
|
||||||
|
cdef Vector2D vdiff
|
||||||
|
|
||||||
|
cdef FLOAT_T [:] site_energy = np.full(self.sites.shape[0], PI*self.r**2)
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
for i in prange(self.sites.shape[0], nogil=True):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
e = xi.edge(&xi)
|
||||||
|
|
||||||
|
site_energy[i] = (xi.cache.area(&xi, NAN) - site_energy[i])**2
|
||||||
|
xi.cache.energy(&xi, site_energy[i])
|
||||||
|
|
||||||
|
j = 0
|
||||||
|
while j < xi.edge_num(&xi):
|
||||||
|
em, ep = e.prev(&e), e.next(&e)
|
||||||
|
vdiff = em.origin(&em)
|
||||||
|
vdiff.self.vsub(&vdiff, ep.origin(&ep))
|
||||||
|
e.cache.dVdv(&e, R.vecmul(&R, vdiff))
|
||||||
|
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
|
||||||
|
|
||||||
|
e = e.next(&e)
|
||||||
|
j = j + 1
|
||||||
|
|
||||||
|
self.energy = np.sum(site_energy[:self.n])
|
||||||
|
|
||||||
|
|
||||||
|
cdef void calc_grad(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef Site xi, xf
|
||||||
|
cdef HalfEdge e, f
|
||||||
|
cdef Vector2D dedxi_p
|
||||||
|
cdef BitSet edge_set
|
||||||
|
|
||||||
|
cdef INT_T num_edges = self.edges.shape[0]
|
||||||
|
cdef FLOAT_T A = PI*self.r**2
|
||||||
|
|
||||||
|
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
for i in prange(self.n, nogil=True):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
e = xi.edge(&xi)
|
||||||
|
edge_set = _BitSet(num_edges)
|
||||||
|
j = 0
|
||||||
|
while j < xi.edge_num(&xi): # Looping through site edges.
|
||||||
|
f = e
|
||||||
|
while True: # Circling this vertex.
|
||||||
|
if not edge_set.add(&edge_set, f.arr_index):
|
||||||
|
xf = f.face(&f)
|
||||||
|
dedxi_p = f.cache.dVdv(&f, NAN_VECTOR) #dVdv
|
||||||
|
dedxi_p.self.smul(&dedxi_p, xf.cache.area(&xf, NAN) - A)
|
||||||
|
dedxi_p.self.matmul(&dedxi_p, e.cache.H(&e, NAN_MATRIX))
|
||||||
|
dedx[i][0] -= dedxi_p.x
|
||||||
|
dedx[i][1] -= dedxi_p.y
|
||||||
|
|
||||||
|
f = f.twin(&f)
|
||||||
|
f = f.next(&f)
|
||||||
|
if f.arr_index == e.arr_index:
|
||||||
|
break
|
||||||
|
|
||||||
|
e = e.next(&e)
|
||||||
|
j = j + 1
|
||||||
|
edge_set.free(&edge_set)
|
||||||
|
self.grad = dedx
|
||||||
|
|
||||||
|
|
||||||
|
cdef class RadialALEnergy(VoronoiContainer):
|
||||||
|
"""
|
||||||
|
Class for formulas relevant to the Area energy.
|
||||||
|
:param n: [int] how many sites to generate.
|
||||||
|
:param w: [float] width of the bounding domain.
|
||||||
|
:param h: [float] height of the bounding domain.
|
||||||
|
:param r: [float] radius of zero energy circle.
|
||||||
|
:param sites: [np.ndarray] collection of sites.
|
||||||
|
"""
|
||||||
|
|
||||||
|
attr_str = "radial-al"
|
||||||
|
title_str = "Radial[AL]"
|
||||||
|
|
||||||
|
|
||||||
|
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
||||||
|
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
||||||
|
#self.edge_cache_map = &AREA_EDGE_CACHE_MAP
|
||||||
|
self.energy = 0.0
|
||||||
|
|
||||||
|
super().__init__(n, w, h, r, site_arr)
|
||||||
|
|
||||||
|
|
||||||
|
cdef void precompute(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
pass
|
||||||
|
|
||||||
|
|
||||||
|
cdef void calc_grad(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
pass
|
||||||
|
|
||||||
|
|
||||||
|
cdef class RadialTEnergy(VoronoiContainer):
|
||||||
|
"""
|
||||||
|
Class for formulas relevant to the Area energy.
|
||||||
|
:param n: [int] how many sites to generate.
|
||||||
|
:param w: [float] width of the bounding domain.
|
||||||
|
:param h: [float] height of the bounding domain.
|
||||||
|
:param r: [float] radius of zero energy circle.
|
||||||
|
:param sites: [np.ndarray] collection of sites.
|
||||||
|
"""
|
||||||
|
|
||||||
|
attr_str = "radial-t"
|
||||||
|
title_str = "Radial[T]"
|
||||||
|
def __init__(AreaEnergy self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
||||||
|
np.ndarray[FLOAT_T, ndim=2] site_arr):
|
||||||
|
self.edge_cache_map = &RADIALT_ECM
|
||||||
|
self.energy = 0.0
|
||||||
|
|
||||||
|
super().__init__(n, w, h, r, site_arr)
|
||||||
|
|
||||||
|
|
||||||
|
cdef void precompute(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef Site xi
|
||||||
|
cdef HalfEdge e, em, ep
|
||||||
|
cdef Vector2D la
|
||||||
|
|
||||||
|
# All energy has a 2pir_0 term.
|
||||||
|
cdef FLOAT_T [:] site_energy = np.full(self.sites.shape[0], 2*PI*self.r**2)
|
||||||
|
cdef FLOAT_T [:] avg_radii = np.zeros(self.sites.shape[0])
|
||||||
|
cdef FLOAT_T sm, sp
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
for i in prange(self.sites.shape[0], nogil=True):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
e = xi.edge(&xi)
|
||||||
|
j = 0
|
||||||
|
while j < xi.edge_num(&xi):
|
||||||
|
em, ep = e.prev(&e), e.next(&e)
|
||||||
|
e.cache.H(&e, VoronoiContainer.calc_H(em, e))
|
||||||
|
|
||||||
|
la = e.cache.la(&e, NAN_VECTOR)
|
||||||
|
sp = la.dot(&la, ep.cache.da(&ep, NAN_VECTOR)) # dap . la
|
||||||
|
sm = la.dot(&la, e.cache.da(&e, NAN_VECTOR)) # da . la
|
||||||
|
|
||||||
|
sp = sp / (ep.cache.da_mag(&ep, NAN) * e.cache.la_mag(&e, NAN))
|
||||||
|
sm = sm / (e.cache.da_mag(&e, NAN) * e.cache.la_mag(&e, NAN))
|
||||||
|
|
||||||
|
e.cache.calI(&e, <FLOAT_T>(atanh(<double>sp) - atanh(<double>sm)))
|
||||||
|
|
||||||
|
avg_radii[i] += (
|
||||||
|
e.cache.area_p(&e, NAN) * e.cache.calI(&e, NAN)
|
||||||
|
/ e.cache.la_mag(&e, NAN)
|
||||||
|
)
|
||||||
|
|
||||||
|
e = e.next(&e)
|
||||||
|
j = j + 1
|
||||||
|
|
||||||
|
site_energy[i] += 2*(xi.cache.area(&xi, NAN) - self.r*avg_radii[i])
|
||||||
|
|
||||||
|
xi.cache.avg_radius(&xi, avg_radii[i]/(2*PI))
|
||||||
|
xi.cache.energy(&xi, site_energy[i])
|
||||||
|
|
||||||
|
self.energy = np.sum(site_energy[:self.n])
|
||||||
|
|
||||||
|
|
||||||
|
cdef void calc_grad(self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef Site xi
|
||||||
|
cdef HalfEdge e, fm, f, fp
|
||||||
|
cdef Vector2D temp1, temp2, temp3, dedxi_p
|
||||||
|
cdef BitSet edge_set
|
||||||
|
|
||||||
|
cdef INT_T num_edges = self.edges.shape[0]
|
||||||
|
|
||||||
|
cdef FLOAT_T [:, ::1] dedx = np.zeros((self.n, 2), dtype=FLOAT)
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
for i in prange(self.n, nogil=True):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
e = xi.edge(&xi)
|
||||||
|
edge_set = _BitSet(num_edges)
|
||||||
|
|
||||||
|
j = 0
|
||||||
|
while j < xi.edge_num(&xi): # Looping through site edges.
|
||||||
|
f = e
|
||||||
|
dedxi_p = _Vector2D(0, 0)
|
||||||
|
# dedx (only x)
|
||||||
|
temp1 = f.cache.la(&f, NAN_VECTOR)
|
||||||
|
temp1 = temp1.rot(&temp1)
|
||||||
|
dedxi_p = temp1.copy.smul(
|
||||||
|
&temp1,
|
||||||
|
f.cache.calI(&f, NAN) / f.cache.la_mag(&f, NAN)
|
||||||
|
)
|
||||||
|
|
||||||
|
while True: # Circling this vertex.
|
||||||
|
fm, fp = f.prev(&f), f.next(&f)
|
||||||
|
|
||||||
|
if not edge_set.add(&edge_set, f.arr_index):
|
||||||
|
# ( -rot(dap) ) / |la|
|
||||||
|
temp1 = fp.cache.da(&fp, NAN_VECTOR)
|
||||||
|
temp1 = temp1.rot(&temp1)
|
||||||
|
temp1.self.sdiv(&temp1, -f.cache.la_mag(&f, NAN))
|
||||||
|
|
||||||
|
# la * area_p / |la|^2
|
||||||
|
temp3 = f.cache.la(&f, NAN_VECTOR)
|
||||||
|
temp3.self.smul(
|
||||||
|
&temp3,
|
||||||
|
f.cache.area_p(&f, NAN) / f.cache.la_mag(&f, NAN)**3
|
||||||
|
)
|
||||||
|
# Combine * calI
|
||||||
|
temp1.self.vadd(&temp1, temp3)
|
||||||
|
temp1.self.smul(&temp1, f.cache.calI(&f, NAN))
|
||||||
|
|
||||||
|
# rot(dam) / |lam|
|
||||||
|
temp2 = fm.cache.da(&fm, NAN_VECTOR)
|
||||||
|
temp2 = temp2.rot(&temp2)
|
||||||
|
temp2.self.sdiv(&temp2, fm.cache.la_mag(&fm, NAN))
|
||||||
|
|
||||||
|
# lam * area_pm / |lam|^2
|
||||||
|
temp3 = fm.cache.la(&fm, NAN_VECTOR)
|
||||||
|
temp3.self.smul(
|
||||||
|
&temp3,
|
||||||
|
fm.cache.area_p(&fm, NAN) / fm.cache.la_mag(&fm, NAN)**3
|
||||||
|
)
|
||||||
|
# Combine * calIm
|
||||||
|
temp2.self.vsub(&temp2, temp3)
|
||||||
|
temp2.self.smul(&temp2, fm.cache.calI(&fm, NAN))
|
||||||
|
|
||||||
|
temp1.self.vadd(&temp1, temp2)
|
||||||
|
temp1.self.matmul(&temp1, e.get_H(&e, xi))
|
||||||
|
|
||||||
|
dedxi_p.self.vadd(&dedxi_p, temp1)
|
||||||
|
|
||||||
|
f = f.twin(&f)
|
||||||
|
f = f.next(&f)
|
||||||
|
|
||||||
|
if f.arr_index == e.arr_index:
|
||||||
|
break
|
||||||
|
|
||||||
|
dedx[i][0] -= -2*self.r*dedxi_p.x
|
||||||
|
dedx[i][1] -= -2*self.r*dedxi_p.y
|
||||||
|
|
||||||
|
e = e.next(&e)
|
||||||
|
j = j + 1
|
||||||
|
|
||||||
|
edge_set.free(&edge_set)
|
||||||
|
self.grad = dedx
|
||||||
@ -8,28 +8,22 @@ Config = Tuple[int, int]
|
|||||||
|
|
||||||
|
|
||||||
def configurations(domain: DomainParams) -> List[Config]:
|
def configurations(domain: DomainParams) -> List[Config]:
|
||||||
n, w, h = domain.n, domain.w, domain.h
|
n = domain.n
|
||||||
valid = []
|
coprimes, valid = [], []
|
||||||
mults = np.arange(n)
|
for i in range(n):
|
||||||
configs = np.dstack((np.repeat(mults, n).T, np.tile(mults, n).T))[0][1:]
|
for j in range(i):
|
||||||
for i in range(len(configs)):
|
if gcd(i, j) == 1:
|
||||||
eq_x = n if configs[i][0] == 0 else configs[i][0]
|
coprimes.append((j, i))
|
||||||
eq_y = n if configs[i][1] == 0 else configs[i][1]
|
|
||||||
|
|
||||||
if gcd(eq_x, eq_y) != 1:
|
coprimes = set(coprimes)
|
||||||
continue
|
while len(coprimes) > 0:
|
||||||
|
first = coprimes.pop()
|
||||||
vecs = (
|
valid.append(first)
|
||||||
configs[i]
|
for i in range(2, n):
|
||||||
* np.dstack((w * mults, h * mults)).swapaxes(0, 1)
|
try:
|
||||||
/ n
|
coprimes.remove(((first[0] * i) % n, (first[1] * i) % n))
|
||||||
% domain.dim
|
except KeyError:
|
||||||
)
|
pass
|
||||||
vmod2 = np.squeeze(np.matmul(vecs, vecs.transpose(0, 2, 1)))
|
|
||||||
vmodv = np.squeeze(vecs).dot(vecs[1].T).T.flatten()
|
|
||||||
|
|
||||||
if np.all(vmod2 >= vmodv):
|
|
||||||
valid.append(tuple(configs[i]))
|
|
||||||
|
|
||||||
return valid
|
return valid
|
||||||
|
|
||||||
@ -38,11 +32,15 @@ def get_config_generators(
|
|||||||
domain: DomainParams, config: Config
|
domain: DomainParams, config: Config
|
||||||
) -> Tuple[Config, Config]:
|
) -> Tuple[Config, Config]:
|
||||||
n, w, h = domain.n, domain.w, domain.h
|
n, w, h = domain.n, domain.w, domain.h
|
||||||
q1 = sites(domain, config)
|
q1 = sites(domain, config)[1:]
|
||||||
v = q1[1]
|
all_sites = np.concatenate(
|
||||||
# Sites to check can ignore 0*v and v itself.
|
(q1, q1 - np.array([w, 0]), q1 - np.array([0, h]), q1 - domain.dim)
|
||||||
all_sites = np.concatenate((q1, q1 - [w, 0], q1 - [w, h], q1 - [0, h]))[2:]
|
)
|
||||||
|
# Sort sites by magnitude and smallest.
|
||||||
|
all_sites = sorted(list(all_sites), key=lambda x: np.linalg.norm(x))
|
||||||
|
v = all_sites[0] # Smallest vector set to v.
|
||||||
|
|
||||||
|
all_sites = np.array(all_sites[1:]) # Remove v from search set.
|
||||||
# Checking 0 < ax + by < v*v to make the sites are within the region.
|
# Checking 0 < ax + by < v*v to make the sites are within the region.
|
||||||
tol = 1e-3
|
tol = 1e-3
|
||||||
vdot = np.matmul(all_sites, v)
|
vdot = np.matmul(all_sites, v)
|
||||||
@ -51,11 +49,13 @@ def get_config_generators(
|
|||||||
0, 1
|
0, 1
|
||||||
) # Used for the next step, getting site*site
|
) # Used for the next step, getting site*site
|
||||||
|
|
||||||
w = in_box[
|
v2 = in_box[
|
||||||
np.argmin(np.squeeze(np.matmul(in_box, in_box.transpose(0, 2, 1))))
|
np.argmin(np.squeeze(np.matmul(in_box, in_box.transpose(0, 2, 1))))
|
||||||
].flatten()
|
].flatten()
|
||||||
|
|
||||||
return tuple(v), tuple(w)
|
if np.all(v == v2):
|
||||||
|
print(v, v2, n, w, h, config)
|
||||||
|
return tuple(v), tuple(v2)
|
||||||
|
|
||||||
|
|
||||||
def sites(domain: DomainParams, config: Config) -> numpy.ndarray:
|
def sites(domain: DomainParams, config: Config) -> numpy.ndarray:
|
||||||
@ -92,8 +92,10 @@ def avg_rp(d: float, l: float) -> float:
|
|||||||
return (d / (4 * pi)) * log(tan(0.5 * (atan(l / d) + pi / 2)) ** 2)
|
return (d / (4 * pi)) * log(tan(0.5 * (atan(l / d) + pi / 2)) ** 2)
|
||||||
|
|
||||||
|
|
||||||
def circumcenter(v: numpy.ndarray, w: numpy.ndarray) -> Config:
|
def circumcenter(v: numpy.ndarray, w: numpy.ndarray) -> numpy.ndarray:
|
||||||
det = 1 / (2 * rot(v).dot(w))
|
det = 1 / (2 * rot(v).dot(w))
|
||||||
|
if rot(v).dot(w) == 0:
|
||||||
|
print(v, w)
|
||||||
v2, w2 = v.dot(v), w.dot(w)
|
v2, w2 = v.dot(v), w.dot(w)
|
||||||
c = np.empty((2,))
|
c = np.empty((2,))
|
||||||
c[0], c[1] = w[1] * v2 - v[1] * w2, -w[0] * v2 + v[0] * w2
|
c[0], c[1] = w[1] * v2 - v[1] * w2, -w[0] * v2 + v[0] * w2
|
||||||
|
|||||||
@ -2,7 +2,7 @@ from __future__ import annotations
|
|||||||
from typing import Optional
|
from typing import Optional
|
||||||
|
|
||||||
import pickle, numpy as np
|
import pickle, numpy as np
|
||||||
from math import log10
|
from math import log10, sqrt
|
||||||
from scipy.linalg import null_space
|
from scipy.linalg import null_space
|
||||||
from timeit import default_timer as timer
|
from timeit import default_timer as timer
|
||||||
from pathlib import Path
|
from pathlib import Path
|
||||||
@ -57,6 +57,22 @@ class Simulation:
|
|||||||
|
|
||||||
self.frames.append(self.energy.mode(*self.domain, points % self.domain.dim))
|
self.frames.append(self.energy.mode(*self.domain, points % self.domain.dim))
|
||||||
|
|
||||||
|
def normalize(self) -> None:
|
||||||
|
new_frames = []
|
||||||
|
for frame in self.frames:
|
||||||
|
aspect = frame.w / frame.h
|
||||||
|
new_domain = DomainParams(
|
||||||
|
frame.n, sqrt(frame.n * aspect), sqrt(frame.n / aspect), frame.r
|
||||||
|
)
|
||||||
|
|
||||||
|
new_points = frame.site_arr * np.array(
|
||||||
|
[new_domain.w / frame.w, new_domain.h / frame.h]
|
||||||
|
)
|
||||||
|
|
||||||
|
new_frames.append(self.energy.mode(*new_domain, new_points))
|
||||||
|
|
||||||
|
self.frames = new_frames
|
||||||
|
|
||||||
def get_distinct(self) -> List[int]:
|
def get_distinct(self) -> List[int]:
|
||||||
"""Gets the distinct configurations based on the average radii of the sites.
|
"""Gets the distinct configurations based on the average radii of the sites.
|
||||||
and returns the number of configurations for each distinct configuration.
|
and returns the number of configurations for each distinct configuration.
|
||||||
|
|||||||
File diff suppressed because it is too large
Load Diff
99
squish/voronoi.pxd
Normal file
99
squish/voronoi.pxd
Normal file
@ -0,0 +1,99 @@
|
|||||||
|
cimport numpy as np
|
||||||
|
from squish.core cimport INT_T, FLOAT_T, IArray, FArray, Vector2D, Matrix2x2
|
||||||
|
|
||||||
|
# Psuedo-class that handles caching for sites.
|
||||||
|
ctypedef struct SiteCacheMap:
|
||||||
|
INT_T iarea, iperim, iisoparam, ienergy, iavg_radius, icentroid, imaxcenter
|
||||||
|
|
||||||
|
FLOAT_T (*area)(Site*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*perim)(Site*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*isoparam)(Site*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*energy)(Site*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*avg_radius)(Site*, FLOAT_T) nogil
|
||||||
|
|
||||||
|
Vector2D (*centroid)(Site*, Vector2D) nogil
|
||||||
|
Vector2D (*maxcenter)(Site*, Vector2D) nogil
|
||||||
|
|
||||||
|
# Psuedo-class that handles caching for edges.
|
||||||
|
ctypedef struct EdgeCacheMap:
|
||||||
|
INT_T iH, ila, ida, ixij, idVdv, ila_mag, ida_mag, iarea_p, icalI, size
|
||||||
|
|
||||||
|
Matrix2x2 (*H)(HalfEdge*, Matrix2x2) nogil
|
||||||
|
|
||||||
|
Vector2D (*la)(HalfEdge*, Vector2D) nogil
|
||||||
|
Vector2D (*da)(HalfEdge*, Vector2D) nogil
|
||||||
|
Vector2D (*xij)(HalfEdge*, Vector2D) nogil
|
||||||
|
Vector2D (*dVdv)(HalfEdge*, Vector2D) nogil
|
||||||
|
|
||||||
|
FLOAT_T (*la_mag)(HalfEdge*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*da_mag)(HalfEdge*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*area_p)(HalfEdge*, FLOAT_T) nogil
|
||||||
|
FLOAT_T (*calI)(HalfEdge*, FLOAT_T) nogil
|
||||||
|
|
||||||
|
# Psuedo-class to just contain all pertaining info for sites and edges.
|
||||||
|
ctypedef struct VoronoiInfo:
|
||||||
|
IArray sites, edges
|
||||||
|
FArray points, vertices, site_cache, edge_cache
|
||||||
|
EdgeCacheMap* edge_cache_map
|
||||||
|
|
||||||
|
# Psuedo-class for a Site.
|
||||||
|
ctypedef struct Site:
|
||||||
|
INT_T arr_index
|
||||||
|
VoronoiInfo* info
|
||||||
|
SiteCacheMap* cache
|
||||||
|
|
||||||
|
INT_T (*index)(Site*) nogil
|
||||||
|
Vector2D (*vec)(Site*) nogil
|
||||||
|
HalfEdge (*edge)(Site*) nogil
|
||||||
|
INT_T (*edge_num)(Site*) nogil
|
||||||
|
|
||||||
|
# Psuedo-class for an HalfEdge.
|
||||||
|
ctypedef struct HalfEdge:
|
||||||
|
INT_T orig_arr_index, arr_index
|
||||||
|
VoronoiInfo* info
|
||||||
|
EdgeCacheMap* cache
|
||||||
|
|
||||||
|
INT_T (*origin_index)(HalfEdge*) nogil
|
||||||
|
Vector2D (*origin)(HalfEdge*) nogil
|
||||||
|
Site (*face)(HalfEdge*) nogil
|
||||||
|
HalfEdge (*next)(HalfEdge*) nogil
|
||||||
|
HalfEdge (*prev)(HalfEdge*) nogil
|
||||||
|
HalfEdge (*twin)(HalfEdge*) nogil
|
||||||
|
Matrix2x2 (*get_H)(HalfEdge*, Site) nogil
|
||||||
|
|
||||||
|
|
||||||
|
cdef class VoronoiContainer:
|
||||||
|
cdef readonly INT_T n
|
||||||
|
cdef readonly FLOAT_T w, h, r, energy
|
||||||
|
cdef FLOAT_T [2] dim
|
||||||
|
cdef FLOAT_T [:, ::1] points, vertices, site_cache, edge_cache, grad
|
||||||
|
cdef INT_T [:, ::1] sites, edges
|
||||||
|
cdef EdgeCacheMap* edge_cache_map
|
||||||
|
cdef dict __dict__
|
||||||
|
|
||||||
|
cdef void calculate_voronoi(VoronoiContainer self,
|
||||||
|
np.ndarray[FLOAT_T, ndim=2] site_arr) except *
|
||||||
|
cdef void generate_dcel(VoronoiContainer self) except *
|
||||||
|
cdef void common_cache(VoronoiContainer self) except *
|
||||||
|
cdef void precompute(self) except *
|
||||||
|
cdef void calc_grad(self) except *
|
||||||
|
cdef void get_statistics(VoronoiContainer self) except *
|
||||||
|
|
||||||
|
@staticmethod
|
||||||
|
cdef inline Matrix2x2 calc_H(HalfEdge, HalfEdge) nogil
|
||||||
|
@staticmethod
|
||||||
|
cdef inline bint sign(FLOAT_T [::1], FLOAT_T [::1], FLOAT_T [::1])
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
cdef SiteCacheMap _SiteCacheMap(INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T) nogil
|
||||||
|
cdef EdgeCacheMap _EdgeCacheMap(INT_T, INT_T, INT_T, INT_T, INT_T, INT_T, INT_T,
|
||||||
|
INT_T, INT_T, INT_T) nogil
|
||||||
|
cdef VoronoiInfo _VoronoiInfo(INT_T [:, ::1], INT_T[:, ::1], FLOAT_T[:, ::1],
|
||||||
|
FLOAT_T[:, ::1], FLOAT_T[:, ::1], FLOAT_T[:, ::1],
|
||||||
|
EdgeCacheMap*) nogil
|
||||||
|
cdef Site _Site(INT_T, VoronoiInfo*) nogil
|
||||||
|
cdef HalfEdge _HalfEdge(INT_T, VoronoiInfo*) nogil
|
||||||
|
|
||||||
|
cdef Vector2D NAN_VECTOR
|
||||||
|
cdef Matrix2x2 R, NAN_MATRIX
|
||||||
736
squish/voronoi.pyx
Normal file
736
squish/voronoi.pyx
Normal file
@ -0,0 +1,736 @@
|
|||||||
|
import array, scipy.spatial, numpy as np
|
||||||
|
from timeit import default_timer as timer
|
||||||
|
from cython.parallel import parallel, prange
|
||||||
|
|
||||||
|
cimport numpy as np
|
||||||
|
from cpython cimport array
|
||||||
|
from libc.math cimport isnan, NAN, pi as PI
|
||||||
|
|
||||||
|
from squish.core cimport INT_T, FLOAT_T, \
|
||||||
|
IArray, FArray, Vector2D, Matrix2x2, \
|
||||||
|
_IArray, _FArray, _Vector2D, _Matrix2x2
|
||||||
|
|
||||||
|
from squish.voronoi cimport SiteCacheMap, EdgeCacheMap, VoronoiInfo, Site, HalfEdge
|
||||||
|
|
||||||
|
#### Constants ####
|
||||||
|
|
||||||
|
INT = np.int64
|
||||||
|
FLOAT = np.float64
|
||||||
|
|
||||||
|
cdef Vector2D NAN_VECTOR = _Vector2D(NAN, NAN)
|
||||||
|
cdef Matrix2x2 NAN_MATRIX = _Matrix2x2(NAN, NAN, NAN, NAN)
|
||||||
|
|
||||||
|
cdef FLOAT_T[18] SYMM = [0,0, 1,0, 1,1, 0,1, -1,1, -1,0, -1,-1, 0,-1, 1,-1]
|
||||||
|
cdef Matrix2x2 R = _Matrix2x2(0, -1, 1, 0)
|
||||||
|
|
||||||
|
cdef SiteCacheMap SITE_CACHE_MAP = _SiteCacheMap(0, 1, 2, 3, 4, 5, -1)
|
||||||
|
|
||||||
|
#### SiteCacheMap Methods ####
|
||||||
|
|
||||||
|
cdef inline SiteCacheMap _SiteCacheMap(INT_T iarea, INT_T iperim, INT_T iisoparam,
|
||||||
|
INT_T ienergy, INT_T iavg_radius,
|
||||||
|
INT_T icentroid, INT_T imaxcenter) nogil:
|
||||||
|
cdef SiteCacheMap sc
|
||||||
|
sc.iarea, sc.iperim, sc.iisoparam, sc.ienergy, sc.iavg_radius = (
|
||||||
|
iarea, iperim, iisoparam, ienergy, iavg_radius
|
||||||
|
)
|
||||||
|
sc.icentroid, sc.imaxcenter = icentroid, imaxcenter
|
||||||
|
|
||||||
|
sc.area, sc.perim, sc.isoparam, sc.energy, sc.avg_radius = (
|
||||||
|
area, perim, isoparam, energy, avg_radius
|
||||||
|
)
|
||||||
|
sc.centroid, sc.maxcenter = centroid, maxcenter
|
||||||
|
|
||||||
|
return sc
|
||||||
|
|
||||||
|
cdef inline FLOAT_T area(Site* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iarea)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iarea), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T perim(Site* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iperim)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iperim), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T isoparam(Site* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iisoparam)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iisoparam), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T energy(Site* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.ienergy)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.ienergy), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T avg_radius(Site* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iavg_radius)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.iavg_radius), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D centroid(Site* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.icentroid)
|
||||||
|
),
|
||||||
|
self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.icentroid+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.icentroid), val.x)
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.icentroid+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D maxcenter(Site* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.imaxcenter)
|
||||||
|
),
|
||||||
|
self.info.site_cache.get(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.imaxcenter+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.imaxcenter), val.x)
|
||||||
|
self.info.site_cache.set(&self.info.site_cache,
|
||||||
|
(self.arr_index, self.cache.imaxcenter+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
|
||||||
|
#### EdgeCacheMap Methods ####
|
||||||
|
|
||||||
|
cdef inline EdgeCacheMap _EdgeCacheMap(INT_T iH, INT_T ila, INT_T ida, INT_T ixij,
|
||||||
|
INT_T idVdv, INT_T ila_mag, INT_T ida_mag,
|
||||||
|
INT_T iarea_p, INT_T icalI, INT_T size) nogil:
|
||||||
|
cdef EdgeCacheMap ec
|
||||||
|
ec.iH, ec.ila, ec.ida, ec.ixij, ec.idVdv = iH, ila, ida, ixij, idVdv
|
||||||
|
ec.ila_mag, ec.ida_mag, ec.iarea_p, ec.icalI = ila_mag, ida_mag, iarea_p, icalI
|
||||||
|
ec.size = size
|
||||||
|
|
||||||
|
ec.H, ec.la, ec.da, ec.xij, ec.dVdv = H, la, da, xij, dVdv
|
||||||
|
ec.la_mag, ec.da_mag, ec.area_p, ec.calI = la_mag, da_mag, area_p, calI
|
||||||
|
|
||||||
|
return ec
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 H(HalfEdge* self, Matrix2x2 val) nogil:
|
||||||
|
if isnan(<double>val.a):
|
||||||
|
return _Matrix2x2(
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+1)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+2)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+3)
|
||||||
|
),
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH), val.a)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+1), val.b)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+2), val.c)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iH+3), val.d)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D la(HalfEdge* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila), val.x)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D da(HalfEdge* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida), val.x)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D xij(HalfEdge* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ixij)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ixij+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ixij), val.x)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ixij+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline Vector2D dVdv(HalfEdge* self, Vector2D val) nogil:
|
||||||
|
if isnan(<double>val.x):
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.idVdv)
|
||||||
|
),
|
||||||
|
self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.idVdv+1)
|
||||||
|
)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.idVdv), val.x)
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.idVdv+1), val.y)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T la_mag(HalfEdge* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila_mag)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ila_mag), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T da_mag(HalfEdge* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida_mag)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.ida_mag), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T area_p(HalfEdge* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iarea_p)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.iarea_p), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
cdef inline FLOAT_T calI(HalfEdge* self, FLOAT_T val) nogil:
|
||||||
|
if isnan(<double>val):
|
||||||
|
return self.info.edge_cache.get(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.icalI)
|
||||||
|
)
|
||||||
|
else:
|
||||||
|
self.info.edge_cache.set(&self.info.edge_cache,
|
||||||
|
(self.arr_index, self.cache.icalI), val)
|
||||||
|
return val
|
||||||
|
|
||||||
|
#### VoronoiInfo Methods ####
|
||||||
|
|
||||||
|
cdef inline VoronoiInfo _VoronoiInfo(INT_T [:, ::1] sites, INT_T [:, ::1] edges,
|
||||||
|
FLOAT_T [:, ::1] points, FLOAT_T [:, ::1] vertices,
|
||||||
|
FLOAT_T [:, ::1] site_cache,
|
||||||
|
FLOAT_T [:, ::1] edge_cache,
|
||||||
|
EdgeCacheMap* edge_cache_map) nogil:
|
||||||
|
cdef VoronoiInfo info
|
||||||
|
info.sites = _IArray(&sites[0,0], (<INT_T>sites.shape[0], <INT_T>sites.shape[1]))
|
||||||
|
info.edges = _IArray(&edges[0,0], (<INT_T>edges.shape[0], <INT_T>edges.shape[1]))
|
||||||
|
info.points = _FArray(
|
||||||
|
&points[0,0],
|
||||||
|
(<INT_T>points.shape[0], <INT_T>points.shape[1])
|
||||||
|
)
|
||||||
|
info.vertices = _FArray(
|
||||||
|
&vertices[0,0],
|
||||||
|
(<INT_T>vertices.shape[0], <INT_T>vertices.shape[1])
|
||||||
|
)
|
||||||
|
info.site_cache = _FArray(
|
||||||
|
&site_cache[0,0],
|
||||||
|
(<INT_T>site_cache.shape[0], <INT_T>site_cache.shape[1])
|
||||||
|
)
|
||||||
|
info.edge_cache = _FArray(
|
||||||
|
&edge_cache[0,0],
|
||||||
|
(<INT_T>edge_cache.shape[0], <INT_T>edge_cache.shape[1])
|
||||||
|
)
|
||||||
|
info.edge_cache_map = edge_cache_map
|
||||||
|
|
||||||
|
return info
|
||||||
|
|
||||||
|
|
||||||
|
#### Site Methods ####
|
||||||
|
|
||||||
|
cdef inline Site _Site(INT_T arr_index, VoronoiInfo* info) nogil:
|
||||||
|
cdef Site site
|
||||||
|
site.arr_index, site.info, site.cache = arr_index, info, &SITE_CACHE_MAP
|
||||||
|
|
||||||
|
site.index, site.vec, site.edge, site.edge_num = index, vec, edge, edge_num
|
||||||
|
|
||||||
|
return site
|
||||||
|
|
||||||
|
|
||||||
|
cdef inline INT_T index(Site* self) nogil:
|
||||||
|
return self.info.sites.get(&self.info.sites, (self.arr_index, 0))
|
||||||
|
|
||||||
|
cdef inline Vector2D vec(Site* self) nogil:
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.points.get(&self.info.points, (self.index(self), 0)),
|
||||||
|
self.info.points.get(&self.info.points, (self.index(self), 1))
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline HalfEdge edge(Site* self) nogil:
|
||||||
|
return _HalfEdge(
|
||||||
|
self.info.sites.get(&self.info.sites, (self.arr_index, 1)), self.info
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline INT_T edge_num(Site* self) nogil:
|
||||||
|
return self.info.sites.get(&self.info.sites, (self.arr_index, 2))
|
||||||
|
|
||||||
|
|
||||||
|
#### HalfEdge Methods ####
|
||||||
|
|
||||||
|
cdef inline HalfEdge _HalfEdge(INT_T arr_index, VoronoiInfo* info) nogil:
|
||||||
|
cdef HalfEdge e
|
||||||
|
e.arr_index, e.info, e.cache = arr_index, info, info.edge_cache_map
|
||||||
|
e.orig_arr_index = arr_index
|
||||||
|
|
||||||
|
e.origin_index, e.origin, e.face, e.next, e.prev, e.twin, e.get_H = (
|
||||||
|
origin_index, origin, face, edge_next, prev, twin, get_H
|
||||||
|
)
|
||||||
|
|
||||||
|
return e
|
||||||
|
|
||||||
|
|
||||||
|
cdef inline INT_T origin_index(HalfEdge* self) nogil:
|
||||||
|
return self.info.edges.get(&self.info.edges, (self.arr_index, 0))
|
||||||
|
|
||||||
|
cdef inline Vector2D origin(HalfEdge* self) nogil:
|
||||||
|
return _Vector2D(
|
||||||
|
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 0)),
|
||||||
|
self.info.vertices.get(&self.info.vertices, (self.origin_index(self), 1))
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline Site face(HalfEdge* self) nogil:
|
||||||
|
return _Site(
|
||||||
|
self.info.edges.get(&self.info.edges, (self.arr_index, 1)), self.info
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline HalfEdge edge_next(HalfEdge* self) nogil:
|
||||||
|
|
||||||
|
return _HalfEdge(
|
||||||
|
self.info.edges.get(&self.info.edges, (self.arr_index, 2)), self.info
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline HalfEdge prev(HalfEdge* self) nogil:
|
||||||
|
return _HalfEdge(
|
||||||
|
self.info.edges.get(&self.info.edges, (self.arr_index, 3)), self.info
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline HalfEdge twin(HalfEdge* self) nogil:
|
||||||
|
return _HalfEdge(
|
||||||
|
self.info.edges.get(&self.info.edges, (self.arr_index, 4)), self.info
|
||||||
|
)
|
||||||
|
|
||||||
|
cdef inline Matrix2x2 get_H(HalfEdge* self, Site xi) nogil:
|
||||||
|
cdef INT_T this_e = self.origin_index(self)
|
||||||
|
cdef HalfEdge s_e = xi.edge(&xi)
|
||||||
|
|
||||||
|
for _ in range(xi.edge_num(&xi)):
|
||||||
|
if s_e.origin_index(&s_e) == this_e:
|
||||||
|
return s_e.cache.H(&s_e, NAN_MATRIX)
|
||||||
|
s_e = s_e.next(&s_e)
|
||||||
|
return _Matrix2x2(0.0, 0.0, 0.0, 0.0)
|
||||||
|
|
||||||
|
|
||||||
|
cdef class VoronoiContainer:
|
||||||
|
"""
|
||||||
|
Class for Voronoi diagrams, stored in a modified DCEL.
|
||||||
|
:param n: [int] how many sites to generate.
|
||||||
|
:param w: [float] width of the bounding domain.
|
||||||
|
:param h: [float] height of the bounding domain.
|
||||||
|
:param r: [float] radius of zero energy circle.
|
||||||
|
:param sites: np.ndarray collection of sites.
|
||||||
|
"""
|
||||||
|
|
||||||
|
def __init__(VoronoiContainer self, INT_T n, FLOAT_T w, FLOAT_T h, FLOAT_T r,
|
||||||
|
object site_arr):
|
||||||
|
self.n, self.w, self.h, self.r = n, w, h, r
|
||||||
|
self.dim = [w, h]
|
||||||
|
|
||||||
|
self.calculate_voronoi(site_arr.astype(FLOAT))
|
||||||
|
self.generate_dcel()
|
||||||
|
|
||||||
|
self.common_cache()
|
||||||
|
self.precompute()
|
||||||
|
self.calc_grad()
|
||||||
|
self.get_statistics()
|
||||||
|
|
||||||
|
cdef void calculate_voronoi(VoronoiContainer self,
|
||||||
|
np.ndarray[FLOAT_T, ndim=2] site_arr) except *:
|
||||||
|
"""
|
||||||
|
Does all necessary computation and caching once points are set.
|
||||||
|
:param site_arr: initial points for this container.
|
||||||
|
"""
|
||||||
|
global SYMM
|
||||||
|
cdef np.ndarray[FLOAT_T, ndim=2] symm = np.asarray(SYMM).reshape(9,2)
|
||||||
|
cdef np.ndarray[FLOAT_T, ndim=1] dim = np.asarray(self.dim)
|
||||||
|
cdef np.ndarray[FLOAT_T, ndim=2] full_site_arr = np.empty(
|
||||||
|
(self.n*9+8, 2),
|
||||||
|
dtype=FLOAT
|
||||||
|
)
|
||||||
|
|
||||||
|
# Generate periodic sites and sites that bound periodic sites.
|
||||||
|
cdef INT_T i
|
||||||
|
for i in range(9):
|
||||||
|
full_site_arr[self.n*i:self.n*(i+1)] = site_arr + symm[i]*dim
|
||||||
|
if i > 0:
|
||||||
|
full_site_arr[9*self.n+i-1] = dim/2 + 2*dim*symm[i]
|
||||||
|
|
||||||
|
# Use SciPy to compute the Voronoi set.
|
||||||
|
self.scipy_vor = scipy.spatial.Voronoi(full_site_arr)
|
||||||
|
self.points = self.scipy_vor.points
|
||||||
|
self.vertices = self.scipy_vor.vertices
|
||||||
|
|
||||||
|
|
||||||
|
cdef void generate_dcel(VoronoiContainer self) except *:
|
||||||
|
cdef array.array int_tmplt = array.array('q', [])
|
||||||
|
|
||||||
|
cdef np.ndarray[INT_T, ndim=1] offsets = np.zeros(self.n*9+1, dtype=INT)
|
||||||
|
cdef array.array vert_indices = array.clone(int_tmplt, 0, False)
|
||||||
|
|
||||||
|
# Flatten regions into array, so it can be used later.
|
||||||
|
cdef INT_T i
|
||||||
|
for i in range(self.n*9):
|
||||||
|
verts = self.scipy_vor.regions[self.scipy_vor.point_region[i]]
|
||||||
|
offsets[i+1] = offsets[i] + len(verts) # Build offsets.
|
||||||
|
vert_indices.extend(array.array('q', verts)) # Flatten
|
||||||
|
|
||||||
|
# Get vertices of original N sites.
|
||||||
|
cdef np.ndarray[INT_T, ndim=1] vert_indices_np = np.asarray(vert_indices)
|
||||||
|
cdef np.ndarray[INT_T, ndim=1] border_sites = np.unique(np.searchsorted(
|
||||||
|
np.asarray(offsets), # Check indices where below matches would be inserted
|
||||||
|
np.nonzero(np.isin( # Indices of other verts being in bound verts.
|
||||||
|
vert_indices_np[offsets[self.n]:], # Rest of the verts to check.
|
||||||
|
np.unique(vert_indices_np[:offsets[self.n]]) # Bound verts
|
||||||
|
))[0] + offsets[self.n],
|
||||||
|
side='right' # If on index == offset_number, should be part of the next site.
|
||||||
|
) - 1) # Subtract by one to get actual site number.
|
||||||
|
|
||||||
|
cdef INT_T border_num = len(border_sites)
|
||||||
|
|
||||||
|
# Build sites array.
|
||||||
|
# [Site Index, Edge Index/Offset, Edge Count]
|
||||||
|
self.sites = np.empty((self.n+border_num, 3), dtype=INT)
|
||||||
|
self.sites.base[:self.n, 0] = np.arange(self.n, dtype=INT)
|
||||||
|
self.sites.base[self.n:, 0] = border_sites
|
||||||
|
self.sites.base[:self.n+1, 1] = offsets[:self.n+1]
|
||||||
|
for i in range(self.n):
|
||||||
|
self.sites[i, 2] = self.sites[i+1, 1] - self.sites[i, 1]
|
||||||
|
|
||||||
|
cdef INT_T edge_count = offsets[self.n]
|
||||||
|
cdef INT_T diff
|
||||||
|
for i in range(border_num):
|
||||||
|
diff = offsets[border_sites[i]+1] - offsets[border_sites[i]]
|
||||||
|
edge_count += diff
|
||||||
|
self.sites[self.n+i, 2] = diff
|
||||||
|
if i < border_num - 1:
|
||||||
|
self.sites[self.n+i+1, 1] = self.sites[self.n+i, 1] + diff
|
||||||
|
|
||||||
|
# Build edges array
|
||||||
|
# [Origin Index, Site Index, Next Index, Prev Index, Twin Index]
|
||||||
|
self.edges = np.empty((edge_count, 5), dtype=INT)
|
||||||
|
cdef np.ndarray[INT_T, ndim=1] site_verts
|
||||||
|
cdef INT_T j, site_i, edge_i, edge_offset, vert_num, twin_index
|
||||||
|
|
||||||
|
edge_indices = dict()
|
||||||
|
|
||||||
|
for i in range(self.n + border_num):
|
||||||
|
site_i = self.sites[i, 0]
|
||||||
|
edge_offset = self.sites[i, 1]
|
||||||
|
site_verts = vert_indices_np[offsets[site_i]:offsets[site_i+1]]
|
||||||
|
|
||||||
|
# Scipy outputs sorted vertices, but reverse if not counterclockwise.
|
||||||
|
if not VoronoiContainer.sign(self.points[site_i],
|
||||||
|
self.vertices[site_verts[0]], self.vertices[site_verts[1]]):
|
||||||
|
site_verts = np.flip(site_verts)
|
||||||
|
|
||||||
|
vert_num = offsets[site_i+1] - offsets[site_i]
|
||||||
|
|
||||||
|
for j in range(vert_num):
|
||||||
|
edge_i = edge_offset+j
|
||||||
|
self.edges[edge_i, 0] = site_verts[j]
|
||||||
|
self.edges[edge_i, 1] = i
|
||||||
|
# Add vert_num because of C modulo to get always positive.
|
||||||
|
self.edges[edge_i, 2] = (j+vert_num+1) % vert_num + edge_offset
|
||||||
|
self.edges[edge_i, 3] = (j+vert_num-1) % vert_num + edge_offset
|
||||||
|
|
||||||
|
# Get reversed tuple to theck for twin.
|
||||||
|
twin_index = edge_indices.get(
|
||||||
|
(site_verts[(j+1) % vert_num], site_verts[j]
|
||||||
|
), -1)
|
||||||
|
|
||||||
|
self.edges[edge_i, 4] = twin_index
|
||||||
|
if twin_index == -1:
|
||||||
|
edge_indices[(site_verts[j], site_verts[(j+1) % vert_num])] = \
|
||||||
|
j + edge_offset
|
||||||
|
else:
|
||||||
|
self.edges[twin_index, 4] = j + edge_offset
|
||||||
|
|
||||||
|
self.site_cache = np.empty((self.n + border_num, 7), dtype=FLOAT)
|
||||||
|
self.edge_cache = np.empty((edge_count, self.edge_cache_map.size), dtype=FLOAT)
|
||||||
|
|
||||||
|
|
||||||
|
cdef void common_cache(VoronoiContainer self) except *:
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef Site xi
|
||||||
|
cdef HalfEdge em, ep
|
||||||
|
cdef Vector2D p, q, la, da, Rla, centroid, cent_part
|
||||||
|
|
||||||
|
cdef FLOAT_T [:] area = np.zeros(self.sites.shape[0], dtype=FLOAT)
|
||||||
|
cdef FLOAT_T [:] perim = np.zeros(self.sites.shape[0], dtype=FLOAT)
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
cdef FLOAT_T area_p, la_mag
|
||||||
|
for i in prange(self.sites.shape[0], nogil=True):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
centroid = _Vector2D(0, 0)
|
||||||
|
em = xi.edge(&xi)
|
||||||
|
j = 0
|
||||||
|
while j < xi.edge_num(&xi):
|
||||||
|
ep = em.next(&em)
|
||||||
|
p, q = em.origin(&em), ep.origin(&ep)
|
||||||
|
# vp - vm, vm - xi
|
||||||
|
la, da = q.copy.vsub(&q, p), p.copy.vsub(&p, xi.vec(&xi))
|
||||||
|
la_mag = la.mag(&la)
|
||||||
|
area_p = la.dot(&la, da.rot(&da))
|
||||||
|
Rla = la.rot(&la)
|
||||||
|
|
||||||
|
# Calculating centroid.
|
||||||
|
cent_part = p.copy.vadd(&p, q)
|
||||||
|
cent_part.self.vadd(¢_part, xi.vec(&xi))
|
||||||
|
centroid.self.vadd(¢roid, cent_part.copy.smul(¢_part, area_p))
|
||||||
|
|
||||||
|
# Caching
|
||||||
|
em.cache.la(&em, la)
|
||||||
|
em.cache.la_mag(&em, la_mag)
|
||||||
|
em.cache.da(&em, da)
|
||||||
|
em.cache.da_mag(&em, da.mag(&da))
|
||||||
|
em.cache.area_p(&em, area_p)
|
||||||
|
em.cache.xij(&em, Rla.copy.smul(&Rla, -area_p/la.dot(&la, la)))
|
||||||
|
|
||||||
|
area[i] += area_p
|
||||||
|
perim[i] += la_mag
|
||||||
|
|
||||||
|
em = em.next(&em)
|
||||||
|
j = j + 1
|
||||||
|
|
||||||
|
xi.cache.area(&xi, area[i]/2)
|
||||||
|
xi.cache.perim(&xi, perim[i])
|
||||||
|
xi.cache.isoparam(&xi, 2*PI*area[i]/(perim[i]**2))
|
||||||
|
xi.cache.centroid(&xi, centroid.copy.sdiv(¢roid, 3*area[i]))
|
||||||
|
|
||||||
|
|
||||||
|
@staticmethod
|
||||||
|
cdef inline Matrix2x2 calc_H(HalfEdge em, HalfEdge ep) nogil:
|
||||||
|
cdef Vector2D xmv, xpv, im, mp, right, Rpm, Rim, f
|
||||||
|
cdef Matrix2x2 h
|
||||||
|
cdef FLOAT_T im2, mp2
|
||||||
|
|
||||||
|
# Vectors from xi to xm and xp.
|
||||||
|
xmv, xpv = em.cache.xij(&em, NAN_VECTOR), ep.cache.xij(&ep, NAN_VECTOR)
|
||||||
|
im, mp = xmv.copy.neg(&xmv), xmv.copy.vsub(&xmv, xpv) # -xmv, xmv - xpv
|
||||||
|
im2, mp2 = -(xmv.dot(&xmv, xmv)), xmv.dot(&xmv, xmv) - xpv.dot(&xpv, xpv)
|
||||||
|
# (-xmv*xmv, xmv*xmv - xpv*xpv)
|
||||||
|
right = _Vector2D(im2, mp2)
|
||||||
|
Rpm, Rim = R.vecmul(&R, mp.copy.neg(&mp)), im.rot(&im) # R*-mp, R*im
|
||||||
|
|
||||||
|
h = _Matrix2x2(Rpm.x, Rim.x, Rpm.y, Rim.y) # [Rpm | Rim], h is temporary.
|
||||||
|
f = h.vecmul(&h, right) # [Rpm | Rim]*right
|
||||||
|
h = R.copy.smul(&R, mp2*(2*mp.dot(&mp, Rim))) # fp*g, g is a scalar.
|
||||||
|
# (fp*g - f*gp)/(g**2). f is a column vector, gp = 2*Rpm is a row vector.
|
||||||
|
h.self.msub(&h, _Matrix2x2(
|
||||||
|
f.x*2*Rpm.x, f.x*2*Rpm.y, f.y*2*Rpm.x, f.y*2*Rpm.y
|
||||||
|
))
|
||||||
|
h.self.sdiv(&h, (2*mp.dot(&mp, Rim))**2)
|
||||||
|
|
||||||
|
return h
|
||||||
|
|
||||||
|
|
||||||
|
@staticmethod
|
||||||
|
cdef inline bint sign(FLOAT_T [::1] ref, FLOAT_T [::1] p, FLOAT_T [::1] q):
|
||||||
|
"""
|
||||||
|
Outputs if p2 - self is counterclockwise of p1 - self.
|
||||||
|
:param p1: [List[float]] first vector
|
||||||
|
:param p2: [List[float]] second vector
|
||||||
|
:return: [bool] returns if counterclockwise.
|
||||||
|
"""
|
||||||
|
return ((q[0] - ref[0])*-(p[1] - ref[1]) + \
|
||||||
|
(q[1] - ref[1])*(p[0] - ref[0])) >= 0
|
||||||
|
|
||||||
|
# global ROT
|
||||||
|
# cdef np.ndarray[FLOAT_T, ndim=2] rot = np.asarray(ROT).reshape(2,2)
|
||||||
|
# return (q - ref).dot(rot.dot(p - ref)) >= 0
|
||||||
|
|
||||||
|
cdef void precompute(self) except *:
|
||||||
|
pass
|
||||||
|
|
||||||
|
cdef void calc_grad(self) except *:
|
||||||
|
pass
|
||||||
|
|
||||||
|
cdef void get_statistics(self) except *:
|
||||||
|
self.stats = {}
|
||||||
|
cache = self.site_cache[:self.n, :]
|
||||||
|
|
||||||
|
self.stats["site_areas"] = np.asarray(cache[:, SITE_CACHE_MAP.iarea])
|
||||||
|
self.stats["site_edge_count"] = np.asarray(self.sites[:self.n, 2])
|
||||||
|
|
||||||
|
self.stats["site_isos"] = np.asarray(cache[:, SITE_CACHE_MAP.iisoparam])
|
||||||
|
self.stats["site_energies"] = np.asarray(cache[:, SITE_CACHE_MAP.ienergy])
|
||||||
|
self.stats["avg_radius"] = np.asarray(cache[:, SITE_CACHE_MAP.iavg_radius])
|
||||||
|
self.stats["centroids"] = np.asarray(
|
||||||
|
cache[:, SITE_CACHE_MAP.icentroid:SITE_CACHE_MAP.icentroid+2]
|
||||||
|
)
|
||||||
|
|
||||||
|
self.stats["isoparam_avg"] = self.stats["site_areas"] / \
|
||||||
|
(PI*self.stats["avg_radius"]**2)
|
||||||
|
|
||||||
|
edges = np.asarray(self.edges)
|
||||||
|
|
||||||
|
mask = np.nonzero(edges[:, 0] != -1)[0]
|
||||||
|
all_edges = mask[(mask % 2 == 0)]
|
||||||
|
caches = edges[all_edges, 4]
|
||||||
|
|
||||||
|
edge_cache = np.asarray(self.edge_cache)
|
||||||
|
|
||||||
|
self.stats["edge_lengths"] = edge_cache[caches, self.edge_cache_map.ila_mag]
|
||||||
|
|
||||||
|
@property
|
||||||
|
def site_arr(self):
|
||||||
|
return np.asarray(self.points[:self.n], dtype=FLOAT)
|
||||||
|
|
||||||
|
@property
|
||||||
|
def vor_data(self):
|
||||||
|
return self.scipy_vor
|
||||||
|
|
||||||
|
@property
|
||||||
|
def gradient(self):
|
||||||
|
return np.asarray(self.grad, dtype=FLOAT)
|
||||||
|
|
||||||
|
def add_sites(self, add):
|
||||||
|
return (self.site_arr + add) % np.asarray(self.dim, dtype=FLOAT)
|
||||||
|
|
||||||
|
def iterate(self, FLOAT_T step):
|
||||||
|
k1 = self.gradient
|
||||||
|
k2 = self.__class__(self.n, self.w, self.h, self.r,
|
||||||
|
self.add_sites(step*k1)
|
||||||
|
).gradient
|
||||||
|
|
||||||
|
return (step/2)*(k1+k2), k1
|
||||||
|
|
||||||
|
|
||||||
|
def hessian(self, d: float) -> np.ndarray:
|
||||||
|
"""
|
||||||
|
Obtains the approximate Hessian.
|
||||||
|
:param d: [float] small d for approximation.
|
||||||
|
:return: 2Nx2N array that represents Hessian.
|
||||||
|
"""
|
||||||
|
HE = np.zeros((2*self.n, 2*self.n))
|
||||||
|
new_sites = np.copy(self.site_arr) # Maintain one copy for speed.
|
||||||
|
for i in range(self.n):
|
||||||
|
for j in range(2):
|
||||||
|
mod = self.w if j == 0 else self.h
|
||||||
|
new_sites[i][j] = (new_sites[i][j] + d) % mod
|
||||||
|
Ep = self.__class__(self.n, self.w, self.h, self.r, new_sites)
|
||||||
|
new_sites[i][j] = (new_sites[i][j] - 2*d) % mod
|
||||||
|
Em = self.__class__(self.n, self.w, self.h, self.r, new_sites)
|
||||||
|
new_sites[i][j] = (new_sites[i][j] + d) % mod
|
||||||
|
|
||||||
|
HE[:, 2*i+j] = ((Ep.gradient - Em.gradient)/(2*d)).flatten()
|
||||||
|
|
||||||
|
# Average out discrepencies, since it should be symmetric.
|
||||||
|
for i in range(2*self.n):
|
||||||
|
for j in range(i, 2*self.n):
|
||||||
|
HE[i][j] = (HE[i][j] + HE[j][i])/2
|
||||||
|
HE[j][i] = HE[i][j]
|
||||||
|
|
||||||
|
return HE
|
||||||
|
|
||||||
|
|
||||||
|
def site_vert_arr(self): # -> List[np.ndarray]
|
||||||
|
cdef VoronoiInfo info = _VoronoiInfo(self.sites, self.edges, self.points,
|
||||||
|
self.vertices, self.site_cache, self.edge_cache, self.edge_cache_map)
|
||||||
|
|
||||||
|
cdef INT_T i, j
|
||||||
|
cdef Site xi
|
||||||
|
cdef HalfEdge e
|
||||||
|
cdef Vector2D v
|
||||||
|
|
||||||
|
sites, site_verts = [], []
|
||||||
|
|
||||||
|
for i in range(self.n):
|
||||||
|
xi = _Site(i, &info)
|
||||||
|
v = xi.vec(&xi)
|
||||||
|
sites.append(np.array([v.x, v.y]))
|
||||||
|
verts = np.empty((xi.edge_num(&xi), 2))
|
||||||
|
e = xi.edge(&xi)
|
||||||
|
for j in range(xi.edge_num(&xi)):
|
||||||
|
v = e.origin(&e)
|
||||||
|
verts[j, 0], verts[j, 1] = v.x, v.y
|
||||||
|
e = e.next(&e)
|
||||||
|
|
||||||
|
site_verts.append(verts)
|
||||||
|
|
||||||
|
return sites, site_verts
|
||||||
Loading…
x
Reference in New Issue
Block a user