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////////////////////////////////////////////////////////////////////////////////////// OpenGL Mathematics (glm.g-truc.net)////// Copyright (c) 2005 - 2013 G-Truc Creation (www.g-truc.net)/// Permission is hereby granted, free of charge, to any person obtaining a copy/// of this software and associated documentation files (the "Software"), to deal/// in the Software without restriction, including without limitation the rights/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell/// copies of the Software, and to permit persons to whom the Software is/// furnished to do so, subject to the following conditions:/// /// The above copyright notice and this permission notice shall be included in/// all copies or substantial portions of the Software./// /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN/// THE SOFTWARE.////// @ref gtc_noise/// @file glm/gtc/noise.inl/// @date 2011-04-21 / 2012-04-07/// @author Christophe Riccio///////////////////////////////////////////////////////////////////////////////////// Based on the work of Stefan Gustavson and Ashima Arts on "webgl-noise": // https://github.com/ashima/webgl-noise // Following Stefan Gustavson's paper "Simplex noise demystified": // http://www.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf///////////////////////////////////////////////////////////////////////////////////
namespace glm{ template <typename T> GLM_FUNC_QUALIFIER T mod289(T const & x) { return x - floor(x * T(1.0 / 289.0)) * T(289.0); }
template <typename T> GLM_FUNC_QUALIFIER T permute(T const & x) { return mod289(((x * T(34)) + T(1)) * x); }
template <typename T, template<typename> class vecType> GLM_FUNC_QUALIFIER vecType<T> permute(vecType<T> const & x) { return mod289(((x * T(34)) + T(1)) * x); } template <typename T> GLM_FUNC_QUALIFIER T taylorInvSqrt(T const & r) { return T(1.79284291400159) - T(0.85373472095314) * r; }
template <typename T, template<typename> class vecType> GLM_FUNC_QUALIFIER vecType<T> taylorInvSqrt(vecType<T> const & r) { return T(1.79284291400159) - T(0.85373472095314) * r; }
template <typename T, template <typename> class vecType> GLM_FUNC_QUALIFIER vecType<T> fade(vecType<T> const & t) { return t * t * t * (t * (t * T(6) - T(15)) + T(10)); }
template <typename T> GLM_FUNC_QUALIFIER detail::tvec4<T> grad4(T const & j, detail::tvec4<T> const & ip) { detail::tvec3<T> pXYZ = floor(fract(detail::tvec3<T>(j) * detail::tvec3<T>(ip)) * T(7)) * ip[2] - T(1); T pW = T(1.5) - dot(abs(pXYZ), detail::tvec3<T>(1)); detail::tvec4<T> s = detail::tvec4<T>(lessThan(detail::tvec4<T>(pXYZ, pW), detail::tvec4<T>(0.0))); pXYZ = pXYZ + (detail::tvec3<T>(s) * T(2) - T(1)) * s.w; return detail::tvec4<T>(pXYZ, pW); }
// Classic Perlin noise template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T> const & P) { detail::tvec4<T> Pi = glm::floor(detail::tvec4<T>(P.x, P.y, P.x, P.y)) + detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); detail::tvec4<T> Pf = glm::fract(detail::tvec4<T>(P.x, P.y, P.x, P.y)) - detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation detail::tvec4<T> ix(Pi.x, Pi.z, Pi.x, Pi.z); detail::tvec4<T> iy(Pi.y, Pi.y, Pi.w, Pi.w); detail::tvec4<T> fx(Pf.x, Pf.z, Pf.x, Pf.z); detail::tvec4<T> fy(Pf.y, Pf.y, Pf.w, Pf.w);
detail::tvec4<T> i = glm::permute(glm::permute(ix) + iy);
detail::tvec4<T> gx = T(2) * glm::fract(i / T(41)) - T(1); detail::tvec4<T> gy = glm::abs(gx) - T(0.5); detail::tvec4<T> tx = glm::floor(gx + T(0.5)); gx = gx - tx;
detail::tvec2<T> g00(gx.x, gy.x); detail::tvec2<T> g10(gx.y, gy.y); detail::tvec2<T> g01(gx.z, gy.z); detail::tvec2<T> g11(gx.w, gy.w);
detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); g00 *= norm.x; g01 *= norm.y; g10 *= norm.z; g11 *= norm.w;
T n00 = dot(g00, detail::tvec2<T>(fx.x, fy.x)); T n10 = dot(g10, detail::tvec2<T>(fx.y, fy.y)); T n01 = dot(g01, detail::tvec2<T>(fx.z, fy.z)); T n11 = dot(g11, detail::tvec2<T>(fx.w, fy.w));
detail::tvec2<T> fade_xy = fade(detail::tvec2<T>(Pf.x, Pf.y)); detail::tvec2<T> n_x = mix(detail::tvec2<T>(n00, n01), detail::tvec2<T>(n10, n11), fade_xy.x); T n_xy = mix(n_x.x, n_x.y, fade_xy.y); return T(2.3) * n_xy; }
// Classic Perlin noise template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P) { detail::tvec3<T> Pi0 = floor(P); // Integer part for indexing detail::tvec3<T> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = mod289(Pi0); Pi1 = mod289(Pi1); detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation detail::tvec3<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); detail::tvec4<T> iy = detail::tvec4<T>(detail::tvec2<T>(Pi0.y), detail::tvec2<T>(Pi1.y)); detail::tvec4<T> iz0(Pi0.z); detail::tvec4<T> iz1(Pi1.z);
detail::tvec4<T> ixy = permute(permute(ix) + iy); detail::tvec4<T> ixy0 = permute(ixy + iz0); detail::tvec4<T> ixy1 = permute(ixy + iz1);
detail::tvec4<T> gx0 = ixy0 * T(1.0 / 7.0); detail::tvec4<T> gy0 = fract(floor(gx0) * T(1.0 / 7.0)) - T(0.5); gx0 = fract(gx0); detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0.0)); gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); gy0 -= sz0 * (step(T(0), gy0) - T(0.5));
detail::tvec4<T> gx1 = ixy1 * T(1.0 / 7.0); detail::tvec4<T> gy1 = fract(floor(gx1) * T(1.0 / 7.0)) - T(0.5); gx1 = fract(gx1); detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); gy1 -= sz1 * (step(T(0), gy1) - T(0.5));
detail::tvec3<T> g000(gx0.x, gy0.x, gz0.x); detail::tvec3<T> g100(gx0.y, gy0.y, gz0.y); detail::tvec3<T> g010(gx0.z, gy0.z, gz0.z); detail::tvec3<T> g110(gx0.w, gy0.w, gz0.w); detail::tvec3<T> g001(gx1.x, gy1.x, gz1.x); detail::tvec3<T> g101(gx1.y, gy1.y, gz1.y); detail::tvec3<T> g011(gx1.z, gy1.z, gz1.z); detail::tvec3<T> g111(gx1.w, gy1.w, gz1.w);
detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); g001 *= norm1.x; g011 *= norm1.y; g101 *= norm1.z; g111 *= norm1.w;
T n000 = dot(g000, Pf0); T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1);
detail::tvec3<T> fade_xyz = fade(Pf0); detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); detail::tvec2<T> n_yz = mix(detail::tvec2<T>(n_z.x, n_z.y), detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); return T(2.2) * n_xyz; } /* // Classic Perlin noise template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P) { detail::tvec3<T> Pi0 = floor(P); // Integer part for indexing detail::tvec3<T> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = mod(Pi0, T(289)); Pi1 = mod(Pi1, T(289)); detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation detail::tvec3<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); detail::tvec4<T> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); detail::tvec4<T> iz0(Pi0.z); detail::tvec4<T> iz1(Pi1.z);
detail::tvec4<T> ixy = permute(permute(ix) + iy); detail::tvec4<T> ixy0 = permute(ixy + iz0); detail::tvec4<T> ixy1 = permute(ixy + iz1);
detail::tvec4<T> gx0 = ixy0 / T(7); detail::tvec4<T> gy0 = fract(floor(gx0) / T(7)) - T(0.5); gx0 = fract(gx0); detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0.0)); gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); gy0 -= sz0 * (step(0.0, gy0) - T(0.5));
detail::tvec4<T> gx1 = ixy1 / T(7); detail::tvec4<T> gy1 = fract(floor(gx1) / T(7)) - T(0.5); gx1 = fract(gx1); detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); gy1 -= sz1 * (step(T(0), gy1) - T(0.5));
detail::tvec3<T> g000(gx0.x, gy0.x, gz0.x); detail::tvec3<T> g100(gx0.y, gy0.y, gz0.y); detail::tvec3<T> g010(gx0.z, gy0.z, gz0.z); detail::tvec3<T> g110(gx0.w, gy0.w, gz0.w); detail::tvec3<T> g001(gx1.x, gy1.x, gz1.x); detail::tvec3<T> g101(gx1.y, gy1.y, gz1.y); detail::tvec3<T> g011(gx1.z, gy1.z, gz1.z); detail::tvec3<T> g111(gx1.w, gy1.w, gz1.w);
detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); g001 *= norm1.x; g011 *= norm1.y; g101 *= norm1.z; g111 *= norm1.w;
T n000 = dot(g000, Pf0); T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1);
detail::tvec3<T> fade_xyz = fade(Pf0); detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); detail::tvec2<T> n_yz = mix( detail::tvec2<T>(n_z.x, n_z.y), detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); return T(2.2) * n_xyz; } */ // Classic Perlin noise template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T> const & P) { detail::tvec4<T> Pi0 = floor(P); // Integer part for indexing detail::tvec4<T> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = mod(Pi0, T(289)); Pi1 = mod(Pi1, T(289)); detail::tvec4<T> Pf0 = fract(P); // Fractional part for interpolation detail::tvec4<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 detail::tvec4<T> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); detail::tvec4<T> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); detail::tvec4<T> iz0(Pi0.z); detail::tvec4<T> iz1(Pi1.z); detail::tvec4<T> iw0(Pi0.w); detail::tvec4<T> iw1(Pi1.w);
detail::tvec4<T> ixy = permute(permute(ix) + iy); detail::tvec4<T> ixy0 = permute(ixy + iz0); detail::tvec4<T> ixy1 = permute(ixy + iz1); detail::tvec4<T> ixy00 = permute(ixy0 + iw0); detail::tvec4<T> ixy01 = permute(ixy0 + iw1); detail::tvec4<T> ixy10 = permute(ixy1 + iw0); detail::tvec4<T> ixy11 = permute(ixy1 + iw1);
detail::tvec4<T> gx00 = ixy00 / T(7); detail::tvec4<T> gy00 = floor(gx00) / T(7); detail::tvec4<T> gz00 = floor(gy00) / T(6); gx00 = fract(gx00) - T(0.5); gy00 = fract(gy00) - T(0.5); gz00 = fract(gz00) - T(0.5); detail::tvec4<T> gw00 = detail::tvec4<T>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); detail::tvec4<T> sw00 = step(gw00, detail::tvec4<T>(0.0)); gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); gy00 -= sw00 * (step(T(0), gy00) - T(0.5));
detail::tvec4<T> gx01 = ixy01 / T(7); detail::tvec4<T> gy01 = floor(gx01) / T(7); detail::tvec4<T> gz01 = floor(gy01) / T(6); gx01 = fract(gx01) - T(0.5); gy01 = fract(gy01) - T(0.5); gz01 = fract(gz01) - T(0.5); detail::tvec4<T> gw01 = detail::tvec4<T>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); detail::tvec4<T> sw01 = step(gw01, detail::tvec4<T>(0.0)); gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); gy01 -= sw01 * (step(T(0), gy01) - T(0.5));
detail::tvec4<T> gx10 = ixy10 / T(7); detail::tvec4<T> gy10 = floor(gx10) / T(7); detail::tvec4<T> gz10 = floor(gy10) / T(6); gx10 = fract(gx10) - T(0.5); gy10 = fract(gy10) - T(0.5); gz10 = fract(gz10) - T(0.5); detail::tvec4<T> gw10 = detail::tvec4<T>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); detail::tvec4<T> sw10 = step(gw10, detail::tvec4<T>(0)); gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); gy10 -= sw10 * (step(T(0), gy10) - T(0.5));
detail::tvec4<T> gx11 = ixy11 / T(7); detail::tvec4<T> gy11 = floor(gx11) / T(7); detail::tvec4<T> gz11 = floor(gy11) / T(6); gx11 = fract(gx11) - T(0.5); gy11 = fract(gy11) - T(0.5); gz11 = fract(gz11) - T(0.5); detail::tvec4<T> gw11 = detail::tvec4<T>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); detail::tvec4<T> sw11 = step(gw11, detail::tvec4<T>(0.0)); gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); gy11 -= sw11 * (step(T(0), gy11) - T(0.5));
detail::tvec4<T> g0000(gx00.x, gy00.x, gz00.x, gw00.x); detail::tvec4<T> g1000(gx00.y, gy00.y, gz00.y, gw00.y); detail::tvec4<T> g0100(gx00.z, gy00.z, gz00.z, gw00.z); detail::tvec4<T> g1100(gx00.w, gy00.w, gz00.w, gw00.w); detail::tvec4<T> g0010(gx10.x, gy10.x, gz10.x, gw10.x); detail::tvec4<T> g1010(gx10.y, gy10.y, gz10.y, gw10.y); detail::tvec4<T> g0110(gx10.z, gy10.z, gz10.z, gw10.z); detail::tvec4<T> g1110(gx10.w, gy10.w, gz10.w, gw10.w); detail::tvec4<T> g0001(gx01.x, gy01.x, gz01.x, gw01.x); detail::tvec4<T> g1001(gx01.y, gy01.y, gz01.y, gw01.y); detail::tvec4<T> g0101(gx01.z, gy01.z, gz01.z, gw01.z); detail::tvec4<T> g1101(gx01.w, gy01.w, gz01.w, gw01.w); detail::tvec4<T> g0011(gx11.x, gy11.x, gz11.x, gw11.x); detail::tvec4<T> g1011(gx11.y, gy11.y, gz11.y, gw11.y); detail::tvec4<T> g0111(gx11.z, gy11.z, gz11.z, gw11.z); detail::tvec4<T> g1111(gx11.w, gy11.w, gz11.w, gw11.w);
detail::tvec4<T> norm00 = taylorInvSqrt(detail::tvec4<T>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); g0000 *= norm00.x; g0100 *= norm00.y; g1000 *= norm00.z; g1100 *= norm00.w;
detail::tvec4<T> norm01 = taylorInvSqrt(detail::tvec4<T>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); g0001 *= norm01.x; g0101 *= norm01.y; g1001 *= norm01.z; g1101 *= norm01.w;
detail::tvec4<T> norm10 = taylorInvSqrt(detail::tvec4<T>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); g0010 *= norm10.x; g0110 *= norm10.y; g1010 *= norm10.z; g1110 *= norm10.w;
detail::tvec4<T> norm11 = taylorInvSqrt(detail::tvec4<T>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); g0011 *= norm11.x; g0111 *= norm11.y; g1011 *= norm11.z; g1111 *= norm11.w;
T n0000 = dot(g0000, Pf0); T n1000 = dot(g1000, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); T n0100 = dot(g0100, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); T n1100 = dot(g1100, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); T n0010 = dot(g0010, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); T n1010 = dot(g1010, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); T n0110 = dot(g0110, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); T n1110 = dot(g1110, detail::tvec4<T>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); T n0001 = dot(g0001, detail::tvec4<T>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); T n1001 = dot(g1001, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); T n0101 = dot(g0101, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); T n1101 = dot(g1101, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); T n0011 = dot(g0011, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); T n1011 = dot(g1011, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); T n0111 = dot(g0111, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); T n1111 = dot(g1111, Pf1);
detail::tvec4<T> fade_xyzw = fade(Pf0); detail::tvec4<T> n_0w = mix(detail::tvec4<T>(n0000, n1000, n0100, n1100), detail::tvec4<T>(n0001, n1001, n0101, n1101), fade_xyzw.w); detail::tvec4<T> n_1w = mix(detail::tvec4<T>(n0010, n1010, n0110, n1110), detail::tvec4<T>(n0011, n1011, n0111, n1111), fade_xyzw.w); detail::tvec4<T> n_zw = mix(n_0w, n_1w, fade_xyzw.z); detail::tvec2<T> n_yzw = mix(detail::tvec2<T>(n_zw.x, n_zw.y), detail::tvec2<T>(n_zw.z, n_zw.w), fade_xyzw.y); T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); return T(2.2) * n_xyzw; }
// Classic Perlin noise, periodic variant template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec2<T> const & P, detail::tvec2<T> const & rep) { detail::tvec4<T> Pi = floor(detail::tvec4<T>(P.x, P.y, P.x, P.y)) + detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); detail::tvec4<T> Pf = fract(detail::tvec4<T>(P.x, P.y, P.x, P.y)) - detail::tvec4<T>(0.0, 0.0, 1.0, 1.0); Pi = mod(Pi, detail::tvec4<T>(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation detail::tvec4<T> ix(Pi.x, Pi.z, Pi.x, Pi.z); detail::tvec4<T> iy(Pi.y, Pi.y, Pi.w, Pi.w); detail::tvec4<T> fx(Pf.x, Pf.z, Pf.x, Pf.z); detail::tvec4<T> fy(Pf.y, Pf.y, Pf.w, Pf.w);
detail::tvec4<T> i = permute(permute(ix) + iy);
detail::tvec4<T> gx = T(2) * fract(i / T(41)) - T(1); detail::tvec4<T> gy = abs(gx) - T(0.5); detail::tvec4<T> tx = floor(gx + T(0.5)); gx = gx - tx;
detail::tvec2<T> g00(gx.x, gy.x); detail::tvec2<T> g10(gx.y, gy.y); detail::tvec2<T> g01(gx.z, gy.z); detail::tvec2<T> g11(gx.w, gy.w);
detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(g00, g00), dot(g01, g01), dot(g10, g10), dot(g11, g11))); g00 *= norm.x; g01 *= norm.y; g10 *= norm.z; g11 *= norm.w;
T n00 = dot(g00, detail::tvec2<T>(fx.x, fy.x)); T n10 = dot(g10, detail::tvec2<T>(fx.y, fy.y)); T n01 = dot(g01, detail::tvec2<T>(fx.z, fy.z)); T n11 = dot(g11, detail::tvec2<T>(fx.w, fy.w));
detail::tvec2<T> fade_xy = fade(detail::tvec2<T>(Pf.x, Pf.y)); detail::tvec2<T> n_x = mix(detail::tvec2<T>(n00, n01), detail::tvec2<T>(n10, n11), fade_xy.x); T n_xy = mix(n_x.x, n_x.y, fade_xy.y); return T(2.3) * n_xy; }
// Classic Perlin noise, periodic variant template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec3<T> const & P, detail::tvec3<T> const & rep) { detail::tvec3<T> Pi0 = mod(floor(P), rep); // Integer part, modulo period detail::tvec3<T> Pi1 = mod(Pi0 + detail::tvec3<T>(1.0), rep); // Integer part + 1, mod period Pi0 = mod(Pi0, T(289)); Pi1 = mod(Pi1, T(289)); detail::tvec3<T> Pf0 = fract(P); // Fractional part for interpolation detail::tvec3<T> Pf1 = Pf0 - detail::tvec3<T>(1.0); // Fractional part - 1.0 detail::tvec4<T> ix = detail::tvec4<T>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); detail::tvec4<T> iy = detail::tvec4<T>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); detail::tvec4<T> iz0(Pi0.z); detail::tvec4<T> iz1(Pi1.z);
detail::tvec4<T> ixy = permute(permute(ix) + iy); detail::tvec4<T> ixy0 = permute(ixy + iz0); detail::tvec4<T> ixy1 = permute(ixy + iz1);
detail::tvec4<T> gx0 = ixy0 / T(7); detail::tvec4<T> gy0 = fract(floor(gx0) / T(7)) - T(0.5); gx0 = fract(gx0); detail::tvec4<T> gz0 = detail::tvec4<T>(0.5) - abs(gx0) - abs(gy0); detail::tvec4<T> sz0 = step(gz0, detail::tvec4<T>(0)); gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); gy0 -= sz0 * (step(0.0, gy0) - T(0.5));
detail::tvec4<T> gx1 = ixy1 / T(7); detail::tvec4<T> gy1 = fract(floor(gx1) / T(7)) - T(0.5); gx1 = fract(gx1); detail::tvec4<T> gz1 = detail::tvec4<T>(0.5) - abs(gx1) - abs(gy1); detail::tvec4<T> sz1 = step(gz1, detail::tvec4<T>(0.0)); gx1 -= sz1 * (step(0.0, gx1) - T(0.5)); gy1 -= sz1 * (step(0.0, gy1) - T(0.5));
detail::tvec3<T> g000 = detail::tvec3<T>(gx0.x, gy0.x, gz0.x); detail::tvec3<T> g100 = detail::tvec3<T>(gx0.y, gy0.y, gz0.y); detail::tvec3<T> g010 = detail::tvec3<T>(gx0.z, gy0.z, gz0.z); detail::tvec3<T> g110 = detail::tvec3<T>(gx0.w, gy0.w, gz0.w); detail::tvec3<T> g001 = detail::tvec3<T>(gx1.x, gy1.x, gz1.x); detail::tvec3<T> g101 = detail::tvec3<T>(gx1.y, gy1.y, gz1.y); detail::tvec3<T> g011 = detail::tvec3<T>(gx1.z, gy1.z, gz1.z); detail::tvec3<T> g111 = detail::tvec3<T>(gx1.w, gy1.w, gz1.w);
detail::tvec4<T> norm0 = taylorInvSqrt(detail::tvec4<T>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; detail::tvec4<T> norm1 = taylorInvSqrt(detail::tvec4<T>(dot(g001, g001), dot(g011, g011), dot(g101, g101), dot(g111, g111))); g001 *= norm1.x; g011 *= norm1.y; g101 *= norm1.z; g111 *= norm1.w;
T n000 = dot(g000, Pf0); T n100 = dot(g100, detail::tvec3<T>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, detail::tvec3<T>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, detail::tvec3<T>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, detail::tvec3<T>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, detail::tvec3<T>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, detail::tvec3<T>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1);
detail::tvec3<T> fade_xyz = fade(Pf0); detail::tvec4<T> n_z = mix(detail::tvec4<T>(n000, n100, n010, n110), detail::tvec4<T>(n001, n101, n011, n111), fade_xyz.z); detail::tvec2<T> n_yz = mix(detail::tvec2<T>(n_z.x, n_z.y), detail::tvec2<T>(n_z.z, n_z.w), fade_xyz.y); T n_xyz = mix(n_yz.x, n_yz.y, fade_xyz.x); return T(2.2) * n_xyz; }
// Classic Perlin noise, periodic version template <typename T> GLM_FUNC_QUALIFIER T perlin(detail::tvec4<T> const & P, detail::tvec4<T> const & rep) { detail::tvec4<T> Pi0 = mod(floor(P), rep); // Integer part modulo rep detail::tvec4<T> Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep detail::tvec4<T> Pf0 = fract(P); // Fractional part for interpolation detail::tvec4<T> Pf1 = Pf0 - T(1); // Fractional part - 1.0 detail::tvec4<T> ix = detail::tvec4<T>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); detail::tvec4<T> iy = detail::tvec4<T>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); detail::tvec4<T> iz0(Pi0.z); detail::tvec4<T> iz1(Pi1.z); detail::tvec4<T> iw0(Pi0.w); detail::tvec4<T> iw1(Pi1.w);
detail::tvec4<T> ixy = permute(permute(ix) + iy); detail::tvec4<T> ixy0 = permute(ixy + iz0); detail::tvec4<T> ixy1 = permute(ixy + iz1); detail::tvec4<T> ixy00 = permute(ixy0 + iw0); detail::tvec4<T> ixy01 = permute(ixy0 + iw1); detail::tvec4<T> ixy10 = permute(ixy1 + iw0); detail::tvec4<T> ixy11 = permute(ixy1 + iw1);
detail::tvec4<T> gx00 = ixy00 / T(7); detail::tvec4<T> gy00 = floor(gx00) / T(7); detail::tvec4<T> gz00 = floor(gy00) / T(6); gx00 = fract(gx00) - T(0.5); gy00 = fract(gy00) - T(0.5); gz00 = fract(gz00) - T(0.5); detail::tvec4<T> gw00 = detail::tvec4<T>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); detail::tvec4<T> sw00 = step(gw00, detail::tvec4<T>(0)); gx00 -= sw00 * (step(0.0, gx00) - T(0.5)); gy00 -= sw00 * (step(0.0, gy00) - T(0.5));
detail::tvec4<T> gx01 = ixy01 / T(7); detail::tvec4<T> gy01 = floor(gx01) / T(7); detail::tvec4<T> gz01 = floor(gy01) / T(6); gx01 = fract(gx01) - T(0.5); gy01 = fract(gy01) - T(0.5); gz01 = fract(gz01) - T(0.5); detail::tvec4<T> gw01 = detail::tvec4<T>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); detail::tvec4<T> sw01 = step(gw01, detail::tvec4<T>(0.0)); gx01 -= sw01 * (step(0.0, gx01) - T(0.5)); gy01 -= sw01 * (step(0.0, gy01) - T(0.5));
detail::tvec4<T> gx10 = ixy10 / T(7); detail::tvec4<T> gy10 = floor(gx10) / T(7); detail::tvec4<T> gz10 = floor(gy10) / T(6); gx10 = fract(gx10) - T(0.5); gy10 = fract(gy10) - T(0.5); gz10 = fract(gz10) - T(0.5); detail::tvec4<T> gw10 = detail::tvec4<T>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); detail::tvec4<T> sw10 = step(gw10, detail::tvec4<T>(0.0)); gx10 -= sw10 * (step(0.0, gx10) - T(0.5)); gy10 -= sw10 * (step(0.0, gy10) - T(0.5));
detail::tvec4<T> gx11 = ixy11 / T(7); detail::tvec4<T> gy11 = floor(gx11) / T(7); detail::tvec4<T> gz11 = floor(gy11) / T(6); gx11 = fract(gx11) - T(0.5); gy11 = fract(gy11) - T(0.5); gz11 = fract(gz11) - T(0.5); detail::tvec4<T> gw11 = detail::tvec4<T>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); detail::tvec4<T> sw11 = step(gw11, detail::tvec4<T>(0.0)); gx11 -= sw11 * (step(0.0, gx11) - T(0.5)); gy11 -= sw11 * (step(0.0, gy11) - T(0.5));
detail::tvec4<T> g0000(gx00.x, gy00.x, gz00.x, gw00.x); detail::tvec4<T> g1000(gx00.y, gy00.y, gz00.y, gw00.y); detail::tvec4<T> g0100(gx00.z, gy00.z, gz00.z, gw00.z); detail::tvec4<T> g1100(gx00.w, gy00.w, gz00.w, gw00.w); detail::tvec4<T> g0010(gx10.x, gy10.x, gz10.x, gw10.x); detail::tvec4<T> g1010(gx10.y, gy10.y, gz10.y, gw10.y); detail::tvec4<T> g0110(gx10.z, gy10.z, gz10.z, gw10.z); detail::tvec4<T> g1110(gx10.w, gy10.w, gz10.w, gw10.w); detail::tvec4<T> g0001(gx01.x, gy01.x, gz01.x, gw01.x); detail::tvec4<T> g1001(gx01.y, gy01.y, gz01.y, gw01.y); detail::tvec4<T> g0101(gx01.z, gy01.z, gz01.z, gw01.z); detail::tvec4<T> g1101(gx01.w, gy01.w, gz01.w, gw01.w); detail::tvec4<T> g0011(gx11.x, gy11.x, gz11.x, gw11.x); detail::tvec4<T> g1011(gx11.y, gy11.y, gz11.y, gw11.y); detail::tvec4<T> g0111(gx11.z, gy11.z, gz11.z, gw11.z); detail::tvec4<T> g1111(gx11.w, gy11.w, gz11.w, gw11.w);
detail::tvec4<T> norm00 = taylorInvSqrt(detail::tvec4<T>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); g0000 *= norm00.x; g0100 *= norm00.y; g1000 *= norm00.z; g1100 *= norm00.w;
detail::tvec4<T> norm01 = taylorInvSqrt(detail::tvec4<T>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); g0001 *= norm01.x; g0101 *= norm01.y; g1001 *= norm01.z; g1101 *= norm01.w;
detail::tvec4<T> norm10 = taylorInvSqrt(detail::tvec4<T>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); g0010 *= norm10.x; g0110 *= norm10.y; g1010 *= norm10.z; g1110 *= norm10.w;
detail::tvec4<T> norm11 = taylorInvSqrt(detail::tvec4<T>(dot(g0011, g0011), dot(g0111, g0111), dot(g1011, g1011), dot(g1111, g1111))); g0011 *= norm11.x; g0111 *= norm11.y; g1011 *= norm11.z; g1111 *= norm11.w;
T n0000 = dot(g0000, Pf0); T n1000 = dot(g1000, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); T n0100 = dot(g0100, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); T n1100 = dot(g1100, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); T n0010 = dot(g0010, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); T n1010 = dot(g1010, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); T n0110 = dot(g0110, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); T n1110 = dot(g1110, detail::tvec4<T>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); T n0001 = dot(g0001, detail::tvec4<T>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); T n1001 = dot(g1001, detail::tvec4<T>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); T n0101 = dot(g0101, detail::tvec4<T>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); T n1101 = dot(g1101, detail::tvec4<T>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); T n0011 = dot(g0011, detail::tvec4<T>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); T n1011 = dot(g1011, detail::tvec4<T>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); T n0111 = dot(g0111, detail::tvec4<T>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); T n1111 = dot(g1111, Pf1);
detail::tvec4<T> fade_xyzw = fade(Pf0); detail::tvec4<T> n_0w = mix(detail::tvec4<T>(n0000, n1000, n0100, n1100), detail::tvec4<T>(n0001, n1001, n0101, n1101), fade_xyzw.w); detail::tvec4<T> n_1w = mix(detail::tvec4<T>(n0010, n1010, n0110, n1110), detail::tvec4<T>(n0011, n1011, n0111, n1111), fade_xyzw.w); detail::tvec4<T> n_zw = mix(n_0w, n_1w, fade_xyzw.z); detail::tvec2<T> n_yzw = mix(detail::tvec2<T>(n_zw.x, n_zw.y), detail::tvec2<T>(n_zw.z, n_zw.w), fade_xyzw.y); T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); return T(2.2) * n_xyzw; }
template <typename T> GLM_FUNC_QUALIFIER T simplex(glm::detail::tvec2<T> const & v) { detail::tvec4<T> const C = detail::tvec4<T>( T( 0.211324865405187), // (3.0 - sqrt(3.0)) / 6.0 T( 0.366025403784439), // 0.5 * (sqrt(3.0) - 1.0) T(-0.577350269189626), // -1.0 + 2.0 * C.x T( 0.024390243902439)); // 1.0 / 41.0
// First corner detail::tvec2<T> i = floor(v + dot(v, detail::tvec2<T>(C[1]))); detail::tvec2<T> x0 = v - i + dot(i, detail::tvec2<T>(C[0]));
// Other corners //i1.x = step( x0.y, x0.x ); // x0.x > x0.y ? 1.0 : 0.0 //i1.y = 1.0 - i1.x; detail::tvec2<T> i1 = (x0.x > x0.y) ? detail::tvec2<T>(1, 0) : detail::tvec2<T>(0, 1); // x0 = x0 - 0.0 + 0.0 * C.xx ; // x1 = x0 - i1 + 1.0 * C.xx ; // x2 = x0 - 1.0 + 2.0 * C.xx ; detail::tvec4<T> x12 = detail::tvec4<T>(x0.x, x0.y, x0.x, x0.y) + detail::tvec4<T>(C.x, C.x, C.z, C.z); x12 = detail::tvec4<T>(detail::tvec2<T>(x12) - i1, x12.z, x12.w);
// Permutations i = mod(i, T(289)); // Avoid truncation effects in permutation detail::tvec3<T> p = permute( permute(i.y + detail::tvec3<T>(T(0), i1.y, T(1))) + i.x + detail::tvec3<T>(T(0), i1.x, T(1)));
detail::tvec3<T> m = max(T(0.5) - detail::tvec3<T>( dot(x0, x0), dot(detail::tvec2<T>(x12.x, x12.y), detail::tvec2<T>(x12.x, x12.y)), dot(detail::tvec2<T>(x12.z, x12.w), detail::tvec2<T>(x12.z, x12.w))), T(0)); m = m * m ; m = m * m ;
// Gradients: 41 points uniformly over a line, mapped onto a diamond. // The ring size 17*17 = 289 is close to a multiple of 41 (41*7 = 287)
detail::tvec3<T> x = T(2) * fract(p * C.w) - T(1); detail::tvec3<T> h = abs(x) - T(0.5); detail::tvec3<T> ox = floor(x + T(0.5)); detail::tvec3<T> a0 = x - ox;
// Normalise gradients implicitly by scaling m // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h ); m *= T(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h);
// Compute final noise value at P detail::tvec3<T> g; g.x = a0.x * x0.x + h.x * x0.y; //g.yz = a0.yz * x12.xz + h.yz * x12.yw; g.y = a0.y * x12.x + h.y * x12.y; g.z = a0.z * x12.z + h.z * x12.w; return T(130) * dot(m, g); }
template <typename T> GLM_FUNC_QUALIFIER T simplex(detail::tvec3<T> const & v) { detail::tvec2<T> const C(1.0 / 6.0, 1.0 / 3.0); detail::tvec4<T> const D(0.0, 0.5, 1.0, 2.0);
// First corner detail::tvec3<T> i(floor(v + dot(v, detail::tvec3<T>(C.y)))); detail::tvec3<T> x0(v - i + dot(i, detail::tvec3<T>(C.x)));
// Other corners detail::tvec3<T> g(step(detail::tvec3<T>(x0.y, x0.z, x0.x), x0)); detail::tvec3<T> l(T(1) - g); detail::tvec3<T> i1(min(g, detail::tvec3<T>(l.z, l.x, l.y))); detail::tvec3<T> i2(max(g, detail::tvec3<T>(l.z, l.x, l.y)));
// x0 = x0 - 0.0 + 0.0 * C.xxx; // x1 = x0 - i1 + 1.0 * C.xxx; // x2 = x0 - i2 + 2.0 * C.xxx; // x3 = x0 - 1.0 + 3.0 * C.xxx; detail::tvec3<T> x1(x0 - i1 + C.x); detail::tvec3<T> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y detail::tvec3<T> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y
// Permutations i = mod289(i); detail::tvec4<T> p(permute(permute(permute( i.z + detail::tvec4<T>(T(0), i1.z, i2.z, T(1))) + i.y + detail::tvec4<T>(T(0), i1.y, i2.y, T(1))) + i.x + detail::tvec4<T>(T(0), i1.x, i2.x, T(1))));
// Gradients: 7x7 points over a square, mapped onto an octahedron. // The ring size 17*17 = 289 is close to a multiple of 49 (49*6 = 294) T n_ = T(0.142857142857); // 1.0/7.0 detail::tvec3<T> ns(n_ * detail::tvec3<T>(D.w, D.y, D.z) - detail::tvec3<T>(D.x, D.z, D.x));
detail::tvec4<T> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7)
detail::tvec4<T> x_(floor(j * ns.z)); detail::tvec4<T> y_(floor(j - T(7) * x_)); // mod(j,N)
detail::tvec4<T> x(x_ * ns.x + ns.y); detail::tvec4<T> y(y_ * ns.x + ns.y); detail::tvec4<T> h(T(1) - abs(x) - abs(y));
detail::tvec4<T> b0(x.x, x.y, y.x, y.y); detail::tvec4<T> b1(x.z, x.w, y.z, y.w);
// vec4 s0 = vec4(lessThan(b0,0.0))*2.0 - 1.0; // vec4 s1 = vec4(lessThan(b1,0.0))*2.0 - 1.0; detail::tvec4<T> s0(floor(b0) * T(2) + T(1)); detail::tvec4<T> s1(floor(b1) * T(2) + T(1)); detail::tvec4<T> sh(-step(h, detail::tvec4<T>(0.0)));
detail::tvec4<T> a0 = detail::tvec4<T>(b0.x, b0.z, b0.y, b0.w) + detail::tvec4<T>(s0.x, s0.z, s0.y, s0.w) * detail::tvec4<T>(sh.x, sh.x, sh.y, sh.y); detail::tvec4<T> a1 = detail::tvec4<T>(b1.x, b1.z, b1.y, b1.w) + detail::tvec4<T>(s1.x, s1.z, s1.y, s1.w) * detail::tvec4<T>(sh.z, sh.z, sh.w, sh.w);
detail::tvec3<T> p0(a0.x, a0.y, h.x); detail::tvec3<T> p1(a0.z, a0.w, h.y); detail::tvec3<T> p2(a1.x, a1.y, h.z); detail::tvec3<T> p3(a1.z, a1.w, h.w);
// Normalise gradients detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); p0 *= norm.x; p1 *= norm.y; p2 *= norm.z; p3 *= norm.w;
// Mix final noise value detail::tvec4<T> m = max(T(0.6) - detail::tvec4<T>(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), T(0)); m = m * m; return T(42) * dot(m * m, detail::tvec4<T>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); }
template <typename T> GLM_FUNC_QUALIFIER T simplex(detail::tvec4<T> const & v) { detail::tvec4<T> const C( 0.138196601125011, // (5 - sqrt(5))/20 G4 0.276393202250021, // 2 * G4 0.414589803375032, // 3 * G4 -0.447213595499958); // -1 + 4 * G4
// (sqrt(5) - 1)/4 = F4, used once below T const F4 = T(0.309016994374947451);
// First corner detail::tvec4<T> i = floor(v + dot(v, vec4(F4))); detail::tvec4<T> x0 = v - i + dot(i, vec4(C.x));
// Other corners
// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) detail::tvec4<T> i0; detail::tvec3<T> isX = step(detail::tvec3<T>(x0.y, x0.z, x0.w), detail::tvec3<T>(x0.x)); detail::tvec3<T> isYZ = step(detail::tvec3<T>(x0.z, x0.w, x0.w), detail::tvec3<T>(x0.y, x0.y, x0.z)); // i0.x = dot(isX, vec3(1.0)); //i0.x = isX.x + isX.y + isX.z; //i0.yzw = T(1) - isX; i0 = detail::tvec4<T>(isX.x + isX.y + isX.z, T(1) - isX); // i0.y += dot(isYZ.xy, vec2(1.0)); i0.y += isYZ.x + isYZ.y; //i0.zw += 1.0 - detail::tvec2<T>(isYZ.x, isYZ.y); i0.z += T(1) - isYZ.x; i0.w += T(1) - isYZ.y; i0.z += isYZ.z; i0.w += T(1) - isYZ.z;
// i0 now contains the unique values 0,1,2,3 in each channel detail::tvec4<T> i3 = clamp(i0, 0.0, 1.0); detail::tvec4<T> i2 = clamp(i0 - 1.0, 0.0, 1.0); detail::tvec4<T> i1 = clamp(i0 - 2.0, 0.0, 1.0);
// x0 = x0 - 0.0 + 0.0 * C.xxxx // x1 = x0 - i1 + 0.0 * C.xxxx // x2 = x0 - i2 + 0.0 * C.xxxx // x3 = x0 - i3 + 0.0 * C.xxxx // x4 = x0 - 1.0 + 4.0 * C.xxxx detail::tvec4<T> x1 = x0 - i1 + C.x; detail::tvec4<T> x2 = x0 - i2 + C.y; detail::tvec4<T> x3 = x0 - i3 + C.z; detail::tvec4<T> x4 = x0 + C.w;
// Permutations i = mod(i, T(289)); T j0 = permute(permute(permute(permute(i.w) + i.z) + i.y) + i.x); detail::tvec4<T> j1 = permute(permute(permute(permute( i.w + detail::tvec4<T>(i1.w, i2.w, i3.w, T(1))) + i.z + detail::tvec4<T>(i1.z, i2.z, i3.z, T(1))) + i.y + detail::tvec4<T>(i1.y, i2.y, i3.y, T(1))) + i.x + detail::tvec4<T>(i1.x, i2.x, i3.x, T(1)));
// Gradients: 7x7x6 points over a cube, mapped onto a 4-cross polytope // 7*7*6 = 294, which is close to the ring size 17*17 = 289. detail::tvec4<T> ip = detail::tvec4<T>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0));
detail::tvec4<T> p0 = grad4(j0, ip); detail::tvec4<T> p1 = grad4(j1.x, ip); detail::tvec4<T> p2 = grad4(j1.y, ip); detail::tvec4<T> p3 = grad4(j1.z, ip); detail::tvec4<T> p4 = grad4(j1.w, ip);
// Normalise gradients detail::tvec4<T> norm = taylorInvSqrt(detail::tvec4<T>(dot(p0, p0), dot(p1, p1), dot(p2, p2), dot(p3, p3))); p0 *= norm.x; p1 *= norm.y; p2 *= norm.z; p3 *= norm.w; p4 *= taylorInvSqrt(dot(p4, p4));
// Mix contributions from the five corners detail::tvec3<T> m0 = max(T(0.6) - detail::tvec3<T>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), T(0)); detail::tvec2<T> m1 = max(T(0.6) - detail::tvec2<T>(dot(x3, x3), dot(x4, x4) ), T(0)); m0 = m0 * m0; m1 = m1 * m1; return T(49) * (dot(m0 * m0, detail::tvec3<T>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + dot(m1 * m1, detail::tvec2<T>(dot(p3, x3), dot(p4, x4)))); }}//namespace glm
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