1923 lines
78 KiB
Python
1923 lines
78 KiB
Python
# https://github.com/lmas/opensimplex
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# Based on: https://gist.github.com/KdotJPG/b1270127455a94ac5d19
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import sys
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from ctypes import c_int64
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from math import floor as _floor
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if sys.version_info[0] < 3:
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def floor(num):
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return int(_floor(num))
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else:
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floor = _floor
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STRETCH_CONSTANT_2D = -0.211324865405187 # (1/Math.sqrt(2+1)-1)/2
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SQUISH_CONSTANT_2D = 0.366025403784439 # (Math.sqrt(2+1)-1)/2
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STRETCH_CONSTANT_3D = -1.0 / 6 # (1/Math.sqrt(3+1)-1)/3
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SQUISH_CONSTANT_3D = 1.0 / 3 # (Math.sqrt(3+1)-1)/3
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STRETCH_CONSTANT_4D = -0.138196601125011 # (1/Math.sqrt(4+1)-1)/4
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SQUISH_CONSTANT_4D = 0.309016994374947 # (Math.sqrt(4+1)-1)/4
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NORM_CONSTANT_2D = 47
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NORM_CONSTANT_3D = 103
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NORM_CONSTANT_4D = 30
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DEFAULT_SEED = 0
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# Gradients for 2D. They approximate the directions to the
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# vertices of an octagon from the center.
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GRADIENTS_2D = (
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5, 2, 2, 5,
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-5, 2, -2, 5,
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5, -2, 2, -5,
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-5, -2, -2, -5,
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)
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# Gradients for 3D. They approximate the directions to the
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# vertices of a rhombicuboctahedron from the center, skewed so
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# that the triangular and square facets can be inscribed inside
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# circles of the same radius.
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GRADIENTS_3D = (
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-11, 4, 4, -4, 11, 4, -4, 4, 11,
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11, 4, 4, 4, 11, 4, 4, 4, 11,
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-11, -4, 4, -4, -11, 4, -4, -4, 11,
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11, -4, 4, 4, -11, 4, 4, -4, 11,
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-11, 4, -4, -4, 11, -4, -4, 4, -11,
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11, 4, -4, 4, 11, -4, 4, 4, -11,
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-11, -4, -4, -4, -11, -4, -4, -4, -11,
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11, -4, -4, 4, -11, -4, 4, -4, -11,
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)
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# Gradients for 4D. They approximate the directions to the
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# vertices of a disprismatotesseractihexadecachoron from the center,
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# skewed so that the tetrahedral and cubic facets can be inscribed inside
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# spheres of the same radius.
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GRADIENTS_4D = (
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3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3,
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-3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3,
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3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3,
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-3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3,
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3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3,
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-3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3,
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3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3,
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-3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3,
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3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3,
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-3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3,
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3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3,
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-3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3,
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3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3,
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-3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3,
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3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3,
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-3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3,
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)
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def overflow(x):
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# Since normal python ints and longs can be quite humongous we have to use
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# this hack to make them be able to overflow
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return c_int64(x).value
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class OpenSimplex(object):
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"""
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OpenSimplex n-dimensional gradient noise functions.
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"""
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def __init__(self, seed=DEFAULT_SEED):
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"""
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Initiate the class using a permutation array generated from a 64-bit seed number.
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"""
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# Generates a proper permutation (i.e. doesn't merely perform N
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# successive pair swaps on a base array)
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perm = self._perm = [0] * 256 # Have to zero fill so we can properly loop over it later
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perm_grad_index_3D = self._perm_grad_index_3D = [0] * 256
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source = [i for i in range(0, 256)]
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seed = overflow(seed * 6364136223846793005 + 1442695040888963407)
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seed = overflow(seed * 6364136223846793005 + 1442695040888963407)
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seed = overflow(seed * 6364136223846793005 + 1442695040888963407)
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for i in range(255, -1, -1):
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seed = overflow(seed * 6364136223846793005 + 1442695040888963407)
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r = int((seed + 31) % (i + 1))
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if r < 0:
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r += i + 1
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perm[i] = source[r]
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perm_grad_index_3D[i] = int((perm[i] % (len(GRADIENTS_3D) / 3)) * 3)
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source[r] = source[i]
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def _extrapolate2d(self, xsb, ysb, dx, dy):
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perm = self._perm
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index = perm[(perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E
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g1, g2 = GRADIENTS_2D[index:index + 2]
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return g1 * dx + g2 * dy
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def _extrapolate3d(self, xsb, ysb, zsb, dx, dy, dz):
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perm = self._perm
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index = self._perm_grad_index_3D[
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(perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF
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]
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g1, g2, g3 = GRADIENTS_3D[index:index + 3]
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return g1 * dx + g2 * dy + g3 * dz
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def _extrapolate4d(self, xsb, ysb, zsb, wsb, dx, dy, dz, dw):
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perm = self._perm
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index = perm[(
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perm[(
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perm[(perm[xsb & 0xFF] + ysb) & 0xFF] + zsb
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) & 0xFF] + wsb
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) & 0xFF] & 0xFC
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g1, g2, g3, g4 = GRADIENTS_4D[index:index + 4]
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return g1 * dx + g2 * dy + g3 * dz + g4 * dw
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def noise2d(self, x, y):
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"""
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Generate 2D OpenSimplex noise from X,Y coordinates.
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"""
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# Place input coordinates onto grid.
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stretch_offset = (x + y) * STRETCH_CONSTANT_2D
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xs = x + stretch_offset
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ys = y + stretch_offset
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# Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
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xsb = floor(xs)
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ysb = floor(ys)
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# Skew out to get actual coordinates of rhombus origin. We'll need these later.
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squish_offset = (xsb + ysb) * SQUISH_CONSTANT_2D
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xb = xsb + squish_offset
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yb = ysb + squish_offset
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# Compute grid coordinates relative to rhombus origin.
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xins = xs - xsb
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yins = ys - ysb
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# Sum those together to get a value that determines which region we're in.
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in_sum = xins + yins
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# Positions relative to origin point.
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dx0 = x - xb
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dy0 = y - yb
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value = 0
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# Contribution (1,0)
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dx1 = dx0 - 1 - SQUISH_CONSTANT_2D
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dy1 = dy0 - 0 - SQUISH_CONSTANT_2D
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attn1 = 2 - dx1 * dx1 - dy1 * dy1
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extrapolate = self._extrapolate2d
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if attn1 > 0:
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attn1 *= attn1
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value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1)
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# Contribution (0,1)
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dx2 = dx0 - 0 - SQUISH_CONSTANT_2D
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dy2 = dy0 - 1 - SQUISH_CONSTANT_2D
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attn2 = 2 - dx2 * dx2 - dy2 * dy2
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if attn2 > 0:
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attn2 *= attn2
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value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2)
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if in_sum <= 1: # We're inside the triangle (2-Simplex) at (0,0)
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zins = 1 - in_sum
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if zins > xins or zins > yins: # (0,0) is one of the closest two triangular vertices
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if xins > yins:
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xsv_ext = xsb + 1
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ysv_ext = ysb - 1
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dx_ext = dx0 - 1
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dy_ext = dy0 + 1
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else:
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xsv_ext = xsb - 1
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ysv_ext = ysb + 1
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dx_ext = dx0 + 1
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dy_ext = dy0 - 1
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else: # (1,0) and (0,1) are the closest two vertices.
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xsv_ext = xsb + 1
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ysv_ext = ysb + 1
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dx_ext = dx0 - 1 - 2 * SQUISH_CONSTANT_2D
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dy_ext = dy0 - 1 - 2 * SQUISH_CONSTANT_2D
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else: # We're inside the triangle (2-Simplex) at (1,1)
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zins = 2 - in_sum
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if zins < xins or zins < yins: # (0,0) is one of the closest two triangular vertices
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if xins > yins:
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xsv_ext = xsb + 2
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ysv_ext = ysb + 0
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dx_ext = dx0 - 2 - 2 * SQUISH_CONSTANT_2D
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dy_ext = dy0 + 0 - 2 * SQUISH_CONSTANT_2D
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else:
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xsv_ext = xsb + 0
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ysv_ext = ysb + 2
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dx_ext = dx0 + 0 - 2 * SQUISH_CONSTANT_2D
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dy_ext = dy0 - 2 - 2 * SQUISH_CONSTANT_2D
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else: # (1,0) and (0,1) are the closest two vertices.
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dx_ext = dx0
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dy_ext = dy0
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xsv_ext = xsb
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ysv_ext = ysb
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xsb += 1
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ysb += 1
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dx0 = dx0 - 1 - 2 * SQUISH_CONSTANT_2D
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dy0 = dy0 - 1 - 2 * SQUISH_CONSTANT_2D
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# Contribution (0,0) or (1,1)
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attn0 = 2 - dx0 * dx0 - dy0 * dy0
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if attn0 > 0:
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attn0 *= attn0
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value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0)
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# Extra Vertex
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attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext
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if attn_ext > 0:
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attn_ext *= attn_ext
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value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext)
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return value / NORM_CONSTANT_2D
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def noise3d(self, x, y, z):
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"""
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Generate 3D OpenSimplex noise from X,Y,Z coordinates.
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"""
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# Place input coordinates on simplectic honeycomb.
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stretch_offset = (x + y + z) * STRETCH_CONSTANT_3D
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xs = x + stretch_offset
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ys = y + stretch_offset
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zs = z + stretch_offset
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# Floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
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xsb = floor(xs)
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ysb = floor(ys)
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zsb = floor(zs)
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# Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
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squish_offset = (xsb + ysb + zsb) * SQUISH_CONSTANT_3D
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xb = xsb + squish_offset
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yb = ysb + squish_offset
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zb = zsb + squish_offset
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# Compute simplectic honeycomb coordinates relative to rhombohedral origin.
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xins = xs - xsb
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yins = ys - ysb
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zins = zs - zsb
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# Sum those together to get a value that determines which region we're in.
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in_sum = xins + yins + zins
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# Positions relative to origin point.
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dx0 = x - xb
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dy0 = y - yb
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dz0 = z - zb
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value = 0
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extrapolate = self._extrapolate3d
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if in_sum <= 1: # We're inside the tetrahedron (3-Simplex) at (0,0,0)
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# Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest.
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a_point = 0x01
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a_score = xins
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b_point = 0x02
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b_score = yins
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if a_score >= b_score and zins > b_score:
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b_score = zins
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b_point = 0x04
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elif a_score < b_score and zins > a_score:
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a_score = zins
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a_point = 0x04
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# Now we determine the two lattice points not part of the tetrahedron that may contribute.
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# This depends on the closest two tetrahedral vertices, including (0,0,0)
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wins = 1 - in_sum
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if wins > a_score or wins > b_score: # (0,0,0) is one of the closest two tetrahedral vertices.
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c = b_point if (b_score > a_score) else a_point # Our other closest vertex is the closest out of a and b.
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if (c & 0x01) == 0:
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xsv_ext0 = xsb - 1
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xsv_ext1 = xsb
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dx_ext0 = dx0 + 1
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dx_ext1 = dx0
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else:
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xsv_ext0 = xsv_ext1 = xsb + 1
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dx_ext0 = dx_ext1 = dx0 - 1
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if (c & 0x02) == 0:
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ysv_ext0 = ysv_ext1 = ysb
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dy_ext0 = dy_ext1 = dy0
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if (c & 0x01) == 0:
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ysv_ext1 -= 1
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dy_ext1 += 1
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else:
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ysv_ext0 -= 1
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dy_ext0 += 1
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else:
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ysv_ext0 = ysv_ext1 = ysb + 1
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dy_ext0 = dy_ext1 = dy0 - 1
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if (c & 0x04) == 0:
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zsv_ext0 = zsb
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zsv_ext1 = zsb - 1
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dz_ext0 = dz0
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dz_ext1 = dz0 + 1
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else:
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zsv_ext0 = zsv_ext1 = zsb + 1
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dz_ext0 = dz_ext1 = dz0 - 1
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else: # (0,0,0) is not one of the closest two tetrahedral vertices.
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c = (a_point | b_point) # Our two extra vertices are determined by the closest two.
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if (c & 0x01) == 0:
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xsv_ext0 = xsb
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xsv_ext1 = xsb - 1
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dx_ext0 = dx0 - 2 * SQUISH_CONSTANT_3D
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dx_ext1 = dx0 + 1 - SQUISH_CONSTANT_3D
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else:
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xsv_ext0 = xsv_ext1 = xsb + 1
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dx_ext0 = dx0 - 1 - 2 * SQUISH_CONSTANT_3D
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dx_ext1 = dx0 - 1 - SQUISH_CONSTANT_3D
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if (c & 0x02) == 0:
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ysv_ext0 = ysb
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ysv_ext1 = ysb - 1
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dy_ext0 = dy0 - 2 * SQUISH_CONSTANT_3D
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dy_ext1 = dy0 + 1 - SQUISH_CONSTANT_3D
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else:
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ysv_ext0 = ysv_ext1 = ysb + 1
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dy_ext0 = dy0 - 1 - 2 * SQUISH_CONSTANT_3D
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dy_ext1 = dy0 - 1 - SQUISH_CONSTANT_3D
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if (c & 0x04) == 0:
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zsv_ext0 = zsb
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zsv_ext1 = zsb - 1
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dz_ext0 = dz0 - 2 * SQUISH_CONSTANT_3D
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dz_ext1 = dz0 + 1 - SQUISH_CONSTANT_3D
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else:
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zsv_ext0 = zsv_ext1 = zsb + 1
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dz_ext0 = dz0 - 1 - 2 * SQUISH_CONSTANT_3D
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dz_ext1 = dz0 - 1 - SQUISH_CONSTANT_3D
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# Contribution (0,0,0)
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attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0
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if attn0 > 0:
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attn0 *= attn0
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value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0)
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# Contribution (1,0,0)
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dx1 = dx0 - 1 - SQUISH_CONSTANT_3D
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dy1 = dy0 - 0 - SQUISH_CONSTANT_3D
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dz1 = dz0 - 0 - SQUISH_CONSTANT_3D
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attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1
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if attn1 > 0:
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attn1 *= attn1
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value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, zsb + 0, dx1, dy1, dz1)
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# Contribution (0,1,0)
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dx2 = dx0 - 0 - SQUISH_CONSTANT_3D
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dy2 = dy0 - 1 - SQUISH_CONSTANT_3D
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dz2 = dz1
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attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2
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if attn2 > 0:
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attn2 *= attn2
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value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, zsb + 0, dx2, dy2, dz2)
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# Contribution (0,0,1)
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dx3 = dx2
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dy3 = dy1
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dz3 = dz0 - 1 - SQUISH_CONSTANT_3D
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attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3
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if attn3 > 0:
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attn3 *= attn3
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value += attn3 * attn3 * extrapolate(xsb + 0, ysb + 0, zsb + 1, dx3, dy3, dz3)
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elif in_sum >= 2: # We're inside the tetrahedron (3-Simplex) at (1,1,1)
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# Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1).
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a_point = 0x06
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a_score = xins
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b_point = 0x05
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b_score = yins
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if a_score <= b_score and zins < b_score:
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b_score = zins
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b_point = 0x03
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elif a_score > b_score and zins < a_score:
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a_score = zins
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a_point = 0x03
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# Now we determine the two lattice points not part of the tetrahedron that may contribute.
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# This depends on the closest two tetrahedral vertices, including (1,1,1)
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wins = 3 - in_sum
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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
|