2542 lines
72 KiB
C++
2542 lines
72 KiB
C++
#include "opensimplex.h"
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#include <cmath>
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namespace OpenSimplexNoise
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{
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using namespace std;
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Noise::Noise()
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: m_stretch2d(-0.211324865405187) //(1/Math.sqrt(2+1)-1)/2;
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, m_squish2d(0.366025403784439) //(Math.sqrt(2+1)-1)/2;
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, m_stretch3d(-1.0 / 6) //(1/Math.sqrt(3+1)-1)/3;
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, m_squish3d(1.0 / 3) //(Math.sqrt(3+1)-1)/3;
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, m_stretch4d(-0.138196601125011) //(1/Math.sqrt(4+1)-1)/4;
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, m_squish4d(0.309016994374947) //(Math.sqrt(4+1)-1)/4;
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, m_norm2d(47)
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, m_norm3d(103)
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, m_norm4d(30)
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, m_defaultSeed(0)
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, m_perm{0}
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, m_permGradIndex3d{0}
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, m_gradients2d{ 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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, m_gradients3d{-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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, m_gradients4d{ 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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}
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Noise::Noise(int64_t seed)
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: Noise()
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{
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short source[256];
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for (short i = 0; i < 256; i++)
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{
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source[i] = i;
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}
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seed = seed * 6364136223846793005l + 1442695040888963407l;
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seed = seed * 6364136223846793005l + 1442695040888963407l;
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seed = seed * 6364136223846793005l + 1442695040888963407l;
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for (int i = 255; i >= 0; i--)
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{
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seed = seed * 6364136223846793005l + 1442695040888963407l;
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int r = static_cast<int>((seed + 31) % (i + 1));
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if (r < 0)
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{
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r += (i + 1);
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}
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m_perm[i] = source[r];
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m_permGradIndex3d[i] = static_cast<short>((m_perm[i] % (m_gradients3d.size() / 3)) * 3);
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source[r] = source[i];
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}
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}
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double Noise::eval(double x, double y) const
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{
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//Place input coordinates onto grid.
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double stretchOffset = (x + y) * m_stretch2d;
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double xs = x + stretchOffset;
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double ys = y + stretchOffset;
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//Floor to get grid coordinates of rhombus (stretched square) super-cell origin.
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int xsb = static_cast<int>(floor(xs));
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int ysb = static_cast<int>(floor(ys));
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//Skew out to get actual coordinates of rhombus origin. We'll need these later.
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double squishOffset = (xsb + ysb) * m_squish2d;
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double xb = xsb + squishOffset;
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double yb = ysb + squishOffset;
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//Compute grid coordinates relative to rhombus origin.
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double xins = xs - xsb;
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double 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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double inSum = xins + yins;
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//Positions relative to origin point.
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double dx0 = x - xb;
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double dy0 = y - yb;
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//We'll be defining these inside the next block and using them afterwards.
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double dx_ext, dy_ext;
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int xsv_ext, ysv_ext;
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double value = 0;
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//Contribution (1,0)
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double dx1 = dx0 - 1 - m_squish2d;
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double dy1 = dy0 - 0 - m_squish2d;
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double attn1 = 2 - dx1 * dx1 - dy1 * dy1;
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if (attn1 > 0)
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{
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attn1 *= attn1;
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value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1);
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}
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//Contribution (0,1)
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double dx2 = dx0 - 0 - m_squish2d;
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double dy2 = dy0 - 1 - m_squish2d;
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double attn2 = 2 - dx2 * dx2 - dy2 * dy2;
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if (attn2 > 0)
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{
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attn2 *= attn2;
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value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2);
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}
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if (inSum <= 1)
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{ //We're inside the triangle (2-Simplex) at (0,0)
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double zins = 1 - inSum;
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if (zins > xins || zins > yins)
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{ //(0,0) is one of the closest two triangular vertices
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if (xins > yins)
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{
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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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}
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else
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{
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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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}
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}
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else
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{ //(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 * m_squish2d;
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dy_ext = dy0 - 1 - 2 * m_squish2d;
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}
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}
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else
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{ //We're inside the triangle (2-Simplex) at (1,1)
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double zins = 2 - inSum;
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if (zins < xins || zins < yins)
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{ //(0,0) is one of the closest two triangular vertices
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if (xins > yins)
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{
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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 * m_squish2d;
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dy_ext = dy0 + 0 - 2 * m_squish2d;
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}
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else
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{
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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 * m_squish2d;
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dy_ext = dy0 - 2 - 2 * m_squish2d;
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}
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}
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else
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{ //(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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}
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xsb += 1;
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ysb += 1;
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dx0 = dx0 - 1 - 2 * m_squish2d;
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dy0 = dy0 - 1 - 2 * m_squish2d;
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}
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//Contribution (0,0) or (1,1)
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double attn0 = 2 - dx0 * dx0 - dy0 * dy0;
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if (attn0 > 0)
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{
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attn0 *= attn0;
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value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0);
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}
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//Extra Vertex
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double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext;
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if (attn_ext > 0)
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{
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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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}
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return value / m_norm2d;
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}
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double Noise::eval(double x, double y, double z) const
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{
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//Place input coordinates on simplectic honeycomb.
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double stretchOffset = (x + y + z) * m_stretch3d;
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double xs = x + stretchOffset;
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double ys = y + stretchOffset;
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double zs = z + stretchOffset;
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//static_cast<int>(floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin.
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int xsb = static_cast<int>(floor(xs));
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int ysb = static_cast<int>(floor(ys));
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int zsb = static_cast<int>(floor(zs));
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//Skew out to get actual coordinates of rhombohedron origin. We'll need these later.
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double squishOffset = (xsb + ysb + zsb) * m_squish3d;
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double xb = xsb + squishOffset;
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double yb = ysb + squishOffset;
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double zb = zsb + squishOffset;
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//Compute simplectic honeycomb coordinates relative to rhombohedral origin.
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double xins = xs - xsb;
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double yins = ys - ysb;
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double 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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double inSum = xins + yins + zins;
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//Positions relative to origin point.
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double dx0 = x - xb;
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double dy0 = y - yb;
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double dz0 = z - zb;
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//We'll be defining these inside the next block and using them afterwards.
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double dx_ext0, dy_ext0, dz_ext0;
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double dx_ext1, dy_ext1, dz_ext1;
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int xsv_ext0, ysv_ext0, zsv_ext0;
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int xsv_ext1, ysv_ext1, zsv_ext1;
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double value = 0;
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if (inSum <= 1)
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{ //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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char aPoint = 0x01;
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double aScore = xins;
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char bPoint = 0x02;
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double bScore = yins;
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if (aScore >= bScore && zins > bScore)
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{
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bScore = zins;
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bPoint = 0x04;
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}
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else if (aScore < bScore && zins > aScore)
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{
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aScore = zins;
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aPoint = 0x04;
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}
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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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double wins = 1 - inSum;
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if (wins > aScore || wins > bScore)
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{ //(0,0,0) is one of the closest two tetrahedral vertices.
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char c = (bScore > aScore ? bPoint : aPoint); //Our other closest vertex is the closest out of a and b.
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if ((c & 0x01) == 0)
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{
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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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}
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else
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{
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xsv_ext0 = xsv_ext1 = xsb + 1;
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dx_ext0 = dx_ext1 = dx0 - 1;
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}
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if ((c & 0x02) == 0)
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{
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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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{
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ysv_ext1 -= 1;
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dy_ext1 += 1;
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}
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else
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{
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ysv_ext0 -= 1;
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dy_ext0 += 1;
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}
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}
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else
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{
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ysv_ext0 = ysv_ext1 = ysb + 1;
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dy_ext0 = dy_ext1 = dy0 - 1;
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}
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if ((c & 0x04) == 0)
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{
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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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}
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else
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{
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zsv_ext0 = zsv_ext1 = zsb + 1;
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dz_ext0 = dz_ext1 = dz0 - 1;
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}
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}
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else
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{ //(0,0,0) is not one of the closest two tetrahedral vertices.
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char c = static_cast<char>(aPoint | bPoint); //Our two extra vertices are determined by the closest two.
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if ((c & 0x01) == 0)
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{
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xsv_ext0 = xsb;
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xsv_ext1 = xsb - 1;
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dx_ext0 = dx0 - 2 * m_squish3d;
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dx_ext1 = dx0 + 1 - m_squish3d;
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}
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else
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{
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xsv_ext0 = xsv_ext1 = xsb + 1;
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dx_ext0 = dx0 - 1 - 2 * m_squish3d;
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dx_ext1 = dx0 - 1 - m_squish3d;
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}
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if ((c & 0x02) == 0)
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{
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ysv_ext0 = ysb;
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ysv_ext1 = ysb - 1;
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dy_ext0 = dy0 - 2 * m_squish3d;
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dy_ext1 = dy0 + 1 - m_squish3d;
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}
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else
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{
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ysv_ext0 = ysv_ext1 = ysb + 1;
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dy_ext0 = dy0 - 1 - 2 * m_squish3d;
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dy_ext1 = dy0 - 1 - m_squish3d;
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}
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if ((c & 0x04) == 0)
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{
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zsv_ext0 = zsb;
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zsv_ext1 = zsb - 1;
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dz_ext0 = dz0 - 2 * m_squish3d;
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dz_ext1 = dz0 + 1 - m_squish3d;
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}
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else
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{
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zsv_ext0 = zsv_ext1 = zsb + 1;
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dz_ext0 = dz0 - 1 - 2 * m_squish3d;
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dz_ext1 = dz0 - 1 - m_squish3d;
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}
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}
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//Contribution (0,0,0)
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double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0;
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if (attn0 > 0)
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{
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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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}
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//Contribution (1,0,0)
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double dx1 = dx0 - 1 - m_squish3d;
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double dy1 = dy0 - 0 - m_squish3d;
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double dz1 = dz0 - 0 - m_squish3d;
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double attn1 = 2 - dx1 * dx1 - dy1 * dy1 - dz1 * dz1;
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if (attn1 > 0)
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{
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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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}
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//Contribution (0,1,0)
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double dx2 = dx0 - 0 - m_squish3d;
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double dy2 = dy0 - 1 - m_squish3d;
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double dz2 = dz1;
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double attn2 = 2 - dx2 * dx2 - dy2 * dy2 - dz2 * dz2;
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if (attn2 > 0)
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{
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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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}
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//Contribution (0,0,1)
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double dx3 = dx2;
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double dy3 = dy1;
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double dz3 = dz0 - 1 - m_squish3d;
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double attn3 = 2 - dx3 * dx3 - dy3 * dy3 - dz3 * dz3;
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if (attn3 > 0)
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{
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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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}
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}
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else if (inSum >= 2)
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{ //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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char aPoint = 0x06;
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double aScore = xins;
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char bPoint = 0x05;
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double bScore = yins;
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if (aScore <= bScore && zins < bScore)
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{
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bScore = zins;
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bPoint = 0x03;
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}
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else if (aScore > bScore && zins < aScore)
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{
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aScore = zins;
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aPoint = 0x03;
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}
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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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double wins = 3 - inSum;
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if (wins < aScore || wins < bScore)
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{ //(1,1,1) is one of the closest two tetrahedral vertices.
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char c = (bScore < aScore ? bPoint : aPoint); //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 + 2;
|
|
xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx0 - 2 - 3 * m_squish3d;
|
|
dx_ext1 = dx0 - 1 - 3 * m_squish3d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb;
|
|
dx_ext0 = dx_ext1 = dx0 - 3 * m_squish3d;
|
|
}
|
|
|
|
if ((c & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb + 1;
|
|
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish3d;
|
|
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 * m_squish3d;
|
|
}
|
|
|
|
if ((c & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsb + 1;
|
|
zsv_ext1 = zsb + 2;
|
|
dz_ext0 = dz0 - 1 - 3 * m_squish3d;
|
|
dz_ext1 = dz0 - 2 - 3 * m_squish3d;
|
|
}
|
|
else
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb;
|
|
dz_ext0 = dz_ext1 = dz0 - 3 * m_squish3d;
|
|
}
|
|
}
|
|
else
|
|
{ //(1,1,1) is not one of the closest two tetrahedral vertices.
|
|
char c = static_cast<char>(aPoint & bPoint); //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 - m_squish3d;
|
|
dx_ext1 = dx0 - 2 - 2 * m_squish3d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb;
|
|
dx_ext0 = dx0 - m_squish3d;
|
|
dx_ext1 = dx0 - 2 * m_squish3d;
|
|
}
|
|
|
|
if ((c & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysb + 1;
|
|
ysv_ext1 = ysb + 2;
|
|
dy_ext0 = dy0 - 1 - m_squish3d;
|
|
dy_ext1 = dy0 - 2 - 2 * m_squish3d;
|
|
}
|
|
else
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb;
|
|
dy_ext0 = dy0 - m_squish3d;
|
|
dy_ext1 = dy0 - 2 * m_squish3d;
|
|
}
|
|
|
|
if ((c & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsb + 1;
|
|
zsv_ext1 = zsb + 2;
|
|
dz_ext0 = dz0 - 1 - m_squish3d;
|
|
dz_ext1 = dz0 - 2 - 2 * m_squish3d;
|
|
}
|
|
else
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb;
|
|
dz_ext0 = dz0 - m_squish3d;
|
|
dz_ext1 = dz0 - 2 * m_squish3d;
|
|
}
|
|
}
|
|
|
|
//Contribution (1,1,0)
|
|
double dx3 = dx0 - 1 - 2 * m_squish3d;
|
|
double dy3 = dy0 - 1 - 2 * m_squish3d;
|
|
double dz3 = dz0 - 0 - 2 * m_squish3d;
|
|
double 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)
|
|
double dx2 = dx3;
|
|
double dy2 = dy0 - 0 - 2 * m_squish3d;
|
|
double dz2 = dz0 - 1 - 2 * m_squish3d;
|
|
double 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)
|
|
double dx1 = dx0 - 0 - 2 * m_squish3d;
|
|
double dy1 = dy3;
|
|
double dz1 = dz2;
|
|
double 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 * m_squish3d;
|
|
dy0 = dy0 - 1 - 3 * m_squish3d;
|
|
dz0 = dz0 - 1 - 3 * m_squish3d;
|
|
double 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.
|
|
double aScore;
|
|
char aPoint;
|
|
bool aIsFurtherSide;
|
|
double bScore;
|
|
char bPoint;
|
|
bool bIsFurtherSide;
|
|
|
|
//Decide between point (0,0,1) and (1,1,0) as closest
|
|
double p1 = xins + yins;
|
|
if (p1 > 1)
|
|
{
|
|
aScore = p1 - 1;
|
|
aPoint = 0x03;
|
|
aIsFurtherSide = true;
|
|
}
|
|
else
|
|
{
|
|
aScore = 1 - p1;
|
|
aPoint = 0x04;
|
|
aIsFurtherSide = false;
|
|
}
|
|
|
|
//Decide between point (0,1,0) and (1,0,1) as closest
|
|
double p2 = xins + zins;
|
|
if (p2 > 1)
|
|
{
|
|
bScore = p2 - 1;
|
|
bPoint = 0x05;
|
|
bIsFurtherSide = true;
|
|
}
|
|
else
|
|
{
|
|
bScore = 1 - p2;
|
|
bPoint = 0x02;
|
|
bIsFurtherSide = 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.
|
|
double p3 = yins + zins;
|
|
if (p3 > 1)
|
|
{
|
|
double score = p3 - 1;
|
|
if (aScore <= bScore && aScore < score)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x06;
|
|
aIsFurtherSide = true;
|
|
}
|
|
else if (aScore > bScore && bScore < score)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x06;
|
|
bIsFurtherSide = true;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double score = 1 - p3;
|
|
if (aScore <= bScore && aScore < score)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x01;
|
|
aIsFurtherSide = false;
|
|
}
|
|
else if (aScore > bScore && bScore < score)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x01;
|
|
bIsFurtherSide = false;
|
|
}
|
|
}
|
|
|
|
//Where each of the two closest points are determines how the extra two vertices are calculated.
|
|
if (aIsFurtherSide == bIsFurtherSide)
|
|
{
|
|
if (aIsFurtherSide)
|
|
{ //Both closest points on (1,1,1) side
|
|
|
|
//One of the two extra points is (1,1,1)
|
|
dx_ext0 = dx0 - 1 - 3 * m_squish3d;
|
|
dy_ext0 = dy0 - 1 - 3 * m_squish3d;
|
|
dz_ext0 = dz0 - 1 - 3 * m_squish3d;
|
|
xsv_ext0 = xsb + 1;
|
|
ysv_ext0 = ysb + 1;
|
|
zsv_ext0 = zsb + 1;
|
|
|
|
//Other extra point is based on the shared axis.
|
|
char c = static_cast<char>(aPoint & bPoint);
|
|
if ((c & 0x01) != 0)
|
|
{
|
|
dx_ext1 = dx0 - 2 - 2 * m_squish3d;
|
|
dy_ext1 = dy0 - 2 * m_squish3d;
|
|
dz_ext1 = dz0 - 2 * m_squish3d;
|
|
xsv_ext1 = xsb + 2;
|
|
ysv_ext1 = ysb;
|
|
zsv_ext1 = zsb;
|
|
}
|
|
else if ((c & 0x02) != 0)
|
|
{
|
|
dx_ext1 = dx0 - 2 * m_squish3d;
|
|
dy_ext1 = dy0 - 2 - 2 * m_squish3d;
|
|
dz_ext1 = dz0 - 2 * m_squish3d;
|
|
xsv_ext1 = xsb;
|
|
ysv_ext1 = ysb + 2;
|
|
zsv_ext1 = zsb;
|
|
}
|
|
else
|
|
{
|
|
dx_ext1 = dx0 - 2 * m_squish3d;
|
|
dy_ext1 = dy0 - 2 * m_squish3d;
|
|
dz_ext1 = dz0 - 2 - 2 * m_squish3d;
|
|
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.
|
|
char c = static_cast<char>(aPoint | bPoint);
|
|
if ((c & 0x01) == 0)
|
|
{
|
|
dx_ext1 = dx0 + 1 - m_squish3d;
|
|
dy_ext1 = dy0 - 1 - m_squish3d;
|
|
dz_ext1 = dz0 - 1 - m_squish3d;
|
|
xsv_ext1 = xsb - 1;
|
|
ysv_ext1 = ysb + 1;
|
|
zsv_ext1 = zsb + 1;
|
|
}
|
|
else if ((c & 0x02) == 0)
|
|
{
|
|
dx_ext1 = dx0 - 1 - m_squish3d;
|
|
dy_ext1 = dy0 + 1 - m_squish3d;
|
|
dz_ext1 = dz0 - 1 - m_squish3d;
|
|
xsv_ext1 = xsb + 1;
|
|
ysv_ext1 = ysb - 1;
|
|
zsv_ext1 = zsb + 1;
|
|
}
|
|
else
|
|
{
|
|
dx_ext1 = dx0 - 1 - m_squish3d;
|
|
dy_ext1 = dy0 - 1 - m_squish3d;
|
|
dz_ext1 = dz0 + 1 - m_squish3d;
|
|
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
|
|
char c1, c2;
|
|
if (aIsFurtherSide)
|
|
{
|
|
c1 = aPoint;
|
|
c2 = bPoint;
|
|
}
|
|
else
|
|
{
|
|
c1 = bPoint;
|
|
c2 = aPoint;
|
|
}
|
|
|
|
//One contribution is a permutation of (1,1,-1)
|
|
if ((c1 & 0x01) == 0)
|
|
{
|
|
dx_ext0 = dx0 + 1 - m_squish3d;
|
|
dy_ext0 = dy0 - 1 - m_squish3d;
|
|
dz_ext0 = dz0 - 1 - m_squish3d;
|
|
xsv_ext0 = xsb - 1;
|
|
ysv_ext0 = ysb + 1;
|
|
zsv_ext0 = zsb + 1;
|
|
}
|
|
else if ((c1 & 0x02) == 0)
|
|
{
|
|
dx_ext0 = dx0 - 1 - m_squish3d;
|
|
dy_ext0 = dy0 + 1 - m_squish3d;
|
|
dz_ext0 = dz0 - 1 - m_squish3d;
|
|
xsv_ext0 = xsb + 1;
|
|
ysv_ext0 = ysb - 1;
|
|
zsv_ext0 = zsb + 1;
|
|
}
|
|
else
|
|
{
|
|
dx_ext0 = dx0 - 1 - m_squish3d;
|
|
dy_ext0 = dy0 - 1 - m_squish3d;
|
|
dz_ext0 = dz0 + 1 - m_squish3d;
|
|
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 * m_squish3d;
|
|
dy_ext1 = dy0 - 2 * m_squish3d;
|
|
dz_ext1 = dz0 - 2 * m_squish3d;
|
|
xsv_ext1 = xsb;
|
|
ysv_ext1 = ysb;
|
|
zsv_ext1 = zsb;
|
|
if ((c2 & 0x01) != 0)
|
|
{
|
|
dx_ext1 -= 2;
|
|
xsv_ext1 += 2;
|
|
}
|
|
else if ((c2 & 0x02) != 0)
|
|
{
|
|
dy_ext1 -= 2;
|
|
ysv_ext1 += 2;
|
|
}
|
|
else
|
|
{
|
|
dz_ext1 -= 2;
|
|
zsv_ext1 += 2;
|
|
}
|
|
}
|
|
|
|
//Contribution (1,0,0)
|
|
double dx1 = dx0 - 1 - m_squish3d;
|
|
double dy1 = dy0 - 0 - m_squish3d;
|
|
double dz1 = dz0 - 0 - m_squish3d;
|
|
double 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)
|
|
double dx2 = dx0 - 0 - m_squish3d;
|
|
double dy2 = dy0 - 1 - m_squish3d;
|
|
double dz2 = dz1;
|
|
double 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)
|
|
double dx3 = dx2;
|
|
double dy3 = dy1;
|
|
double dz3 = dz0 - 1 - m_squish3d;
|
|
double 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)
|
|
double dx4 = dx0 - 1 - 2 * m_squish3d;
|
|
double dy4 = dy0 - 1 - 2 * m_squish3d;
|
|
double dz4 = dz0 - 0 - 2 * m_squish3d;
|
|
double 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)
|
|
double dx5 = dx4;
|
|
double dy5 = dy0 - 0 - 2 * m_squish3d;
|
|
double dz5 = dz0 - 1 - 2 * m_squish3d;
|
|
double 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)
|
|
double dx6 = dx0 - 0 - 2 * m_squish3d;
|
|
double dy6 = dy4;
|
|
double dz6 = dz5;
|
|
double 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
|
|
double 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
|
|
double 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 / m_norm3d;
|
|
}
|
|
|
|
double Noise::eval(double x, double y, double z, double w) const
|
|
{
|
|
//Place input coordinates on simplectic honeycomb.
|
|
double stretchOffset = (x + y + z + w) * m_stretch4d;
|
|
double xs = x + stretchOffset;
|
|
double ys = y + stretchOffset;
|
|
double zs = z + stretchOffset;
|
|
double ws = w + stretchOffset;
|
|
|
|
//static_cast<int>(floor to get simplectic honeycomb coordinates of rhombo-hypercube super-cell origin.
|
|
int xsb = static_cast<int>(floor(xs));
|
|
int ysb = static_cast<int>(floor(ys));
|
|
int zsb = static_cast<int>(floor(zs));
|
|
int wsb = static_cast<int>(floor(ws));
|
|
|
|
//Skew out to get actual coordinates of stretched rhombo-hypercube origin. We'll need these later.
|
|
double squishOffset = (xsb + ysb + zsb + wsb) * m_squish4d;
|
|
double xb = xsb + squishOffset;
|
|
double yb = ysb + squishOffset;
|
|
double zb = zsb + squishOffset;
|
|
double wb = wsb + squishOffset;
|
|
|
|
//Compute simplectic honeycomb coordinates relative to rhombo-hypercube origin.
|
|
double xins = xs - xsb;
|
|
double yins = ys - ysb;
|
|
double zins = zs - zsb;
|
|
double wins = ws - wsb;
|
|
|
|
//Sum those together to get a value that determines which region we're in.
|
|
double inSum = xins + yins + zins + wins;
|
|
|
|
//Positions relative to origin point.
|
|
double dx0 = x - xb;
|
|
double dy0 = y - yb;
|
|
double dz0 = z - zb;
|
|
double dw0 = w - wb;
|
|
|
|
//We'll be defining these inside the next block and using them afterwards.
|
|
double dx_ext0, dy_ext0, dz_ext0, dw_ext0;
|
|
double dx_ext1, dy_ext1, dz_ext1, dw_ext1;
|
|
double dx_ext2, dy_ext2, dz_ext2, dw_ext2;
|
|
int xsv_ext0, ysv_ext0, zsv_ext0, wsv_ext0;
|
|
int xsv_ext1, ysv_ext1, zsv_ext1, wsv_ext1;
|
|
int xsv_ext2, ysv_ext2, zsv_ext2, wsv_ext2;
|
|
|
|
double value = 0;
|
|
if (inSum <= 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.
|
|
char aPoint = 0x01;
|
|
double aScore = xins;
|
|
char bPoint = 0x02;
|
|
double bScore = yins;
|
|
if (aScore >= bScore && zins > bScore)
|
|
{
|
|
bScore = zins;
|
|
bPoint = 0x04;
|
|
}
|
|
else if (aScore < bScore && zins > aScore)
|
|
{
|
|
aScore = zins;
|
|
aPoint = 0x04;
|
|
}
|
|
if (aScore >= bScore && wins > bScore)
|
|
{
|
|
bScore = wins;
|
|
bPoint = 0x08;
|
|
}
|
|
else if (aScore < bScore && wins > aScore)
|
|
{
|
|
aScore = wins;
|
|
aPoint = 0x08;
|
|
}
|
|
|
|
//Now we determine the three lattice points not part of the pentachoron that may contribute.
|
|
//This depends on the closest two pentachoron vertices, including (0,0,0,0)
|
|
double uins = 1 - inSum;
|
|
if (uins > aScore || uins > bScore)
|
|
{ //(0,0,0,0) is one of the closest two pentachoron vertices.
|
|
char c = (bScore > aScore ? bPoint : aPoint); //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.
|
|
char c = static_cast<char>(aPoint | bPoint); //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 * m_squish4d;
|
|
dx_ext1 = dx0 + 1 - m_squish4d;
|
|
dx_ext2 = dx0 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb + 1;
|
|
dx_ext0 = dx0 - 1 - 2 * m_squish4d;
|
|
dx_ext1 = dx_ext2 = dx0 - 1 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x02) == 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb;
|
|
dy_ext0 = dy0 - 2 * m_squish4d;
|
|
dy_ext1 = dy_ext2 = dy0 - m_squish4d;
|
|
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 * m_squish4d;
|
|
dy_ext1 = dy_ext2 = dy0 - 1 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x04) == 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb;
|
|
dz_ext0 = dz0 - 2 * m_squish4d;
|
|
dz_ext1 = dz_ext2 = dz0 - m_squish4d;
|
|
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 * m_squish4d;
|
|
dz_ext1 = dz_ext2 = dz0 - 1 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x08) == 0)
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb;
|
|
wsv_ext2 = wsb - 1;
|
|
dw_ext0 = dw0 - 2 * m_squish4d;
|
|
dw_ext1 = dw0 - m_squish4d;
|
|
dw_ext2 = dw0 + 1 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb + 1;
|
|
dw_ext0 = dw0 - 1 - 2 * m_squish4d;
|
|
dw_ext1 = dw_ext2 = dw0 - 1 - m_squish4d;
|
|
}
|
|
}
|
|
|
|
//Contribution (0,0,0,0)
|
|
double 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)
|
|
double dx1 = dx0 - 1 - m_squish4d;
|
|
double dy1 = dy0 - 0 - m_squish4d;
|
|
double dz1 = dz0 - 0 - m_squish4d;
|
|
double dw1 = dw0 - 0 - m_squish4d;
|
|
double 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)
|
|
double dx2 = dx0 - 0 - m_squish4d;
|
|
double dy2 = dy0 - 1 - m_squish4d;
|
|
double dz2 = dz1;
|
|
double dw2 = dw1;
|
|
double 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)
|
|
double dx3 = dx2;
|
|
double dy3 = dy1;
|
|
double dz3 = dz0 - 1 - m_squish4d;
|
|
double dw3 = dw1;
|
|
double 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)
|
|
double dx4 = dx2;
|
|
double dy4 = dy1;
|
|
double dz4 = dz1;
|
|
double dw4 = dw0 - 1 - m_squish4d;
|
|
double 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);
|
|
}
|
|
}
|
|
else if (inSum >= 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.
|
|
char aPoint = 0x0E;
|
|
double aScore = xins;
|
|
char bPoint = 0x0D;
|
|
double bScore = yins;
|
|
if (aScore <= bScore && zins < bScore)
|
|
{
|
|
bScore = zins;
|
|
bPoint = 0x0B;
|
|
}
|
|
else if (aScore > bScore && zins < aScore)
|
|
{
|
|
aScore = zins;
|
|
aPoint = 0x0B;
|
|
}
|
|
if (aScore <= bScore && wins < bScore)
|
|
{
|
|
bScore = wins;
|
|
bPoint = 0x07;
|
|
}
|
|
else if (aScore > bScore && wins < aScore)
|
|
{
|
|
aScore = wins;
|
|
aPoint = 0x07;
|
|
}
|
|
|
|
//Now we determine the three lattice points not part of the pentachoron that may contribute.
|
|
//This depends on the closest two pentachoron vertices, including (0,0,0,0)
|
|
double uins = 4 - inSum;
|
|
if (uins < aScore || uins < bScore)
|
|
{ //(1,1,1,1) is one of the closest two pentachoron vertices.
|
|
char c = (bScore < aScore ? bPoint : aPoint); //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 * m_squish4d;
|
|
dx_ext1 = dx_ext2 = dx0 - 1 - 4 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
|
|
dx_ext0 = dx_ext1 = dx_ext2 = dx0 - 4 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
|
|
dy_ext0 = dy_ext1 = dy_ext2 = dy0 - 1 - 4 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
|
|
dz_ext0 = dz_ext1 = dz_ext2 = dz0 - 1 - 4 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x08) != 0)
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb + 1;
|
|
wsv_ext2 = wsb + 2;
|
|
dw_ext0 = dw_ext1 = dw0 - 1 - 4 * m_squish4d;
|
|
dw_ext2 = dw0 - 2 - 4 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
|
|
dw_ext0 = dw_ext1 = dw_ext2 = dw0 - 4 * m_squish4d;
|
|
}
|
|
}
|
|
else
|
|
{ //(1,1,1,1) is not one of the closest two pentachoron vertices.
|
|
char c = static_cast<char>(aPoint & bPoint); //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 * m_squish4d;
|
|
dx_ext1 = dx0 - 2 - 3 * m_squish4d;
|
|
dx_ext2 = dx0 - 1 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsv_ext2 = xsb;
|
|
dx_ext0 = dx0 - 2 * m_squish4d;
|
|
dx_ext1 = dx_ext2 = dx0 - 3 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysv_ext2 = ysb + 1;
|
|
dy_ext0 = dy0 - 1 - 2 * m_squish4d;
|
|
dy_ext1 = dy_ext2 = dy0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
dy_ext1 = dy_ext2 = dy0 - 3 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsv_ext2 = zsb + 1;
|
|
dz_ext0 = dz0 - 1 - 2 * m_squish4d;
|
|
dz_ext1 = dz_ext2 = dz0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
dz_ext1 = dz_ext2 = dz0 - 3 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x08) != 0)
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb + 1;
|
|
wsv_ext2 = wsb + 2;
|
|
dw_ext0 = dw0 - 1 - 2 * m_squish4d;
|
|
dw_ext1 = dw0 - 1 - 3 * m_squish4d;
|
|
dw_ext2 = dw0 - 2 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsv_ext2 = wsb;
|
|
dw_ext0 = dw0 - 2 * m_squish4d;
|
|
dw_ext1 = dw_ext2 = dw0 - 3 * m_squish4d;
|
|
}
|
|
}
|
|
|
|
//Contribution (1,1,1,0)
|
|
double dx4 = dx0 - 1 - 3 * m_squish4d;
|
|
double dy4 = dy0 - 1 - 3 * m_squish4d;
|
|
double dz4 = dz0 - 1 - 3 * m_squish4d;
|
|
double dw4 = dw0 - 3 * m_squish4d;
|
|
double 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)
|
|
double dx3 = dx4;
|
|
double dy3 = dy4;
|
|
double dz3 = dz0 - 3 * m_squish4d;
|
|
double dw3 = dw0 - 1 - 3 * m_squish4d;
|
|
double 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)
|
|
double dx2 = dx4;
|
|
double dy2 = dy0 - 3 * m_squish4d;
|
|
double dz2 = dz4;
|
|
double dw2 = dw3;
|
|
double 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)
|
|
double dx1 = dx0 - 3 * m_squish4d;
|
|
double dz1 = dz4;
|
|
double dy1 = dy4;
|
|
double dw1 = dw3;
|
|
double 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 * m_squish4d;
|
|
dy0 = dy0 - 1 - 4 * m_squish4d;
|
|
dz0 = dz0 - 1 - 4 * m_squish4d;
|
|
dw0 = dw0 - 1 - 4 * m_squish4d;
|
|
double 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);
|
|
}
|
|
}
|
|
else if (inSum <= 2)
|
|
{ //We're inside the first dispentachoron (Rectified 4-Simplex)
|
|
double aScore;
|
|
char aPoint;
|
|
bool aIsBiggerSide = true;
|
|
double bScore;
|
|
char bPoint;
|
|
bool bIsBiggerSide = true;
|
|
|
|
//Decide between (1,1,0,0) and (0,0,1,1)
|
|
if (xins + yins > zins + wins)
|
|
{
|
|
aScore = xins + yins;
|
|
aPoint = 0x03;
|
|
}
|
|
else
|
|
{
|
|
aScore = zins + wins;
|
|
aPoint = 0x0C;
|
|
}
|
|
|
|
//Decide between (1,0,1,0) and (0,1,0,1)
|
|
if (xins + zins > yins + wins)
|
|
{
|
|
bScore = xins + zins;
|
|
bPoint = 0x05;
|
|
}
|
|
else
|
|
{
|
|
bScore = yins + wins;
|
|
bPoint = 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)
|
|
{
|
|
double score = xins + wins;
|
|
if (aScore >= bScore && score > bScore)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x09;
|
|
}
|
|
else if (aScore < bScore && score > aScore)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x09;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double score = yins + zins;
|
|
if (aScore >= bScore && score > bScore)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x06;
|
|
}
|
|
else if (aScore < bScore && score > aScore)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x06;
|
|
}
|
|
}
|
|
|
|
//Decide if (1,0,0,0) is closer.
|
|
double p1 = 2 - inSum + xins;
|
|
if (aScore >= bScore && p1 > bScore)
|
|
{
|
|
bScore = p1;
|
|
bPoint = 0x01;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore < bScore && p1 > aScore)
|
|
{
|
|
aScore = p1;
|
|
aPoint = 0x01;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (0,1,0,0) is closer.
|
|
double p2 = 2 - inSum + yins;
|
|
if (aScore >= bScore && p2 > bScore)
|
|
{
|
|
bScore = p2;
|
|
bPoint = 0x02;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore < bScore && p2 > aScore)
|
|
{
|
|
aScore = p2;
|
|
aPoint = 0x02;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (0,0,1,0) is closer.
|
|
double p3 = 2 - inSum + zins;
|
|
if (aScore >= bScore && p3 > bScore)
|
|
{
|
|
bScore = p3;
|
|
bPoint = 0x04;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore < bScore && p3 > aScore)
|
|
{
|
|
aScore = p3;
|
|
aPoint = 0x04;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (0,0,0,1) is closer.
|
|
double p4 = 2 - inSum + wins;
|
|
if (aScore >= bScore && p4 > bScore)
|
|
{
|
|
bScore = p4;
|
|
bPoint = 0x08;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore < bScore && p4 > aScore)
|
|
{
|
|
aScore = p4;
|
|
aPoint = 0x08;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Where each of the two closest points are determines how the extra three vertices are calculated.
|
|
if (aIsBiggerSide == bIsBiggerSide)
|
|
{
|
|
if (aIsBiggerSide)
|
|
{ //Both closest points on the bigger side
|
|
char c1 = static_cast<char>(aPoint | bPoint);
|
|
char c2 = static_cast<char>(aPoint & bPoint);
|
|
if ((c1 & 0x01) == 0)
|
|
{
|
|
xsv_ext0 = xsb;
|
|
xsv_ext1 = xsb - 1;
|
|
dx_ext0 = dx0 - 3 * m_squish4d;
|
|
dx_ext1 = dx0 + 1 - 2 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx0 - 1 - 3 * m_squish4d;
|
|
dx_ext1 = dx0 - 1 - 2 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x02) == 0)
|
|
{
|
|
ysv_ext0 = ysb;
|
|
ysv_ext1 = ysb - 1;
|
|
dy_ext0 = dy0 - 3 * m_squish4d;
|
|
dy_ext1 = dy0 + 1 - 2 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb + 1;
|
|
dy_ext0 = dy0 - 1 - 3 * m_squish4d;
|
|
dy_ext1 = dy0 - 1 - 2 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x04) == 0)
|
|
{
|
|
zsv_ext0 = zsb;
|
|
zsv_ext1 = zsb - 1;
|
|
dz_ext0 = dz0 - 3 * m_squish4d;
|
|
dz_ext1 = dz0 + 1 - 2 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb + 1;
|
|
dz_ext0 = dz0 - 1 - 3 * m_squish4d;
|
|
dz_ext1 = dz0 - 1 - 2 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x08) == 0)
|
|
{
|
|
wsv_ext0 = wsb;
|
|
wsv_ext1 = wsb - 1;
|
|
dw_ext0 = dw0 - 3 * m_squish4d;
|
|
dw_ext1 = dw0 + 1 - 2 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb + 1;
|
|
dw_ext0 = dw0 - 1 - 3 * m_squish4d;
|
|
dw_ext1 = dw0 - 1 - 2 * m_squish4d;
|
|
}
|
|
|
|
//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 * m_squish4d;
|
|
dy_ext2 = dy0 - 2 * m_squish4d;
|
|
dz_ext2 = dz0 - 2 * m_squish4d;
|
|
dw_ext2 = dw0 - 2 * m_squish4d;
|
|
if ((c2 & 0x01) != 0)
|
|
{
|
|
xsv_ext2 += 2;
|
|
dx_ext2 -= 2;
|
|
}
|
|
else if ((c2 & 0x02) != 0)
|
|
{
|
|
ysv_ext2 += 2;
|
|
dy_ext2 -= 2;
|
|
}
|
|
else if ((c2 & 0x04) != 0)
|
|
{
|
|
zsv_ext2 += 2;
|
|
dz_ext2 -= 2;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext2 += 2;
|
|
dw_ext2 -= 2;
|
|
}
|
|
|
|
}
|
|
else
|
|
{ //Both closest points on the smaller side
|
|
//One of the two extra points 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 points are based on the omitted axes.
|
|
char c = static_cast<char>(aPoint | bPoint);
|
|
|
|
if ((c & 0x01) == 0)
|
|
{
|
|
xsv_ext0 = xsb - 1;
|
|
xsv_ext1 = xsb;
|
|
dx_ext0 = dx0 + 1 - m_squish4d;
|
|
dx_ext1 = dx0 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx_ext1 = dx0 - 1 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x02) == 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb;
|
|
dy_ext0 = dy_ext1 = dy0 - m_squish4d;
|
|
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 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x04) == 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb;
|
|
dz_ext0 = dz_ext1 = dz0 - m_squish4d;
|
|
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 - m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x08) == 0)
|
|
{
|
|
wsv_ext0 = wsb;
|
|
wsv_ext1 = wsb - 1;
|
|
dw_ext0 = dw0 - m_squish4d;
|
|
dw_ext1 = dw0 + 1 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb + 1;
|
|
dw_ext0 = dw_ext1 = dw0 - 1 - m_squish4d;
|
|
}
|
|
|
|
}
|
|
}
|
|
else
|
|
{ //One point on each "side"
|
|
char c1, c2;
|
|
if (aIsBiggerSide)
|
|
{
|
|
c1 = aPoint;
|
|
c2 = bPoint;
|
|
}
|
|
else
|
|
{
|
|
c1 = bPoint;
|
|
c2 = aPoint;
|
|
}
|
|
|
|
//Two contributions are the bigger-sided point with each 0 replaced with -1.
|
|
if ((c1 & 0x01) == 0)
|
|
{
|
|
xsv_ext0 = xsb - 1;
|
|
xsv_ext1 = xsb;
|
|
dx_ext0 = dx0 + 1 - m_squish4d;
|
|
dx_ext1 = dx0 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx_ext1 = dx0 - 1 - m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x02) == 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb;
|
|
dy_ext0 = dy_ext1 = dy0 - m_squish4d;
|
|
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 - m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x04) == 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb;
|
|
dz_ext0 = dz_ext1 = dz0 - m_squish4d;
|
|
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 - m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x08) == 0)
|
|
{
|
|
wsv_ext0 = wsb;
|
|
wsv_ext1 = wsb - 1;
|
|
dw_ext0 = dw0 - m_squish4d;
|
|
dw_ext1 = dw0 + 1 - m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb + 1;
|
|
dw_ext0 = dw_ext1 = dw0 - 1 - m_squish4d;
|
|
}
|
|
|
|
//One contribution is a permutation of (0,0,0,2) based on the smaller-sided point
|
|
xsv_ext2 = xsb;
|
|
ysv_ext2 = ysb;
|
|
zsv_ext2 = zsb;
|
|
wsv_ext2 = wsb;
|
|
dx_ext2 = dx0 - 2 * m_squish4d;
|
|
dy_ext2 = dy0 - 2 * m_squish4d;
|
|
dz_ext2 = dz0 - 2 * m_squish4d;
|
|
dw_ext2 = dw0 - 2 * m_squish4d;
|
|
if ((c2 & 0x01) != 0)
|
|
{
|
|
xsv_ext2 += 2;
|
|
dx_ext2 -= 2;
|
|
}
|
|
else if ((c2 & 0x02) != 0)
|
|
{
|
|
ysv_ext2 += 2;
|
|
dy_ext2 -= 2;
|
|
}
|
|
else if ((c2 & 0x04) != 0)
|
|
{
|
|
zsv_ext2 += 2;
|
|
dz_ext2 -= 2;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext2 += 2;
|
|
dw_ext2 -= 2;
|
|
}
|
|
}
|
|
|
|
//Contribution (1,0,0,0)
|
|
double dx1 = dx0 - 1 - m_squish4d;
|
|
double dy1 = dy0 - 0 - m_squish4d;
|
|
double dz1 = dz0 - 0 - m_squish4d;
|
|
double dw1 = dw0 - 0 - m_squish4d;
|
|
double 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)
|
|
double dx2 = dx0 - 0 - m_squish4d;
|
|
double dy2 = dy0 - 1 - m_squish4d;
|
|
double dz2 = dz1;
|
|
double dw2 = dw1;
|
|
double 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)
|
|
double dx3 = dx2;
|
|
double dy3 = dy1;
|
|
double dz3 = dz0 - 1 - m_squish4d;
|
|
double dw3 = dw1;
|
|
double 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)
|
|
double dx4 = dx2;
|
|
double dy4 = dy1;
|
|
double dz4 = dz1;
|
|
double dw4 = dw0 - 1 - m_squish4d;
|
|
double 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)
|
|
double dx5 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy5 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz5 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw5 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx6 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy6 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz6 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw6 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx7 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy7 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz7 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw7 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx8 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy8 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz8 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw8 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx9 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy9 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz9 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw9 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx10 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy10 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz10 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw10 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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)
|
|
double aScore;
|
|
char aPoint;
|
|
bool aIsBiggerSide = true;
|
|
double bScore;
|
|
char bPoint;
|
|
bool bIsBiggerSide = true;
|
|
|
|
//Decide between (0,0,1,1) and (1,1,0,0)
|
|
if (xins + yins < zins + wins)
|
|
{
|
|
aScore = xins + yins;
|
|
aPoint = 0x0C;
|
|
}
|
|
else
|
|
{
|
|
aScore = zins + wins;
|
|
aPoint = 0x03;
|
|
}
|
|
|
|
//Decide between (0,1,0,1) and (1,0,1,0)
|
|
if (xins + zins < yins + wins)
|
|
{
|
|
bScore = xins + zins;
|
|
bPoint = 0x0A;
|
|
}
|
|
else
|
|
{
|
|
bScore = yins + wins;
|
|
bPoint = 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)
|
|
{
|
|
double score = xins + wins;
|
|
if (aScore <= bScore && score < bScore)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x06;
|
|
}
|
|
else if (aScore > bScore && score < aScore)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x06;
|
|
}
|
|
}
|
|
else
|
|
{
|
|
double score = yins + zins;
|
|
if (aScore <= bScore && score < bScore)
|
|
{
|
|
bScore = score;
|
|
bPoint = 0x09;
|
|
}
|
|
else if (aScore > bScore && score < aScore)
|
|
{
|
|
aScore = score;
|
|
aPoint = 0x09;
|
|
}
|
|
}
|
|
|
|
//Decide if (0,1,1,1) is closer.
|
|
double p1 = 3 - inSum + xins;
|
|
if (aScore <= bScore && p1 < bScore)
|
|
{
|
|
bScore = p1;
|
|
bPoint = 0x0E;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore > bScore && p1 < aScore)
|
|
{
|
|
aScore = p1;
|
|
aPoint = 0x0E;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (1,0,1,1) is closer.
|
|
double p2 = 3 - inSum + yins;
|
|
if (aScore <= bScore && p2 < bScore)
|
|
{
|
|
bScore = p2;
|
|
bPoint = 0x0D;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore > bScore && p2 < aScore)
|
|
{
|
|
aScore = p2;
|
|
aPoint = 0x0D;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (1,1,0,1) is closer.
|
|
double p3 = 3 - inSum + zins;
|
|
if (aScore <= bScore && p3 < bScore)
|
|
{
|
|
bScore = p3;
|
|
bPoint = 0x0B;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore > bScore && p3 < aScore)
|
|
{
|
|
aScore = p3;
|
|
aPoint = 0x0B;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Decide if (1,1,1,0) is closer.
|
|
double p4 = 3 - inSum + wins;
|
|
if (aScore <= bScore && p4 < bScore)
|
|
{
|
|
bScore = p4;
|
|
bPoint = 0x07;
|
|
bIsBiggerSide = false;
|
|
}
|
|
else if (aScore > bScore && p4 < aScore)
|
|
{
|
|
aScore = p4;
|
|
aPoint = 0x07;
|
|
aIsBiggerSide = false;
|
|
}
|
|
|
|
//Where each of the two closest points are determines how the extra three vertices are calculated.
|
|
if (aIsBiggerSide == bIsBiggerSide)
|
|
{
|
|
if (aIsBiggerSide)
|
|
{ //Both closest points on the bigger side
|
|
char c1 = static_cast<char>(aPoint & bPoint);
|
|
char c2 = static_cast<char>(aPoint | bPoint);
|
|
|
|
//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 - m_squish4d;
|
|
dy_ext0 = dy0 - m_squish4d;
|
|
dz_ext0 = dz0 - m_squish4d;
|
|
dw_ext0 = dw0 - m_squish4d;
|
|
dx_ext1 = dx0 - 2 * m_squish4d;
|
|
dy_ext1 = dy0 - 2 * m_squish4d;
|
|
dz_ext1 = dz0 - 2 * m_squish4d;
|
|
dw_ext1 = dw0 - 2 * m_squish4d;
|
|
if ((c1 & 0x01) != 0)
|
|
{
|
|
xsv_ext0 += 1;
|
|
dx_ext0 -= 1;
|
|
xsv_ext1 += 2;
|
|
dx_ext1 -= 2;
|
|
}
|
|
else if ((c1 & 0x02) != 0)
|
|
{
|
|
ysv_ext0 += 1;
|
|
dy_ext0 -= 1;
|
|
ysv_ext1 += 2;
|
|
dy_ext1 -= 2;
|
|
}
|
|
else if ((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 * m_squish4d;
|
|
dy_ext2 = dy0 - 1 - 2 * m_squish4d;
|
|
dz_ext2 = dz0 - 1 - 2 * m_squish4d;
|
|
dw_ext2 = dw0 - 1 - 2 * m_squish4d;
|
|
if ((c2 & 0x01) == 0)
|
|
{
|
|
xsv_ext2 -= 2;
|
|
dx_ext2 += 2;
|
|
}
|
|
else if ((c2 & 0x02) == 0)
|
|
{
|
|
ysv_ext2 -= 2;
|
|
dy_ext2 += 2;
|
|
}
|
|
else if ((c2 & 0x04) == 0)
|
|
{
|
|
zsv_ext2 -= 2;
|
|
dz_ext2 += 2;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext2 -= 2;
|
|
dw_ext2 += 2;
|
|
}
|
|
}
|
|
else
|
|
{ //Both closest points on the smaller side
|
|
//One of the two extra points 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 * m_squish4d;
|
|
dy_ext2 = dy0 - 1 - 4 * m_squish4d;
|
|
dz_ext2 = dz0 - 1 - 4 * m_squish4d;
|
|
dw_ext2 = dw0 - 1 - 4 * m_squish4d;
|
|
|
|
//Other two points are based on the shared axes.
|
|
char c = static_cast<char>(aPoint & bPoint);
|
|
|
|
if ((c & 0x01) != 0)
|
|
{
|
|
xsv_ext0 = xsb + 2;
|
|
xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx0 - 2 - 3 * m_squish4d;
|
|
dx_ext1 = dx0 - 1 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb;
|
|
dx_ext0 = dx_ext1 = dx0 - 3 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb + 1;
|
|
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb + 1;
|
|
dz_ext0 = dz_ext1 = dz0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c & 0x08) != 0)
|
|
{
|
|
wsv_ext0 = wsb + 1;
|
|
wsv_ext1 = wsb + 2;
|
|
dw_ext0 = dw0 - 1 - 3 * m_squish4d;
|
|
dw_ext1 = dw0 - 2 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb;
|
|
dw_ext0 = dw_ext1 = dw0 - 3 * m_squish4d;
|
|
}
|
|
}
|
|
}
|
|
else
|
|
{ //One point on each "side"
|
|
char c1, c2;
|
|
if (aIsBiggerSide)
|
|
{
|
|
c1 = aPoint;
|
|
c2 = bPoint;
|
|
}
|
|
else
|
|
{
|
|
c1 = bPoint;
|
|
c2 = aPoint;
|
|
}
|
|
|
|
//Two contributions are the bigger-sided point with each 1 replaced with 2.
|
|
if ((c1 & 0x01) != 0)
|
|
{
|
|
xsv_ext0 = xsb + 2;
|
|
xsv_ext1 = xsb + 1;
|
|
dx_ext0 = dx0 - 2 - 3 * m_squish4d;
|
|
dx_ext1 = dx0 - 1 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
xsv_ext0 = xsv_ext1 = xsb;
|
|
dx_ext0 = dx_ext1 = dx0 - 3 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x02) != 0)
|
|
{
|
|
ysv_ext0 = ysv_ext1 = ysb + 1;
|
|
dy_ext0 = dy_ext1 = dy0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x04) != 0)
|
|
{
|
|
zsv_ext0 = zsv_ext1 = zsb + 1;
|
|
dz_ext0 = dz_ext1 = dz0 - 1 - 3 * m_squish4d;
|
|
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 * m_squish4d;
|
|
}
|
|
|
|
if ((c1 & 0x08) != 0)
|
|
{
|
|
wsv_ext0 = wsb + 1;
|
|
wsv_ext1 = wsb + 2;
|
|
dw_ext0 = dw0 - 1 - 3 * m_squish4d;
|
|
dw_ext1 = dw0 - 2 - 3 * m_squish4d;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext0 = wsv_ext1 = wsb;
|
|
dw_ext0 = dw_ext1 = dw0 - 3 * m_squish4d;
|
|
}
|
|
|
|
//One contribution is a permutation of (1,1,1,-1) based on the smaller-sided point
|
|
xsv_ext2 = xsb + 1;
|
|
ysv_ext2 = ysb + 1;
|
|
zsv_ext2 = zsb + 1;
|
|
wsv_ext2 = wsb + 1;
|
|
dx_ext2 = dx0 - 1 - 2 * m_squish4d;
|
|
dy_ext2 = dy0 - 1 - 2 * m_squish4d;
|
|
dz_ext2 = dz0 - 1 - 2 * m_squish4d;
|
|
dw_ext2 = dw0 - 1 - 2 * m_squish4d;
|
|
if ((c2 & 0x01) == 0)
|
|
{
|
|
xsv_ext2 -= 2;
|
|
dx_ext2 += 2;
|
|
}
|
|
else if ((c2 & 0x02) == 0)
|
|
{
|
|
ysv_ext2 -= 2;
|
|
dy_ext2 += 2;
|
|
}
|
|
else if ((c2 & 0x04) == 0)
|
|
{
|
|
zsv_ext2 -= 2;
|
|
dz_ext2 += 2;
|
|
}
|
|
else
|
|
{
|
|
wsv_ext2 -= 2;
|
|
dw_ext2 += 2;
|
|
}
|
|
}
|
|
|
|
//Contribution (1,1,1,0)
|
|
double dx4 = dx0 - 1 - 3 * m_squish4d;
|
|
double dy4 = dy0 - 1 - 3 * m_squish4d;
|
|
double dz4 = dz0 - 1 - 3 * m_squish4d;
|
|
double dw4 = dw0 - 3 * m_squish4d;
|
|
double 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)
|
|
double dx3 = dx4;
|
|
double dy3 = dy4;
|
|
double dz3 = dz0 - 3 * m_squish4d;
|
|
double dw3 = dw0 - 1 - 3 * m_squish4d;
|
|
double 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)
|
|
double dx2 = dx4;
|
|
double dy2 = dy0 - 3 * m_squish4d;
|
|
double dz2 = dz4;
|
|
double dw2 = dw3;
|
|
double 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)
|
|
double dx1 = dx0 - 3 * m_squish4d;
|
|
double dz1 = dz4;
|
|
double dy1 = dy4;
|
|
double dw1 = dw3;
|
|
double 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)
|
|
double dx5 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy5 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz5 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw5 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx6 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy6 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz6 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw6 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx7 = dx0 - 1 - 2 * m_squish4d;
|
|
double dy7 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz7 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw7 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx8 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy8 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz8 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw8 = dw0 - 0 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx9 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy9 = dy0 - 1 - 2 * m_squish4d;
|
|
double dz9 = dz0 - 0 - 2 * m_squish4d;
|
|
double dw9 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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)
|
|
double dx10 = dx0 - 0 - 2 * m_squish4d;
|
|
double dy10 = dy0 - 0 - 2 * m_squish4d;
|
|
double dz10 = dz0 - 1 - 2 * m_squish4d;
|
|
double dw10 = dw0 - 1 - 2 * m_squish4d;
|
|
double 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
|
|
double 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
|
|
double 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
|
|
double 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 / m_norm4d;
|
|
}
|
|
|
|
double Noise::extrapolate(int xsb, int ysb, double dx, double dy) const
|
|
{
|
|
int index = m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] & 0x0E;
|
|
return m_gradients2d[index] * dx
|
|
+ m_gradients2d[index + 1] * dy;
|
|
}
|
|
|
|
double Noise::extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) const
|
|
{
|
|
int index = m_permGradIndex3d[(m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF];
|
|
return m_gradients3d[index] * dx
|
|
+ m_gradients3d[index + 1] * dy
|
|
+ m_gradients3d[index + 2] * dz;
|
|
}
|
|
|
|
double Noise::extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) const
|
|
{
|
|
int index = m_perm[(m_perm[(m_perm[(m_perm[xsb & 0xFF] + ysb) & 0xFF] + zsb) & 0xFF] + wsb) & 0xFF] & 0xFC;
|
|
return m_gradients4d[index] * dx
|
|
+ m_gradients4d[index + 1] * dy
|
|
+ m_gradients4d[index + 2] * dz
|
|
+ m_gradients4d[index + 3] * dw;
|
|
}
|
|
|
|
} |