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OpenSimplexNoise
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| #include "OpenSimplexNoise.h" | |
| #include <cmath> | |
| namespace OpenSimplexNoise | |
| { | |
| using namespace std; | |
| Noise::Noise() | |
| : m_stretch2d(-0.211324865405187) //(1/Math.sqrt(2+1)-1)/2; | |
| , m_squish2d(0.366025403784439) //(Math.sqrt(2+1)-1)/2; | |
| , m_stretch3d(-1.0 / 6) //(1/Math.sqrt(3+1)-1)/3; | |
| , m_squish3d(1.0 / 3) //(Math.sqrt(3+1)-1)/3; | |
| , m_stretch4d(-0.138196601125011) //(1/Math.sqrt(4+1)-1)/4; | |
| , m_squish4d(0.309016994374947) //(Math.sqrt(4+1)-1)/4; | |
| , m_norm2d(47) | |
| , m_norm3d(103) | |
| , m_norm4d(30) | |
| , m_defaultSeed(0) | |
| , m_perm{0} | |
| , m_permGradIndex3d{0} | |
| , m_gradients2d{ 5, 2, 2, 5, | |
| -5, 2, -2, 5, | |
| 5, -2, 2, -5, | |
| -5, -2, -2, -5, } | |
| , m_gradients3d{-11, 4, 4, -4, 11, 4, -4, 4, 11, | |
| 11, 4, 4, 4, 11, 4, 4, 4, 11, | |
| -11, -4, 4, -4, -11, 4, -4, -4, 11, | |
| 11, -4, 4, 4, -11, 4, 4, -4, 11, | |
| -11, 4, -4, -4, 11, -4, -4, 4, -11, | |
| 11, 4, -4, 4, 11, -4, 4, 4, -11, | |
| -11, -4, -4, -4, -11, -4, -4, -4, -11, | |
| 11, -4, -4, 4, -11, -4, 4, -4, -11, } | |
| , m_gradients4d{ 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, | |
| -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, | |
| 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, 1, 1, -1, 1, 3, | |
| -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, | |
| 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, 1, 1, 1, -1, 3, | |
| -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, | |
| 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, 1, 1, -1, -1, 3, | |
| -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, | |
| 3, 1, 1, -1, 1, 3, 1, -1, 1, 1, 3, -1, 1, 1, 1, -3, | |
| -3, 1, 1, -1, -1, 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, | |
| 3, -1, 1, -1, 1, -3, 1, -1, 1, -1, 3, -1, 1, -1, 1, -3, | |
| -3, -1, 1, -1, -1, -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, | |
| 3, 1, -1, -1, 1, 3, -1, -1, 1, 1, -3, -1, 1, 1, -1, -3, | |
| -3, 1, -1, -1, -1, 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, | |
| 3, -1, -1, -1, 1, -3, -1, -1, 1, -1, -3, -1, 1, -1, -1, -3, | |
| -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, -1, -1, -1, -1, -3, } | |
| { | |
| } | |
| Noise::Noise(int64_t seed) | |
| : Noise() | |
| { | |
| short source[256]; | |
| for (short i = 0; i < 256; i++) | |
| { | |
| source[i] = i; | |
| } | |
| seed = seed * 6364136223846793005l + 1442695040888963407l; | |
| seed = seed * 6364136223846793005l + 1442695040888963407l; | |
| seed = seed * 6364136223846793005l + 1442695040888963407l; | |
| for (int i = 255; i >= 0; i--) | |
| { | |
| seed = seed * 6364136223846793005l + 1442695040888963407l; | |
| int r = static_cast<int>((seed + 31) % (i + 1)); | |
| if (r < 0) | |
| { | |
| r += (i + 1); | |
| } | |
| m_perm[i] = source[r]; | |
| m_permGradIndex3d[i] = static_cast<short>((m_perm[i] % (m_gradients3d.size() / 3)) * 3); | |
| source[r] = source[i]; | |
| } | |
| } | |
| double Noise::eval(double x, double y) const | |
| { | |
| //Place input coordinates onto grid. | |
| double stretchOffset = (x + y) * m_stretch2d; | |
| double xs = x + stretchOffset; | |
| double ys = y + stretchOffset; | |
| //Floor to get grid coordinates of rhombus (stretched square) super-cell origin. | |
| int xsb = static_cast<int>(floor(xs)); | |
| int ysb = static_cast<int>(floor(ys)); | |
| //Skew out to get actual coordinates of rhombus origin. We'll need these later. | |
| double squishOffset = (xsb + ysb) * m_squish2d; | |
| double xb = xsb + squishOffset; | |
| double yb = ysb + squishOffset; | |
| //Compute grid coordinates relative to rhombus origin. | |
| double xins = xs - xsb; | |
| double yins = ys - ysb; | |
| //Sum those together to get a value that determines which region we're in. | |
| double inSum = xins + yins; | |
| //Positions relative to origin point. | |
| double dx0 = x - xb; | |
| double dy0 = y - yb; | |
| //We'll be defining these inside the next block and using them afterwards. | |
| double dx_ext, dy_ext; | |
| int xsv_ext, ysv_ext; | |
| double value = 0; | |
| //Contribution (1,0) | |
| double dx1 = dx0 - 1 - m_squish2d; | |
| double dy1 = dy0 - 0 - m_squish2d; | |
| double attn1 = 2 - dx1 * dx1 - dy1 * dy1; | |
| if (attn1 > 0) | |
| { | |
| attn1 *= attn1; | |
| value += attn1 * attn1 * extrapolate(xsb + 1, ysb + 0, dx1, dy1); | |
| } | |
| //Contribution (0,1) | |
| double dx2 = dx0 - 0 - m_squish2d; | |
| double dy2 = dy0 - 1 - m_squish2d; | |
| double attn2 = 2 - dx2 * dx2 - dy2 * dy2; | |
| if (attn2 > 0) | |
| { | |
| attn2 *= attn2; | |
| value += attn2 * attn2 * extrapolate(xsb + 0, ysb + 1, dx2, dy2); | |
| } | |
| if (inSum <= 1) | |
| { //We're inside the triangle (2-Simplex) at (0,0) | |
| double zins = 1 - inSum; | |
| if (zins > xins || zins > yins) | |
| { //(0,0) is one of the closest two triangular vertices | |
| if (xins > yins) | |
| { | |
| xsv_ext = xsb + 1; | |
| ysv_ext = ysb - 1; | |
| dx_ext = dx0 - 1; | |
| dy_ext = dy0 + 1; | |
| } | |
| else | |
| { | |
| xsv_ext = xsb - 1; | |
| ysv_ext = ysb + 1; | |
| dx_ext = dx0 + 1; | |
| dy_ext = dy0 - 1; | |
| } | |
| } | |
| else | |
| { //(1,0) and (0,1) are the closest two vertices. | |
| xsv_ext = xsb + 1; | |
| ysv_ext = ysb + 1; | |
| dx_ext = dx0 - 1 - 2 * m_squish2d; | |
| dy_ext = dy0 - 1 - 2 * m_squish2d; | |
| } | |
| } | |
| else | |
| { //We're inside the triangle (2-Simplex) at (1,1) | |
| double zins = 2 - inSum; | |
| if (zins < xins || zins < yins) | |
| { //(0,0) is one of the closest two triangular vertices | |
| if (xins > yins) | |
| { | |
| xsv_ext = xsb + 2; | |
| ysv_ext = ysb + 0; | |
| dx_ext = dx0 - 2 - 2 * m_squish2d; | |
| dy_ext = dy0 + 0 - 2 * m_squish2d; | |
| } | |
| else | |
| { | |
| xsv_ext = xsb + 0; | |
| ysv_ext = ysb + 2; | |
| dx_ext = dx0 + 0 - 2 * m_squish2d; | |
| dy_ext = dy0 - 2 - 2 * m_squish2d; | |
| } | |
| } | |
| else | |
| { //(1,0) and (0,1) are the closest two vertices. | |
| dx_ext = dx0; | |
| dy_ext = dy0; | |
| xsv_ext = xsb; | |
| ysv_ext = ysb; | |
| } | |
| xsb += 1; | |
| ysb += 1; | |
| dx0 = dx0 - 1 - 2 * m_squish2d; | |
| dy0 = dy0 - 1 - 2 * m_squish2d; | |
| } | |
| //Contribution (0,0) or (1,1) | |
| double attn0 = 2 - dx0 * dx0 - dy0 * dy0; | |
| if (attn0 > 0) | |
| { | |
| attn0 *= attn0; | |
| value += attn0 * attn0 * extrapolate(xsb, ysb, dx0, dy0); | |
| } | |
| //Extra Vertex | |
| double attn_ext = 2 - dx_ext * dx_ext - dy_ext * dy_ext; | |
| if (attn_ext > 0) | |
| { | |
| attn_ext *= attn_ext; | |
| value += attn_ext * attn_ext * extrapolate(xsv_ext, ysv_ext, dx_ext, dy_ext); | |
| } | |
| return value / m_norm2d; | |
| } | |
| double Noise::eval(double x, double y, double z) const | |
| { | |
| //Place input coordinates on simplectic honeycomb. | |
| double stretchOffset = (x + y + z) * m_stretch3d; | |
| double xs = x + stretchOffset; | |
| double ys = y + stretchOffset; | |
| double zs = z + stretchOffset; | |
| //static_cast<int>(floor to get simplectic honeycomb coordinates of rhombohedron (stretched cube) super-cell origin. | |
| int xsb = static_cast<int>(floor(xs)); | |
| int ysb = static_cast<int>(floor(ys)); | |
| int zsb = static_cast<int>(floor(zs)); | |
| //Skew out to get actual coordinates of rhombohedron origin. We'll need these later. | |
| double squishOffset = (xsb + ysb + zsb) * m_squish3d; | |
| double xb = xsb + squishOffset; | |
| double yb = ysb + squishOffset; | |
| double zb = zsb + squishOffset; | |
| //Compute simplectic honeycomb coordinates relative to rhombohedral origin. | |
| double xins = xs - xsb; | |
| double yins = ys - ysb; | |
| double zins = zs - zsb; | |
| //Sum those together to get a value that determines which region we're in. | |
| double inSum = xins + yins + zins; | |
| //Positions relative to origin point. | |
| double dx0 = x - xb; | |
| double dy0 = y - yb; | |
| double dz0 = z - zb; | |
| //We'll be defining these inside the next block and using them afterwards. | |
| double dx_ext0, dy_ext0, dz_ext0; | |
| double dx_ext1, dy_ext1, dz_ext1; | |
| int xsv_ext0, ysv_ext0, zsv_ext0; | |
| int xsv_ext1, ysv_ext1, zsv_ext1; | |
| double value = 0; | |
| if (inSum <= 1) | |
| { //We're inside the tetrahedron (3-Simplex) at (0,0,0) | |
| //Determine which two of (0,0,1), (0,1,0), (1,0,0) are closest. | |
| 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; | |
| } | |
| //Now we determine the two lattice points not part of the tetrahedron that may contribute. | |
| //This depends on the closest two tetrahedral vertices, including (0,0,0) | |
| double wins = 1 - inSum; | |
| if (wins > aScore || wins > bScore) | |
| { //(0,0,0) is one of the closest two tetrahedral 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 = xsb; | |
| dx_ext0 = dx0 + 1; | |
| dx_ext1 = dx0; | |
| } | |
| else | |
| { | |
| xsv_ext0 = xsv_ext1 = xsb + 1; | |
| dx_ext0 = dx_ext1 = dx0 - 1; | |
| } | |
| if ((c & 0x02) == 0) | |
| { | |
| ysv_ext0 = ysv_ext1 = ysb; | |
| dy_ext0 = dy_ext1 = dy0; | |
| if ((c & 0x01) == 0) | |
| { | |
| ysv_ext1 -= 1; | |
| dy_ext1 += 1; | |
| } | |
| else | |
| { | |
| ysv_ext0 -= 1; | |
| dy_ext0 += 1; | |
| } | |
| } | |
| else | |
| { | |
| ysv_ext0 = ysv_ext1 = ysb + 1; | |
| dy_ext0 = dy_ext1 = dy0 - 1; | |
| } | |
| if ((c & 0x04) == 0) | |
| { | |
| zsv_ext0 = zsb; | |
| zsv_ext1 = zsb - 1; | |
| dz_ext0 = dz0; | |
| dz_ext1 = dz0 + 1; | |
| } | |
| else | |
| { | |
| zsv_ext0 = zsv_ext1 = zsb + 1; | |
| dz_ext0 = dz_ext1 = dz0 - 1; | |
| } | |
| } | |
| else | |
| { //(0,0,0) is not one of the closest two tetrahedral vertices. | |
| char c = static_cast<char>(aPoint | bPoint); //Our two extra vertices are determined by the closest two. | |
| if ((c & 0x01) == 0) | |
| { | |
| xsv_ext0 = xsb; | |
| xsv_ext1 = xsb - 1; | |
| dx_ext0 = dx0 - 2 * m_squish3d; | |
| dx_ext1 = dx0 + 1 - m_squish3d; | |
| } | |
| else | |
| { | |
| xsv_ext0 = xsv_ext1 = xsb + 1; | |
| dx_ext0 = dx0 - 1 - 2 * m_squish3d; | |
| dx_ext1 = dx0 - 1 - m_squish3d; | |
| } | |
| if ((c & 0x02) == 0) | |
| { | |
| ysv_ext0 = ysb; | |
| ysv_ext1 = ysb - 1; | |
| dy_ext0 = dy0 - 2 * m_squish3d; | |
| dy_ext1 = dy0 + 1 - m_squish3d; | |
| } | |
| else | |
| { | |
| ysv_ext0 = ysv_ext1 = ysb + 1; | |
| dy_ext0 = dy0 - 1 - 2 * m_squish3d; | |
| dy_ext1 = dy0 - 1 - m_squish3d; | |
| } | |
| if ((c & 0x04) == 0) | |
| { | |
| zsv_ext0 = zsb; | |
| zsv_ext1 = zsb - 1; | |
| dz_ext0 = dz0 - 2 * m_squish3d; | |
| dz_ext1 = dz0 + 1 - m_squish3d; | |
| } | |
| else | |
| { | |
| zsv_ext0 = zsv_ext1 = zsb + 1; | |
| dz_ext0 = dz0 - 1 - 2 * m_squish3d; | |
| dz_ext1 = dz0 - 1 - m_squish3d; | |
| } | |
| } | |
| //Contribution (0,0,0) | |
| double attn0 = 2 - dx0 * dx0 - dy0 * dy0 - dz0 * dz0; | |
| if (attn0 > 0) | |
| { | |
| attn0 *= attn0; | |
| value += attn0 * attn0 * extrapolate(xsb + 0, ysb + 0, zsb + 0, dx0, dy0, dz0); | |
| } | |
| //Contribution (1,0,0) | |
| 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); | |
| } | |
| } | |
| else if (inSum >= 2) | |
| { //We're inside the tetrahedron (3-Simplex) at (1,1,1) | |
| //Determine which two tetrahedral vertices are the closest, out of (1,1,0), (1,0,1), (0,1,1) but not (1,1,1). | |
| char aPoint = 0x06; | |
| double aScore = xins; | |
| char bPoint = 0x05; | |
| double bScore = yins; | |
| if (aScore <= bScore && zins < bScore) | |
| { | |
| bScore = zins; | |
| bPoint = 0x03; | |
| } | |
| else if (aScore > bScore && zins < aScore) | |
| { | |
| aScore = zins; | |
| aPoint = 0x03; | |
| } | |
| //Now we determine the two lattice points not part of the tetrahedron that may contribute. | |
| //This depends on the closest two tetrahedral vertices, including (1,1,1) | |
| double wins = 3 - inSum; | |
| if (wins < aScore || wins < bScore) | |
| { //(1,1,1) is one of the closest two tetrahedral 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 = 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; | |
| } | |
| } |
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| /** | |
| Open Simple Noise for C++ | |
| Port to C++ from https://gist.github.com/KdotJPG/b1270127455a94ac5d19 | |
| by Rickard Lundberg, 2019. | |
| */ | |
| #pragma once | |
| #include <cstdint> | |
| #include <array> | |
| namespace OpenSimplexNoise | |
| { | |
| class Noise | |
| { | |
| public: | |
| Noise(); | |
| Noise(int64_t seed); | |
| //2D Open Simplex Noise. | |
| double eval(const double x, const double y) const; | |
| //3D Open Simplex Noise. | |
| double eval(double x, double y, double z) const; | |
| //4D Open Simplex Noise. | |
| double eval(double x, double y, double z, double w) const; | |
| private: | |
| const double m_stretch2d; | |
| const double m_squish2d; | |
| const double m_stretch3d; | |
| const double m_squish3d; | |
| const double m_stretch4d; | |
| const double m_squish4d; | |
| const double m_norm2d; | |
| const double m_norm3d; | |
| const double m_norm4d; | |
| const long m_defaultSeed; | |
| std::array<short, 256> m_perm; | |
| std::array<short, 256> m_permGradIndex3d; | |
| std::array<char, 16> m_gradients2d; | |
| std::array<char, 72> m_gradients3d; | |
| std::array<char, 256> m_gradients4d; | |
| double extrapolate(int xsb, int ysb, double dx, double dy) const; | |
| double extrapolate(int xsb, int ysb, int zsb, double dx, double dy, double dz) const; | |
| double extrapolate(int xsb, int ysb, int zsb, int wsb, double dx, double dy, double dz, double dw) const; | |
| }; | |
| } |
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