""" This is a copy of the OpenSimplex library, based on commit d861cb290531ad15825f21dc4cc35c5d4f407259 from 20.07.2017. """ # Based on: https://gist.github.com/KdotJPG/b1270127455a94ac5d19 import sys from ctypes import c_long from math import floor as _floor if sys.version_info[0] < 3: def floor(num): return int(_floor(num)) else: floor = _floor STRETCH_CONSTANT_2D = -0.211324865405187 # (1/Math.sqrt(2+1)-1)/2 SQUISH_CONSTANT_2D = 0.366025403784439 # (Math.sqrt(2+1)-1)/2 STRETCH_CONSTANT_3D = -1.0 / 6 # (1/Math.sqrt(3+1)-1)/3 SQUISH_CONSTANT_3D = 1.0 / 3 # (Math.sqrt(3+1)-1)/3 STRETCH_CONSTANT_4D = -0.138196601125011 # (1/Math.sqrt(4+1)-1)/4 SQUISH_CONSTANT_4D = 0.309016994374947 # (Math.sqrt(4+1)-1)/4 NORM_CONSTANT_2D = 47 NORM_CONSTANT_3D = 103 NORM_CONSTANT_4D = 30 DEFAULT_SEED = 0 # Gradients for 2D. They approximate the directions to the # vertices of an octagon from the center. GRADIENTS_2D = ( 5, 2, 2, 5, -5, 2, -2, 5, 5, -2, 2, -5, -5, -2, -2, -5, ) # Gradients for 3D. They approximate the directions to the # vertices of a rhombicuboctahedron from the center, skewed so # that the triangular and square facets can be inscribed inside # circles of the same radius. GRADIENTS_3D = ( -11, 4, 4, -4, 11, 4, -4, 4, 11, 11, 4, 4, 4, 11, 4, 4, 4, 11, -11, -4, 4, -4, -11, 4, -4, -4, 11, 11, -4, 4, 4, -11, 4, 4, -4, 11, -11, 4, -4, -4, 11, -4, -4, 4, -11, 11, 4, -4, 4, 11, -4, 4, 4, -11, -11, -4, -4, -4, -11, -4, -4, -4, -11, 11, -4, -4, 4, -11, -4, 4, -4, -11, ) # Gradients for 4D. They approximate the directions to the # vertices of a disprismatotesseractihexadecachoron from the center, # skewed so that the tetrahedral and cubic facets can be inscribed inside # spheres of the same radius. GRADIENTS_4D = ( 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, ) def overflow(x): # Since normal python ints and longs can be quite humongous we have to use # this hack to make them be able to overflow return c_long(x).value class OpenSimplex(object): """ OpenSimplex n-dimensional gradient noise functions. """ def __init__(self, seed=DEFAULT_SEED): """ Initiate the class and generate permutation arrays from a seed number. """ # Initializes the class using a permutation array generated from a 64-bit seed. # Generates a proper permutation (i.e. doesn't merely perform N # successive pair swaps on a base array) perm = self._perm = [0] * 256 # Have to zero fill so we can properly loop over it later perm_grad_index_3D = self._perm_grad_index_3D = [0] * 256 source = [i for i in range(0, 256)] seed = overflow(seed * 6364136223846793005 + 1442695040888963407) seed = overflow(seed * 6364136223846793005 + 1442695040888963407) seed = overflow(seed * 6364136223846793005 + 1442695040888963407) for i in range(255, -1, -1): seed = overflow(seed * 6364136223846793005 + 1442695040888963407) r = int((seed + 31) % (i + 1)) if r < 0: r += i + 1 perm[i] = source[r] perm_grad_index_3D[i] = int((perm[i] % (len(GRADIENTS_3D) / 3)) * 3) source[r] = source[i] def _extrapolate2d(self, xsb, ysb, dx, dy): perm = self._perm index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E g1, g2 = GRADIENTS_2D[index:index + 2] return g1 * dx + g2 * dy def _extrapolate3d(self, xsb, ysb, zsb, dx, dy, dz): perm = self._perm index = self._perm_grad_index_3D[ (perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF ] g1, g2, g3 = GRADIENTS_3D[index:index + 3] return g1 * dx + g2 * dy + g3 * dz def _extrapolate4d(self, xsb, ysb, zsb, wsb, dx, dy, dz, dw): perm = self._perm index = perm[( perm[( perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb ) & 0xFF] + wsb ) & 0xFF] & 0xFC g1, g2, g3, g4 = GRADIENTS_4D[index:index + 4] return g1 * dx + g2 * dy + g3 * dz + g4 * dw def noise2d(self, x, y): """ Generate 2D OpenSimplex noise from X,Y coordinates. """ # Place input coordinates onto grid. stretch_offset = (x + y) * STRETCH_CONSTANT_2D xs = x + stretch_offset ys = y + stretch_offset # Floor to get grid coordinates of rhombus (stretched square) super-cell origin. xsb = floor(xs) ysb = floor(ys) # Skew out to get actual coordinates of rhombus origin. We'll need these later. squish_offset = (xsb + ysb) * SQUISH_CONSTANT_2D xb = xsb + squish_offset yb = ysb + squish_offset # Compute grid coordinates relative to rhombus origin. xins = xs - xsb yins = ys - ysb # Sum those together to get a value that determines which region we're in. in_sum = xins + yins # Positions relative to origin point. dx0 = x - xb dy0 = y - yb value = 0 # Contribution (1,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_2D dy1 = dy0 - 0 - SQUISH_CONSTANT_2D attn1 = 2 - dx1 * dx1 - dy1 * dy1 extrapolate = self._extrapolate2d if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1) # Contribution (0,1) dx2 = dx0 - 0 - SQUISH_CONSTANT_2D dy2 = dy0 - 1 - SQUISH_CONSTANT_2D attn2 = 2 - dx2 * dx2 - dy2 * dy2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2) if in_sum <= 1: # We're inside the triangle (2-Simplex) at (0,0) zins = 1 - in_sum if zins > xins or zins > yins: # (0,0) is one of the closest two triangular vertices if xins > yins: xsv_ext = xsb + 1 ysv_ext = ysb - 1 dx_ext = dx0 - 1 dy_ext = dy0 + 1 else: xsv_ext = xsb - 1 ysv_ext = ysb + 1 dx_ext = dx0 + 1 dy_ext = dy0 - 1 else: # (1,0) and (0,1) are the closest two vertices. xsv_ext = xsb + 1 ysv_ext = ysb + 1 dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D else: # We're inside the triangle (2-Simplex) at (1,1) zins = 2 - in_sum if zins < xins or zins < yins: # (0,0) is one of the closest two triangular vertices if xins > yins: xsv_ext = xsb + 2 ysv_ext = ysb + 0 dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D else: xsv_ext = xsb + 0 ysv_ext = ysb + 2 dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D else: # (1,0) and (0,1) are the closest two vertices. dx_ext = dx0 dy_ext = dy0 xsv_ext = xsb ysv_ext = ysb xsb += 1 ysb += 1 dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D # Contribution (0,0) or (1,1) attn0 = 2 - dx0 * dx0 - dy0 * dy0 if attn0 > 0: attn0 *= attn0 value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0) # Extra Vertex attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext if attn_ext > 0: attn_ext *= attn_ext value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext) return value / NORM_CONSTANT_2D def noise3d(self, x, y, z): """ Generate 3D OpenSimplex noise from X,Y,Z coordinates. """ # Place input coordinates on simplectic honeycomb. stretch_offset = (x + y + z) * STRETCH_CONSTANT_3D xs = x + stretch_offset ys = y + stretch_offset zs = z + stretch_offset # Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. xsb = floor(xs) ysb = floor(ys) zsb = floor(zs) # Skew out to get actual coordinates of rhombohedron origin. We'll need these later. squish_offset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D xb = xsb + squish_offset yb = ysb + squish_offset zb = zsb + squish_offset # Compute simplectic honeycomb coordinates relative to rhombohedral origin. xins = xs - xsb yins = ys - ysb zins = zs - zsb # Sum those together to get a value that determines which region we're in. in_sum = xins + yins + zins # Positions relative to origin point. dx0 = x - xb dy0 = y - yb dz0 = z - zb value = 0 extrapolate = self._extrapolate3d if in_sum <= 1: # We're inside the tetrahedron (3-Simplex) at (0,0,0) # Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest. a_point = 0x01 a_score = xins b_point = 0x02 b_score = yins if a_score >= b_score and zins > b_score: b_score = zins b_point = 0x04 elif a_score < b_score and zins > a_score: a_score = zins a_point = 0x04 # Now we determine the two lattice points not part of the tetrahedron that may contribute. # This depends on the closest two tetrahedral vertices, including (0,0,0) wins = 1 - in_sum if wins > a_score or wins > b_score: # (0,0,0) is one of the closest two tetrahedral vertices. c = b_point if (b_score > a_score) else a_point # Our other closest vertex is the closest out of a and b. if (c & 0x01) == 0: xsv_ext0 = xsb - 1 xsv_ext1 = xsb dx_ext0 = dx0 + 1 dx_ext1 = dx0 else: xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx_ext1 = dx0 - 1 if (c & 0x02) == 0: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 if (c & 0x01) == 0: ysv_ext1 -= 1 dy_ext1 += 1 else: ysv_ext0 -= 1 dy_ext0 += 1 else: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 if (c & 0x04) == 0: zsv_ext0 = zsb zsv_ext1 = zsb - 1 dz_ext0 = dz0 dz_ext1 = dz0 + 1 else: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 else: # (0,0,0) is not one of the closest two tetrahedral vertices. c = (a_point | b_point) # Our two extra vertices are determined by the closest two. if (c & 0x01) == 0: xsv_ext0 = xsb xsv_ext1 = xsb - 1 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D else: xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D if (c & 0x02) == 0: ysv_ext0 = ysb ysv_ext1 = ysb - 1 dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D else: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D if (c & 0x04) == 0: zsv_ext0 = zsb zsv_ext1 = zsb - 1 dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D else: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D # Contribution (0,0,0) attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 if attn0 > 0: attn0 *= attn0 value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0) # Contribution (1,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_3D dy1 = dy0 - 0 - SQUISH_CONSTANT_3D dz1 = dz0 - 0 - SQUISH_CONSTANT_3D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1) # Contribution (0,1,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_3D dy2 = dy0 - 1 - SQUISH_CONSTANT_3D dz2 = dz1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2) # Contribution (0,0,1) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_3D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3) elif in_sum >= 2: # We're inside the tetrahedron (3-Simplex) at (1,1,1) # Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). a_point = 0x06 a_score = xins b_point = 0x05 b_score = yins if a_score <= b_score and zins < b_score: b_score = zins b_point = 0x03 elif a_score > b_score and zins < a_score: a_score = zins a_point = 0x03 # Now we determine the two lattice points not part of the tetrahedron that may contribute. # This depends on the closest two tetrahedral vertices, including (1,1,1) wins = 3 - in_sum if wins < a_score or wins < b_score: # (1,1,1) is one of the closest two tetrahedral vertices. c = b_point if (b_score < a_score) else a_point # Our other closest vertex is the closest out of a and b. if (c & 0x01) != 0: xsv_ext0 = xsb + 2 xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_3D dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D else: xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_3D if (c & 0x02) != 0: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D if (c & 0x01) != 0: ysv_ext1 += 1 dy_ext1 -= 1 else: ysv_ext0 += 1 dy_ext0 -= 1 else: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_3D if (c & 0x04) != 0: zsv_ext0 = zsb + 1 zsv_ext1 = zsb + 2 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 - 3 * SQUISH_CONSTANT_3D else: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_3D else: # (1,1,1) is not one of the closest two tetrahedral vertices. c = (a_point & b_point) # Our two extra vertices are determined by the closest two. if (c & 0x01) != 0: xsv_ext0 = xsb + 1 xsv_ext1 = xsb + 2 dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D else: xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx0 - SQUISH_CONSTANT_3D dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D if (c & 0x02) != 0: ysv_ext0 = ysb + 1 ysv_ext1 = ysb + 2 dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D else: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy0 - SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D if (c & 0x04) != 0: zsv_ext0 = zsb + 1 zsv_ext1 = zsb + 2 dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D else: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz0 - SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D # Contribution (1,1,0) dx3 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D dy3 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D dz3 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx3, dy3, dz3) # Contribution (1,0,1) dx2 = dx3 dy2 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D dz2 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx2, dy2, dz2) # Contribution (0,1,1) dx1 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D dy1 = dy3 dz1 = dz2 attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx1, dy1, dz1) # Contribution (1,1,1) dx0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D dy0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D dz0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 if attn0 > 0: attn0 *= attn0 value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, dx0, dy0, dz0) else: # We're inside the octahedron (Rectified 3-Simplex) in between. # Decide between point (0,0,1) and (1,1,0) as closest p1 = xins + yins if p1 > 1: a_score = p1 - 1 a_point = 0x03 a_is_further_side = True else: a_score = 1 - p1 a_point = 0x04 a_is_further_side = False # Decide between point (0,1,0) and (1,0,1) as closest p2 = xins + zins if p2 > 1: b_score = p2 - 1 b_point = 0x05 b_is_further_side = True else: b_score = 1 - p2 b_point = 0x02 b_is_further_side = False # The closest out of the two (1,0,0) and (0,1,1) will replace the furthest out of the two decided above, if closer. p3 = yins + zins if p3 > 1: score = p3 - 1 if a_score <= b_score and a_score < score: a_point = 0x06 a_is_further_side = True elif a_score > b_score and b_score < score: b_point = 0x06 b_is_further_side = True else: score = 1 - p3 if a_score <= b_score and a_score < score: a_point = 0x01 a_is_further_side = False elif a_score > b_score and b_score < score: b_point = 0x01 b_is_further_side = False # Where each of the two closest points are determines how the extra two vertices are calculated. if a_is_further_side == b_is_further_side: if a_is_further_side: # Both closest points on (1,1,1) side # One of the two extra points is (1,1,1) dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_3D dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_3D dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_3D xsv_ext0 = xsb + 1 ysv_ext0 = ysb + 1 zsv_ext0 = zsb + 1 # Other extra point is based on the shared axis. c = (a_point & b_point) if (c & 0x01) != 0: dx_ext1 = dx0 - 2 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D xsv_ext1 = xsb + 2 ysv_ext1 = ysb zsv_ext1 = zsb elif (c & 0x02) != 0: dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D xsv_ext1 = xsb ysv_ext1 = ysb + 2 zsv_ext1 = zsb else: dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 - 2 * SQUISH_CONSTANT_3D xsv_ext1 = xsb ysv_ext1 = ysb zsv_ext1 = zsb + 2 else:# Both closest points on (0,0,0) side # One of the two extra points is (0,0,0) dx_ext0 = dx0 dy_ext0 = dy0 dz_ext0 = dz0 xsv_ext0 = xsb ysv_ext0 = ysb zsv_ext0 = zsb # Other extra point is based on the omitted axis. c = (a_point | b_point) if (c & 0x01) == 0: dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D xsv_ext1 = xsb - 1 ysv_ext1 = ysb + 1 zsv_ext1 = zsb + 1 elif (c & 0x02) == 0: dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D xsv_ext1 = xsb + 1 ysv_ext1 = ysb - 1 zsv_ext1 = zsb + 1 else: dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D xsv_ext1 = xsb + 1 ysv_ext1 = ysb + 1 zsv_ext1 = zsb - 1 else: # One point on (0,0,0) side, one point on (1,1,1) side if a_is_further_side: c1 = a_point c2 = b_point else: c1 = b_point c2 = a_point # One contribution is a _permutation of (1,1,-1) if (c1 & 0x01) == 0: dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_3D dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D xsv_ext0 = xsb - 1 ysv_ext0 = ysb + 1 zsv_ext0 = zsb + 1 elif (c1 & 0x02) == 0: dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D dy_ext0 = dy0 + 1 - SQUISH_CONSTANT_3D dz_ext0 = dz0 - 1 - SQUISH_CONSTANT_3D xsv_ext0 = xsb + 1 ysv_ext0 = ysb - 1 zsv_ext0 = zsb + 1 else: dx_ext0 = dx0 - 1 - SQUISH_CONSTANT_3D dy_ext0 = dy0 - 1 - SQUISH_CONSTANT_3D dz_ext0 = dz0 + 1 - SQUISH_CONSTANT_3D xsv_ext0 = xsb + 1 ysv_ext0 = ysb + 1 zsv_ext0 = zsb - 1 # One contribution is a _permutation of (0,0,2) dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_3D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_3D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_3D xsv_ext1 = xsb ysv_ext1 = ysb zsv_ext1 = zsb if (c2 & 0x01) != 0: dx_ext1 -= 2 xsv_ext1 += 2 elif (c2 & 0x02) != 0: dy_ext1 -= 2 ysv_ext1 += 2 else: dz_ext1 -= 2 zsv_ext1 += 2 # Contribution (1,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_3D dy1 = dy0 - 0 - SQUISH_CONSTANT_3D dz1 = dz0 - 0 - SQUISH_CONSTANT_3D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1) # Contribution (0,1,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_3D dy2 = dy0 - 1 - SQUISH_CONSTANT_3D dz2 = dz1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2) # Contribution (0,0,1) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_3D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3) # Contribution (1,1,0) dx4 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D dy4 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D dz4 = dz0 - 0 - 2 * SQUISH_CONSTANT_3D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 if attn4 > 0: attn4 *= attn4 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 0, dx4, dy4, dz4) # Contribution (1,0,1) dx5 = dx4 dy5 = dy0 - 0 - 2 * SQUISH_CONSTANT_3D dz5 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 if attn5 > 0: attn5 *= attn5 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 0, zsb + 1, dx5, dy5, dz5) # Contribution (0,1,1) dx6 = dx0 - 0 - 2 * SQUISH_CONSTANT_3D dy6 = dy4 dz6 = dz5 attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 if attn6 > 0: attn6 *= attn6 value += attn6 * attn6 * extrapolate(xsb + 0, ysb + 1, zsb + 1, dx6, dy6, dz6) # First extra vertex attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 if attn_ext0 > 0: attn_ext0 *= attn_ext0 value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, dx_ext0, dy_ext0, dz_ext0) # Second extra vertex attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 if attn_ext1 > 0: attn_ext1 *= attn_ext1 value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, dx_ext1, dy_ext1, dz_ext1) return value / NORM_CONSTANT_3D def noise4d(self, x, y, z, w): """ Generate 4D OpenSimplex noise from X,Y,Z,W coordinates. """ # Place input coordinates on simplectic honeycomb. stretch_offset = (x + y + z + w) * STRETCH_CONSTANT_4D xs = x + stretch_offset ys = y + stretch_offset zs = z + stretch_offset ws = w + stretch_offset # Floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin. xsb = floor(xs) ysb = floor(ys) zsb = floor(zs) wsb = floor(ws) # Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later. squish_offset = (xsb + ysb + zsb + wsb) * SQUISH_CONSTANT_4D xb = xsb + squish_offset yb = ysb + squish_offset zb = zsb + squish_offset wb = wsb + squish_offset # Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin. xins = xs - xsb yins = ys - ysb zins = zs - zsb wins = ws - wsb # Sum those together to get a value that determines which region we're in. in_sum = xins + yins + zins + wins # Positions relative to origin po. dx0 = x - xb dy0 = y - yb dz0 = z - zb dw0 = w - wb value = 0 extrapolate = self._extrapolate4d if in_sum <= 1: # We're inside the pentachoron (4-Simplex) at (0,0,0,0) # Determine which two of (0,0,0,1), (0,0,1,0), (0,1,0,0), (1,0,0,0) are closest. a_po = 0x01 a_score = xins b_po = 0x02 b_score = yins if a_score >= b_score and zins > b_score: b_score = zins b_po = 0x04 elif a_score < b_score and zins > a_score: a_score = zins a_po = 0x04 if a_score >= b_score and wins > b_score: b_score = wins b_po = 0x08 elif a_score < b_score and wins > a_score: a_score = wins a_po = 0x08 # Now we determine the three lattice pos not part of the pentachoron that may contribute. # This depends on the closest two pentachoron vertices, including (0,0,0,0) uins = 1 - in_sum if uins > a_score or uins > b_score: # (0,0,0,0) is one of the closest two pentachoron vertices. c = b_po if (b_score > a_score) else a_po # Our other closest vertex is the closest out of a and b. if (c & 0x01) == 0: xsv_ext0 = xsb - 1 xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx0 + 1 dx_ext1 = dx_ext2 = dx0 else: xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 1 if (c & 0x02) == 0: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy_ext1 = dy_ext2 = dy0 if (c & 0x01) == 0x01: ysv_ext0 -= 1 dy_ext0 += 1 else: ysv_ext1 -= 1 dy_ext1 += 1 else: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 if (c & 0x04) == 0: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz_ext1 = dz_ext2 = dz0 if (c & 0x03) != 0: if (c & 0x03) == 0x03: zsv_ext0 -= 1 dz_ext0 += 1 else: zsv_ext1 -= 1 dz_ext1 += 1 else: zsv_ext2 -= 1 dz_ext2 += 1 else: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 if (c & 0x08) == 0: wsv_ext0 = wsv_ext1 = wsb wsv_ext2 = wsb - 1 dw_ext0 = dw_ext1 = dw0 dw_ext2 = dw0 + 1 else: wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1 dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 1 else: # (0,0,0,0) is not one of the closest two pentachoron vertices. c = (a_po | b_po) # Our three extra vertices are determined by the closest two. if (c & 0x01) == 0: xsv_ext0 = xsv_ext2 = xsb xsv_ext1 = xsb - 1 dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext2 = dx0 - SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 1 - SQUISH_CONSTANT_4D if (c & 0x02) == 0: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - SQUISH_CONSTANT_4D if (c & 0x01) == 0x01: ysv_ext1 -= 1 dy_ext1 += 1 else: ysv_ext2 -= 1 dy_ext2 += 1 else: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 1 - SQUISH_CONSTANT_4D if (c & 0x04) == 0: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - SQUISH_CONSTANT_4D if (c & 0x03) == 0x03: zsv_ext1 -= 1 dz_ext1 += 1 else: zsv_ext2 -= 1 dz_ext2 += 1 else: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 1 - SQUISH_CONSTANT_4D if (c & 0x08) == 0: wsv_ext0 = wsv_ext1 = wsb wsv_ext2 = wsb - 1 dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - SQUISH_CONSTANT_4D dw_ext2 = dw0 + 1 - SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw_ext2 = dw0 - 1 - SQUISH_CONSTANT_4D # Contribution (0,0,0,0) attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0 if attn0 > 0: attn0 *= attn0 value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 0, dx0, dy0, dz0, dw0) # Contribution (1,0,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_4D dy1 = dy0 - 0 - SQUISH_CONSTANT_4D dz1 = dz0 - 0 - SQUISH_CONSTANT_4D dw1 = dw0 - 0 - SQUISH_CONSTANT_4D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1) # Contribution (0,1,0,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_4D dy2 = dy0 - 1 - SQUISH_CONSTANT_4D dz2 = dz1 dw2 = dw1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2) # Contribution (0,0,1,0) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_4D dw3 = dw1 attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3) # Contribution (0,0,0,1) dx4 = dx2 dy4 = dy1 dz4 = dz1 dw4 = dw0 - 1 - SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0: attn4 *= attn4 value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4) elif in_sum >= 3: # We're inside the pentachoron (4-Simplex) at (1,1,1,1) # Determine which two of (1,1,1,0), (1,1,0,1), (1,0,1,1), (0,1,1,1) are closest. a_po = 0x0E a_score = xins b_po = 0x0D b_score = yins if a_score <= b_score and zins < b_score: b_score = zins b_po = 0x0B elif a_score > b_score and zins < a_score: a_score = zins a_po = 0x0B if a_score <= b_score and wins < b_score: b_score = wins b_po = 0x07 elif a_score > b_score and wins < a_score: a_score = wins a_po = 0x07 # Now we determine the three lattice pos not part of the pentachoron that may contribute. # This depends on the closest two pentachoron vertices, including (0,0,0,0) uins = 4 - in_sum if uins < a_score or uins < b_score: # (1,1,1,1) is one of the closest two pentachoron vertices. c = b_po if (b_score < a_score) else a_po # Our other closest vertex is the closest out of a and b. if (c & 0x01) != 0: xsv_ext0 = xsb + 2 xsv_ext1 = xsv_ext2 = xsb + 1 dx_ext0 = dx0 - 2 - 4 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * SQUISH_CONSTANT_4D if (c & 0x02) != 0: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D if (c & 0x01) != 0: ysv_ext1 += 1 dy_ext1 -= 1 else: ysv_ext0 += 1 dy_ext0 -= 1 else: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 4 * SQUISH_CONSTANT_4D if (c & 0x04) != 0: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D if (c & 0x03) != 0x03: if (c & 0x03) == 0: zsv_ext0 += 1 dz_ext0 -= 1 else: zsv_ext1 += 1 dz_ext1 -= 1 else: zsv_ext2 += 1 dz_ext2 -= 1 else: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 4 * SQUISH_CONSTANT_4D if (c & 0x08) != 0: wsv_ext0 = wsv_ext1 = wsb + 1 wsv_ext2 = wsb + 2 dw_ext0 = dw_ext1 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 - 4 * SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * SQUISH_CONSTANT_4D else: # (1,1,1,1) is not one of the closest two pentachoron vertices. c = (a_po & b_po) # Our three extra vertices are determined by the closest two. if (c & 0x01) != 0: xsv_ext0 = xsv_ext2 = xsb + 1 xsv_ext1 = xsb + 2 dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext2 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_4D dx_ext1 = dx_ext2 = dx0 - 3 * SQUISH_CONSTANT_4D if (c & 0x02) != 0: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1 dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if (c & 0x01) != 0: ysv_ext2 += 1 dy_ext2 -= 1 else: ysv_ext1 += 1 dy_ext1 -= 1 else: ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy_ext2 = dy0 - 3 * SQUISH_CONSTANT_4D if (c & 0x04) != 0: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1 dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if (c & 0x03) != 0: zsv_ext2 += 1 dz_ext2 -= 1 else: zsv_ext1 += 1 dz_ext1 -= 1 else: zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz_ext2 = dz0 - 3 * SQUISH_CONSTANT_4D if (c & 0x08) != 0: wsv_ext0 = wsv_ext1 = wsb + 1 wsv_ext2 = wsb + 2 dw_ext0 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb dw_ext0 = dw0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw_ext2 = dw0 - 3 * SQUISH_CONSTANT_4D # Contribution (1,1,1,0) dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dw4 = dw0 - 3 * SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0: attn4 *= attn4 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4) # Contribution (1,1,0,1) dx3 = dx4 dy3 = dy4 dz3 = dz0 - 3 * SQUISH_CONSTANT_4D dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3) # Contribution (1,0,1,1) dx2 = dx4 dy2 = dy0 - 3 * SQUISH_CONSTANT_4D dz2 = dz4 dw2 = dw3 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2) # Contribution (0,1,1,1) dx1 = dx0 - 3 * SQUISH_CONSTANT_4D dz1 = dz4 dy1 = dy4 dw1 = dw3 attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1) # Contribution (1,1,1,1) dx0 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D dy0 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D dz0 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D dw0 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0 - dw0 * dw0 if attn0 > 0: attn0 *= attn0 value += attn0 * attn0 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 1, dx0, dy0, dz0, dw0) elif in_sum <= 2: # We're inside the first dispentachoron (Rectified 4-Simplex) a_is_bigger_side = True b_is_bigger_side = True # Decide between (1,1,0,0) and (0,0,1,1) if xins + yins > zins + wins: a_score = xins + yins a_po = 0x03 else: a_score = zins + wins a_po = 0x0C # Decide between (1,0,1,0) and (0,1,0,1) if xins + zins > yins + wins: b_score = xins + zins b_po = 0x05 else: b_score = yins + wins b_po = 0x0A # Closer between (1,0,0,1) and (0,1,1,0) will replace the further of a and b, if closer. if xins + wins > yins + zins: score = xins + wins if a_score >= b_score and score > b_score: b_score = score b_po = 0x09 elif a_score < b_score and score > a_score: a_score = score a_po = 0x09 else: score = yins + zins if a_score >= b_score and score > b_score: b_score = score b_po = 0x06 elif a_score < b_score and score > a_score: a_score = score a_po = 0x06 # Decide if (1,0,0,0) is closer. p1 = 2 - in_sum + xins if a_score >= b_score and p1 > b_score: b_score = p1 b_po = 0x01 b_is_bigger_side = False elif a_score < b_score and p1 > a_score: a_score = p1 a_po = 0x01 a_is_bigger_side = False # Decide if (0,1,0,0) is closer. p2 = 2 - in_sum + yins if a_score >= b_score and p2 > b_score: b_score = p2 b_po = 0x02 b_is_bigger_side = False elif a_score < b_score and p2 > a_score: a_score = p2 a_po = 0x02 a_is_bigger_side = False # Decide if (0,0,1,0) is closer. p3 = 2 - in_sum + zins if a_score >= b_score and p3 > b_score: b_score = p3 b_po = 0x04 b_is_bigger_side = False elif a_score < b_score and p3 > a_score: a_score = p3 a_po = 0x04 a_is_bigger_side = False # Decide if (0,0,0,1) is closer. p4 = 2 - in_sum + wins if a_score >= b_score and p4 > b_score: b_po = 0x08 b_is_bigger_side = False elif a_score < b_score and p4 > a_score: a_po = 0x08 a_is_bigger_side = False # Where each of the two closest pos are determines how the extra three vertices are calculated. if a_is_bigger_side == b_is_bigger_side: if a_is_bigger_side: # Both closest pos on the bigger side c1 = (a_po | b_po) c2 = (a_po & b_po) if (c1 & 0x01) == 0: xsv_ext0 = xsb xsv_ext1 = xsb - 1 dx_ext0 = dx0 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 + 1 - 2 * SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D if (c1 & 0x02) == 0: ysv_ext0 = ysb ysv_ext1 = ysb - 1 dy_ext0 = dy0 - 3 * SQUISH_CONSTANT_4D dy_ext1 = dy0 + 1 - 2 * SQUISH_CONSTANT_4D else: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dy_ext1 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D if (c1 & 0x04) == 0: zsv_ext0 = zsb zsv_ext1 = zsb - 1 dz_ext0 = dz0 - 3 * SQUISH_CONSTANT_4D dz_ext1 = dz0 + 1 - 2 * SQUISH_CONSTANT_4D else: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dz_ext1 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D if (c1 & 0x08) == 0: wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - 2 * SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D # One combination is a _permutation of (0,0,0,2) based on c2 xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D if (c2 & 0x01) != 0: xsv_ext2 += 2 dx_ext2 -= 2 elif (c2 & 0x02) != 0: ysv_ext2 += 2 dy_ext2 -= 2 elif (c2 & 0x04) != 0: zsv_ext2 += 2 dz_ext2 -= 2 else: wsv_ext2 += 2 dw_ext2 -= 2 else: # Both closest pos on the smaller side # One of the two extra pos is (0,0,0,0) xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 dy_ext2 = dy0 dz_ext2 = dz0 dw_ext2 = dw0 # Other two pos are based on the omitted axes. c = (a_po | b_po) if (c & 0x01) == 0: xsv_ext0 = xsb - 1 xsv_ext1 = xsb dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D if (c & 0x02) == 0: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D if (c & 0x01) == 0x01: ysv_ext0 -= 1 dy_ext0 += 1 else: ysv_ext1 -= 1 dy_ext1 += 1 else: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D if (c & 0x04) == 0: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D if (c & 0x03) == 0x03: zsv_ext0 -= 1 dz_ext0 += 1 else: zsv_ext1 -= 1 dz_ext1 += 1 else: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D if (c & 0x08) == 0: wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D else: # One po on each "side" if a_is_bigger_side: c1 = a_po c2 = b_po else: c1 = b_po c2 = a_po # Two contributions are the bigger-sided po with each 0 replaced with -1. if (c1 & 0x01) == 0: xsv_ext0 = xsb - 1 xsv_ext1 = xsb dx_ext0 = dx0 + 1 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsb + 1 dx_ext0 = dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_4D if (c1 & 0x02) == 0: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - SQUISH_CONSTANT_4D if (c1 & 0x01) == 0x01: ysv_ext0 -= 1 dy_ext0 += 1 else: ysv_ext1 -= 1 dy_ext1 += 1 else: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_4D if (c1 & 0x04) == 0: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - SQUISH_CONSTANT_4D if (c1 & 0x03) == 0x03: zsv_ext0 -= 1 dz_ext0 += 1 else: zsv_ext1 -= 1 dz_ext1 += 1 else: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_4D if (c1 & 0x08) == 0: wsv_ext0 = wsb wsv_ext1 = wsb - 1 dw_ext0 = dw0 - SQUISH_CONSTANT_4D dw_ext1 = dw0 + 1 - SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsb + 1 dw_ext0 = dw_ext1 = dw0 - 1 - SQUISH_CONSTANT_4D # One contribution is a _permutation of (0,0,0,2) based on the smaller-sided po xsv_ext2 = xsb ysv_ext2 = ysb zsv_ext2 = zsb wsv_ext2 = wsb dx_ext2 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 2 * SQUISH_CONSTANT_4D if (c2 & 0x01) != 0: xsv_ext2 += 2 dx_ext2 -= 2 elif (c2 & 0x02) != 0: ysv_ext2 += 2 dy_ext2 -= 2 elif (c2 & 0x04) != 0: zsv_ext2 += 2 dz_ext2 -= 2 else: wsv_ext2 += 2 dw_ext2 -= 2 # Contribution (1,0,0,0) dx1 = dx0 - 1 - SQUISH_CONSTANT_4D dy1 = dy0 - 0 - SQUISH_CONSTANT_4D dz1 = dz0 - 0 - SQUISH_CONSTANT_4D dw1 = dw0 - 0 - SQUISH_CONSTANT_4D attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 0, dx1, dy1, dz1, dw1) # Contribution (0,1,0,0) dx2 = dx0 - 0 - SQUISH_CONSTANT_4D dy2 = dy0 - 1 - SQUISH_CONSTANT_4D dz2 = dz1 dw2 = dw1 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 0, dx2, dy2, dz2, dw2) # Contribution (0,0,1,0) dx3 = dx2 dy3 = dy1 dz3 = dz0 - 1 - SQUISH_CONSTANT_4D dw3 = dw1 attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 0, dx3, dy3, dz3, dw3) # Contribution (0,0,0,1) dx4 = dx2 dy4 = dy1 dz4 = dz1 dw4 = dw0 - 1 - SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0: attn4 *= attn4 value += attn4 * attn4 * extrapolate(xsb + 0, ysb + 0, zsb + 0, wsb + 1, dx4, dy4, dz4, dw4) # Contribution (1,1,0,0) dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5 if attn5 > 0: attn5 *= attn5 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5) # Contribution (1,0,1,0) dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6 if attn6 > 0: attn6 *= attn6 value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6) # Contribution (1,0,0,1) dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7 if attn7 > 0: attn7 *= attn7 value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7) # Contribution (0,1,1,0) dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8 if attn8 > 0: attn8 *= attn8 value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8) # Contribution (0,1,0,1) dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9 if attn9 > 0: attn9 *= attn9 value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9) # Contribution (0,0,1,1) dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10 if attn10 > 0: attn10 *= attn10 value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10) else: # We're inside the second dispentachoron (Rectified 4-Simplex) a_is_bigger_side = True b_is_bigger_side = True # Decide between (0,0,1,1) and (1,1,0,0) if xins + yins < zins + wins: a_score = xins + yins a_po = 0x0C else: a_score = zins + wins a_po = 0x03 # Decide between (0,1,0,1) and (1,0,1,0) if xins + zins < yins + wins: b_score = xins + zins b_po = 0x0A else: b_score = yins + wins b_po = 0x05 # Closer between (0,1,1,0) and (1,0,0,1) will replace the further of a and b, if closer. if xins + wins < yins + zins: score = xins + wins if a_score <= b_score and score < b_score: b_score = score b_po = 0x06 elif a_score > b_score and score < a_score: a_score = score a_po = 0x06 else: score = yins + zins if a_score <= b_score and score < b_score: b_score = score b_po = 0x09 elif a_score > b_score and score < a_score: a_score = score a_po = 0x09 # Decide if (0,1,1,1) is closer. p1 = 3 - in_sum + xins if a_score <= b_score and p1 < b_score: b_score = p1 b_po = 0x0E b_is_bigger_side = False elif a_score > b_score and p1 < a_score: a_score = p1 a_po = 0x0E a_is_bigger_side = False # Decide if (1,0,1,1) is closer. p2 = 3 - in_sum + yins if a_score <= b_score and p2 < b_score: b_score = p2 b_po = 0x0D b_is_bigger_side = False elif a_score > b_score and p2 < a_score: a_score = p2 a_po = 0x0D a_is_bigger_side = False # Decide if (1,1,0,1) is closer. p3 = 3 - in_sum + zins if a_score <= b_score and p3 < b_score: b_score = p3 b_po = 0x0B b_is_bigger_side = False elif a_score > b_score and p3 < a_score: a_score = p3 a_po = 0x0B a_is_bigger_side = False # Decide if (1,1,1,0) is closer. p4 = 3 - in_sum + wins if a_score <= b_score and p4 < b_score: b_po = 0x07 b_is_bigger_side = False elif a_score > b_score and p4 < a_score: a_po = 0x07 a_is_bigger_side = False # Where each of the two closest pos are determines how the extra three vertices are calculated. if a_is_bigger_side == b_is_bigger_side: if a_is_bigger_side: # Both closest pos on the bigger side c1 = (a_po & b_po) c2 = (a_po | b_po) # Two contributions are _permutations of (0,0,0,1) and (0,0,0,2) based on c1 xsv_ext0 = xsv_ext1 = xsb ysv_ext0 = ysv_ext1 = ysb zsv_ext0 = zsv_ext1 = zsb wsv_ext0 = wsv_ext1 = wsb dx_ext0 = dx0 - SQUISH_CONSTANT_4D dy_ext0 = dy0 - SQUISH_CONSTANT_4D dz_ext0 = dz0 - SQUISH_CONSTANT_4D dw_ext0 = dw0 - SQUISH_CONSTANT_4D dx_ext1 = dx0 - 2 * SQUISH_CONSTANT_4D dy_ext1 = dy0 - 2 * SQUISH_CONSTANT_4D dz_ext1 = dz0 - 2 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 * SQUISH_CONSTANT_4D if (c1 & 0x01) != 0: xsv_ext0 += 1 dx_ext0 -= 1 xsv_ext1 += 2 dx_ext1 -= 2 elif (c1 & 0x02) != 0: ysv_ext0 += 1 dy_ext0 -= 1 ysv_ext1 += 2 dy_ext1 -= 2 elif (c1 & 0x04) != 0: zsv_ext0 += 1 dz_ext0 -= 1 zsv_ext1 += 2 dz_ext1 -= 2 else: wsv_ext0 += 1 dw_ext0 -= 1 wsv_ext1 += 2 dw_ext1 -= 2 # One contribution is a _permutation of (1,1,1,-1) based on c2 xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D if (c2 & 0x01) == 0: xsv_ext2 -= 2 dx_ext2 += 2 elif (c2 & 0x02) == 0: ysv_ext2 -= 2 dy_ext2 += 2 elif (c2 & 0x04) == 0: zsv_ext2 -= 2 dz_ext2 += 2 else: wsv_ext2 -= 2 dw_ext2 += 2 else: # Both closest pos on the smaller side # One of the two extra pos is (1,1,1,1) xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 4 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 4 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 4 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 4 * SQUISH_CONSTANT_4D # Other two pos are based on the shared axes. c = (a_po & b_po) if (c & 0x01) != 0: xsv_ext0 = xsb + 2 xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D if (c & 0x02) != 0: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if (c & 0x01) == 0: ysv_ext0 += 1 dy_ext0 -= 1 else: ysv_ext1 += 1 dy_ext1 -= 1 else: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D if (c & 0x04) != 0: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if (c & 0x03) == 0: zsv_ext0 += 1 dz_ext0 -= 1 else: zsv_ext1 += 1 dz_ext1 -= 1 else: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D if (c & 0x08) != 0: wsv_ext0 = wsb + 1 wsv_ext1 = wsb + 2 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsb dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D else: # One po on each "side" if a_is_bigger_side: c1 = a_po c2 = b_po else: c1 = b_po c2 = a_po # Two contributions are the bigger-sided po with each 1 replaced with 2. if (c1 & 0x01) != 0: xsv_ext0 = xsb + 2 xsv_ext1 = xsb + 1 dx_ext0 = dx0 - 2 - 3 * SQUISH_CONSTANT_4D dx_ext1 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D else: xsv_ext0 = xsv_ext1 = xsb dx_ext0 = dx_ext1 = dx0 - 3 * SQUISH_CONSTANT_4D if (c1 & 0x02) != 0: ysv_ext0 = ysv_ext1 = ysb + 1 dy_ext0 = dy_ext1 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D if (c1 & 0x01) == 0: ysv_ext0 += 1 dy_ext0 -= 1 else: ysv_ext1 += 1 dy_ext1 -= 1 else: ysv_ext0 = ysv_ext1 = ysb dy_ext0 = dy_ext1 = dy0 - 3 * SQUISH_CONSTANT_4D if (c1 & 0x04) != 0: zsv_ext0 = zsv_ext1 = zsb + 1 dz_ext0 = dz_ext1 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D if (c1 & 0x03) == 0: zsv_ext0 += 1 dz_ext0 -= 1 else: zsv_ext1 += 1 dz_ext1 -= 1 else: zsv_ext0 = zsv_ext1 = zsb dz_ext0 = dz_ext1 = dz0 - 3 * SQUISH_CONSTANT_4D if (c1 & 0x08) != 0: wsv_ext0 = wsb + 1 wsv_ext1 = wsb + 2 dw_ext0 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D dw_ext1 = dw0 - 2 - 3 * SQUISH_CONSTANT_4D else: wsv_ext0 = wsv_ext1 = wsb dw_ext0 = dw_ext1 = dw0 - 3 * SQUISH_CONSTANT_4D # One contribution is a _permutation of (1,1,1,-1) based on the smaller-sided po xsv_ext2 = xsb + 1 ysv_ext2 = ysb + 1 zsv_ext2 = zsb + 1 wsv_ext2 = wsb + 1 dx_ext2 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy_ext2 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz_ext2 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw_ext2 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D if (c2 & 0x01) == 0: xsv_ext2 -= 2 dx_ext2 += 2 elif (c2 & 0x02) == 0: ysv_ext2 -= 2 dy_ext2 += 2 elif (c2 & 0x04) == 0: zsv_ext2 -= 2 dz_ext2 += 2 else: wsv_ext2 -= 2 dw_ext2 += 2 # Contribution (1,1,1,0) dx4 = dx0 - 1 - 3 * SQUISH_CONSTANT_4D dy4 = dy0 - 1 - 3 * SQUISH_CONSTANT_4D dz4 = dz0 - 1 - 3 * SQUISH_CONSTANT_4D dw4 = dw0 - 3 * SQUISH_CONSTANT_4D attn4 = 2 - dx4 * dx4 - dy4 * dy4 - dz4 * dz4 - dw4 * dw4 if attn4 > 0: attn4 *= attn4 value += attn4 * attn4 * extrapolate(xsb + 1, ysb + 1, zsb + 1, wsb + 0, dx4, dy4, dz4, dw4) # Contribution (1,1,0,1) dx3 = dx4 dy3 = dy4 dz3 = dz0 - 3 * SQUISH_CONSTANT_4D dw3 = dw0 - 1 - 3 * SQUISH_CONSTANT_4D attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3 - dw3 * dw3 if attn3 > 0: attn3 *= attn3 value += attn3 * attn3 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 1, dx3, dy3, dz3, dw3) # Contribution (1,0,1,1) dx2 = dx4 dy2 = dy0 - 3 * SQUISH_CONSTANT_4D dz2 = dz4 dw2 = dw3 attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2 - dw2 * dw2 if attn2 > 0: attn2 *= attn2 value += attn2 * attn2 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 1, dx2, dy2, dz2, dw2) # Contribution (0,1,1,1) dx1 = dx0 - 3 * SQUISH_CONSTANT_4D dz1 = dz4 dy1 = dy4 dw1 = dw3 attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1 - dw1 * dw1 if attn1 > 0: attn1 *= attn1 value += attn1 * attn1 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 1, dx1, dy1, dz1, dw1) # Contribution (1,1,0,0) dx5 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy5 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz5 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw5 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn5 = 2 - dx5 * dx5 - dy5 * dy5 - dz5 * dz5 - dw5 * dw5 if attn5 > 0: attn5 *= attn5 value += attn5 * attn5 * extrapolate(xsb + 1, ysb + 1, zsb + 0, wsb + 0, dx5, dy5, dz5, dw5) # Contribution (1,0,1,0) dx6 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy6 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz6 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw6 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn6 = 2 - dx6 * dx6 - dy6 * dy6 - dz6 * dz6 - dw6 * dw6 if attn6 > 0: attn6 *= attn6 value += attn6 * attn6 * extrapolate(xsb + 1, ysb + 0, zsb + 1, wsb + 0, dx6, dy6, dz6, dw6) # Contribution (1,0,0,1) dx7 = dx0 - 1 - 2 * SQUISH_CONSTANT_4D dy7 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz7 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw7 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn7 = 2 - dx7 * dx7 - dy7 * dy7 - dz7 * dz7 - dw7 * dw7 if attn7 > 0: attn7 *= attn7 value += attn7 * attn7 * extrapolate(xsb + 1, ysb + 0, zsb + 0, wsb + 1, dx7, dy7, dz7, dw7) # Contribution (0,1,1,0) dx8 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy8 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz8 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw8 = dw0 - 0 - 2 * SQUISH_CONSTANT_4D attn8 = 2 - dx8 * dx8 - dy8 * dy8 - dz8 * dz8 - dw8 * dw8 if attn8 > 0: attn8 *= attn8 value += attn8 * attn8 * extrapolate(xsb + 0, ysb + 1, zsb + 1, wsb + 0, dx8, dy8, dz8, dw8) # Contribution (0,1,0,1) dx9 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy9 = dy0 - 1 - 2 * SQUISH_CONSTANT_4D dz9 = dz0 - 0 - 2 * SQUISH_CONSTANT_4D dw9 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn9 = 2 - dx9 * dx9 - dy9 * dy9 - dz9 * dz9 - dw9 * dw9 if attn9 > 0: attn9 *= attn9 value += attn9 * attn9 * extrapolate(xsb + 0, ysb + 1, zsb + 0, wsb + 1, dx9, dy9, dz9, dw9) # Contribution (0,0,1,1) dx10 = dx0 - 0 - 2 * SQUISH_CONSTANT_4D dy10 = dy0 - 0 - 2 * SQUISH_CONSTANT_4D dz10 = dz0 - 1 - 2 * SQUISH_CONSTANT_4D dw10 = dw0 - 1 - 2 * SQUISH_CONSTANT_4D attn10 = 2 - dx10 * dx10 - dy10 * dy10 - dz10 * dz10 - dw10 * dw10 if attn10 > 0: attn10 *= attn10 value += attn10 * attn10 * extrapolate(xsb + 0, ysb + 0, zsb + 1, wsb + 1, dx10, dy10, dz10, dw10) # First extra vertex attn_ext0 = 2 - dx_ext0 * dx_ext0 - dy_ext0 * dy_ext0 - dz_ext0 * dz_ext0 - dw_ext0 * dw_ext0 if attn_ext0 > 0: attn_ext0 *= attn_ext0 value += attn_ext0 * attn_ext0 * extrapolate(xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0, dx_ext0, dy_ext0, dz_ext0, dw_ext0) # Second extra vertex attn_ext1 = 2 - dx_ext1 * dx_ext1 - dy_ext1 * dy_ext1 - dz_ext1 * dz_ext1 - dw_ext1 * dw_ext1 if attn_ext1 > 0: attn_ext1 *= attn_ext1 value += attn_ext1 * attn_ext1 * extrapolate(xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1, dx_ext1, dy_ext1, dz_ext1, dw_ext1) # Third extra vertex attn_ext2 = 2 - dx_ext2 * dx_ext2 - dy_ext2 * dy_ext2 - dz_ext2 * dz_ext2 - dw_ext2 * dw_ext2 if attn_ext2 > 0: attn_ext2 *= attn_ext2 value += attn_ext2 * attn_ext2 * extrapolate(xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2, dx_ext2, dy_ext2, dz_ext2, dw_ext2) return value / NORM_CONSTANT_4D