/// @ref gtc_noise /// @file glm/gtc/noise.inl /// // 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{ namespace gtc { template <typename T, precision P> GLM_FUNC_QUALIFIER tvec4<T, P> grad4(T const & j, tvec4<T, P> const & ip) { tvec3<T, P> pXYZ = floor(fract(tvec3<T, P>(j) * tvec3<T, P>(ip)) * T(7)) * ip[2] - T(1); T pW = static_cast<T>(1.5) - dot(abs(pXYZ), tvec3<T, P>(1)); tvec4<T, P> s = tvec4<T, P>(lessThan(tvec4<T, P>(pXYZ, pW), tvec4<T, P>(0.0))); pXYZ = pXYZ + (tvec3<T, P>(s) * T(2) - T(1)) * s.w; return tvec4<T, P>(pXYZ, pW); } }//namespace gtc // Classic Perlin noise template <typename T, precision P> GLM_FUNC_QUALIFIER T perlin(tvec2<T, P> const & Position) { tvec4<T, P> Pi = glm::floor(tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) + tvec4<T, P>(0.0, 0.0, 1.0, 1.0); tvec4<T, P> Pf = glm::fract(tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) - tvec4<T, P>(0.0, 0.0, 1.0, 1.0); Pi = mod(Pi, tvec4<T, P>(289)); // To avoid truncation effects in permutation tvec4<T, P> ix(Pi.x, Pi.z, Pi.x, Pi.z); tvec4<T, P> iy(Pi.y, Pi.y, Pi.w, Pi.w); tvec4<T, P> fx(Pf.x, Pf.z, Pf.x, Pf.z); tvec4<T, P> fy(Pf.y, Pf.y, Pf.w, Pf.w); tvec4<T, P> i = detail::permute(detail::permute(ix) + iy); tvec4<T, P> gx = static_cast<T>(2) * glm::fract(i / T(41)) - T(1); tvec4<T, P> gy = glm::abs(gx) - T(0.5); tvec4<T, P> tx = glm::floor(gx + T(0.5)); gx = gx - tx; tvec2<T, P> g00(gx.x, gy.x); tvec2<T, P> g10(gx.y, gy.y); tvec2<T, P> g01(gx.z, gy.z); tvec2<T, P> g11(gx.w, gy.w); tvec4<T, P> norm = detail::taylorInvSqrt(tvec4<T, P>(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, tvec2<T, P>(fx.x, fy.x)); T n10 = dot(g10, tvec2<T, P>(fx.y, fy.y)); T n01 = dot(g01, tvec2<T, P>(fx.z, fy.z)); T n11 = dot(g11, tvec2<T, P>(fx.w, fy.w)); tvec2<T, P> fade_xy = detail::fade(tvec2<T, P>(Pf.x, Pf.y)); tvec2<T, P> n_x = mix(tvec2<T, P>(n00, n01), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec3<T, P> const & Position) { tvec3<T, P> Pi0 = floor(Position); // Integer part for indexing tvec3<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = detail::mod289(Pi0); Pi1 = detail::mod289(Pi1); tvec3<T, P> Pf0 = fract(Position); // Fractional part for interpolation tvec3<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); tvec4<T, P> iy = tvec4<T, P>(tvec2<T, P>(Pi0.y), tvec2<T, P>(Pi1.y)); tvec4<T, P> iz0(Pi0.z); tvec4<T, P> iz1(Pi1.z); tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); tvec4<T, P> ixy0 = detail::permute(ixy + iz0); tvec4<T, P> ixy1 = detail::permute(ixy + iz1); tvec4<T, P> gx0 = ixy0 * T(1.0 / 7.0); tvec4<T, P> gy0 = fract(floor(gx0) * T(1.0 / 7.0)) - T(0.5); gx0 = fract(gx0); tvec4<T, P> gz0 = tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); tvec4<T, P> sz0 = step(gz0, tvec4<T, P>(0.0)); gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); gy0 -= sz0 * (step(T(0), gy0) - T(0.5)); tvec4<T, P> gx1 = ixy1 * T(1.0 / 7.0); tvec4<T, P> gy1 = fract(floor(gx1) * T(1.0 / 7.0)) - T(0.5); gx1 = fract(gx1); tvec4<T, P> gz1 = tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); tvec4<T, P> sz1 = step(gz1, tvec4<T, P>(0.0)); gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); tvec3<T, P> g000(gx0.x, gy0.x, gz0.x); tvec3<T, P> g100(gx0.y, gy0.y, gz0.y); tvec3<T, P> g010(gx0.z, gy0.z, gz0.z); tvec3<T, P> g110(gx0.w, gy0.w, gz0.w); tvec3<T, P> g001(gx1.x, gy1.x, gz1.x); tvec3<T, P> g101(gx1.y, gy1.y, gz1.y); tvec3<T, P> g011(gx1.z, gy1.z, gz1.z); tvec3<T, P> g111(gx1.w, gy1.w, gz1.w); tvec4<T, P> norm0 = detail::taylorInvSqrt(tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; tvec4<T, P> norm1 = detail::taylorInvSqrt(tvec4<T, P>(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, tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1); tvec3<T, P> fade_xyz = detail::fade(Pf0); tvec4<T, P> n_z = mix(tvec4<T, P>(n000, n100, n010, n110), tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); tvec2<T, P> n_yz = mix(tvec2<T, P>(n_z.x, n_z.y), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec3<T, P> const & P) { tvec3<T, P> Pi0 = floor(P); // Integer part for indexing tvec3<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = mod(Pi0, T(289)); Pi1 = mod(Pi1, T(289)); tvec3<T, P> Pf0 = fract(P); // Fractional part for interpolation tvec3<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); tvec4<T, P> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); tvec4<T, P> iz0(Pi0.z); tvec4<T, P> iz1(Pi1.z); tvec4<T, P> ixy = permute(permute(ix) + iy); tvec4<T, P> ixy0 = permute(ixy + iz0); tvec4<T, P> ixy1 = permute(ixy + iz1); tvec4<T, P> gx0 = ixy0 / T(7); tvec4<T, P> gy0 = fract(floor(gx0) / T(7)) - T(0.5); gx0 = fract(gx0); tvec4<T, P> gz0 = tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); tvec4<T, P> sz0 = step(gz0, tvec4<T, P>(0.0)); gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); tvec4<T, P> gx1 = ixy1 / T(7); tvec4<T, P> gy1 = fract(floor(gx1) / T(7)) - T(0.5); gx1 = fract(gx1); tvec4<T, P> gz1 = tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); tvec4<T, P> sz1 = step(gz1, tvec4<T, P>(0.0)); gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); tvec3<T, P> g000(gx0.x, gy0.x, gz0.x); tvec3<T, P> g100(gx0.y, gy0.y, gz0.y); tvec3<T, P> g010(gx0.z, gy0.z, gz0.z); tvec3<T, P> g110(gx0.w, gy0.w, gz0.w); tvec3<T, P> g001(gx1.x, gy1.x, gz1.x); tvec3<T, P> g101(gx1.y, gy1.y, gz1.y); tvec3<T, P> g011(gx1.z, gy1.z, gz1.z); tvec3<T, P> g111(gx1.w, gy1.w, gz1.w); tvec4<T, P> norm0 = taylorInvSqrt(tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; tvec4<T, P> norm1 = taylorInvSqrt(tvec4<T, P>(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, tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1); tvec3<T, P> fade_xyz = fade(Pf0); tvec4<T, P> n_z = mix(tvec4<T, P>(n000, n100, n010, n110), tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); tvec2<T, P> n_yz = mix( tvec2<T, P>(n_z.x, n_z.y), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec4<T, P> const & Position) { tvec4<T, P> Pi0 = floor(Position); // Integer part for indexing tvec4<T, P> Pi1 = Pi0 + T(1); // Integer part + 1 Pi0 = mod(Pi0, tvec4<T, P>(289)); Pi1 = mod(Pi1, tvec4<T, P>(289)); tvec4<T, P> Pf0 = fract(Position); // Fractional part for interpolation tvec4<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 tvec4<T, P> ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); tvec4<T, P> iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y); tvec4<T, P> iz0(Pi0.z); tvec4<T, P> iz1(Pi1.z); tvec4<T, P> iw0(Pi0.w); tvec4<T, P> iw1(Pi1.w); tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); tvec4<T, P> ixy0 = detail::permute(ixy + iz0); tvec4<T, P> ixy1 = detail::permute(ixy + iz1); tvec4<T, P> ixy00 = detail::permute(ixy0 + iw0); tvec4<T, P> ixy01 = detail::permute(ixy0 + iw1); tvec4<T, P> ixy10 = detail::permute(ixy1 + iw0); tvec4<T, P> ixy11 = detail::permute(ixy1 + iw1); tvec4<T, P> gx00 = ixy00 / T(7); tvec4<T, P> gy00 = floor(gx00) / T(7); tvec4<T, P> gz00 = floor(gy00) / T(6); gx00 = fract(gx00) - T(0.5); gy00 = fract(gy00) - T(0.5); gz00 = fract(gz00) - T(0.5); tvec4<T, P> gw00 = tvec4<T, P>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); tvec4<T, P> sw00 = step(gw00, tvec4<T, P>(0.0)); gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); tvec4<T, P> gx01 = ixy01 / T(7); tvec4<T, P> gy01 = floor(gx01) / T(7); tvec4<T, P> gz01 = floor(gy01) / T(6); gx01 = fract(gx01) - T(0.5); gy01 = fract(gy01) - T(0.5); gz01 = fract(gz01) - T(0.5); tvec4<T, P> gw01 = tvec4<T, P>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); tvec4<T, P> sw01 = step(gw01, tvec4<T, P>(0.0)); gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); tvec4<T, P> gx10 = ixy10 / T(7); tvec4<T, P> gy10 = floor(gx10) / T(7); tvec4<T, P> gz10 = floor(gy10) / T(6); gx10 = fract(gx10) - T(0.5); gy10 = fract(gy10) - T(0.5); gz10 = fract(gz10) - T(0.5); tvec4<T, P> gw10 = tvec4<T, P>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); tvec4<T, P> sw10 = step(gw10, tvec4<T, P>(0)); gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); tvec4<T, P> gx11 = ixy11 / T(7); tvec4<T, P> gy11 = floor(gx11) / T(7); tvec4<T, P> gz11 = floor(gy11) / T(6); gx11 = fract(gx11) - T(0.5); gy11 = fract(gy11) - T(0.5); gz11 = fract(gz11) - T(0.5); tvec4<T, P> gw11 = tvec4<T, P>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); tvec4<T, P> sw11 = step(gw11, tvec4<T, P>(0.0)); gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); tvec4<T, P> g0000(gx00.x, gy00.x, gz00.x, gw00.x); tvec4<T, P> g1000(gx00.y, gy00.y, gz00.y, gw00.y); tvec4<T, P> g0100(gx00.z, gy00.z, gz00.z, gw00.z); tvec4<T, P> g1100(gx00.w, gy00.w, gz00.w, gw00.w); tvec4<T, P> g0010(gx10.x, gy10.x, gz10.x, gw10.x); tvec4<T, P> g1010(gx10.y, gy10.y, gz10.y, gw10.y); tvec4<T, P> g0110(gx10.z, gy10.z, gz10.z, gw10.z); tvec4<T, P> g1110(gx10.w, gy10.w, gz10.w, gw10.w); tvec4<T, P> g0001(gx01.x, gy01.x, gz01.x, gw01.x); tvec4<T, P> g1001(gx01.y, gy01.y, gz01.y, gw01.y); tvec4<T, P> g0101(gx01.z, gy01.z, gz01.z, gw01.z); tvec4<T, P> g1101(gx01.w, gy01.w, gz01.w, gw01.w); tvec4<T, P> g0011(gx11.x, gy11.x, gz11.x, gw11.x); tvec4<T, P> g1011(gx11.y, gy11.y, gz11.y, gw11.y); tvec4<T, P> g0111(gx11.z, gy11.z, gz11.z, gw11.z); tvec4<T, P> g1111(gx11.w, gy11.w, gz11.w, gw11.w); tvec4<T, P> norm00 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); g0000 *= norm00.x; g0100 *= norm00.y; g1000 *= norm00.z; g1100 *= norm00.w; tvec4<T, P> norm01 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); g0001 *= norm01.x; g0101 *= norm01.y; g1001 *= norm01.z; g1101 *= norm01.w; tvec4<T, P> norm10 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); g0010 *= norm10.x; g0110 *= norm10.y; g1010 *= norm10.z; g1110 *= norm10.w; tvec4<T, P> norm11 = detail::taylorInvSqrt(tvec4<T, P>(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, tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); T n0100 = dot(g0100, tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); T n1100 = dot(g1100, tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); T n0010 = dot(g0010, tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); T n1010 = dot(g1010, tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); T n0110 = dot(g0110, tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); T n1110 = dot(g1110, tvec4<T, P>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); T n0001 = dot(g0001, tvec4<T, P>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); T n1001 = dot(g1001, tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); T n0101 = dot(g0101, tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); T n1101 = dot(g1101, tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); T n0011 = dot(g0011, tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); T n1011 = dot(g1011, tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); T n0111 = dot(g0111, tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); T n1111 = dot(g1111, Pf1); tvec4<T, P> fade_xyzw = detail::fade(Pf0); tvec4<T, P> n_0w = mix(tvec4<T, P>(n0000, n1000, n0100, n1100), tvec4<T, P>(n0001, n1001, n0101, n1101), fade_xyzw.w); tvec4<T, P> n_1w = mix(tvec4<T, P>(n0010, n1010, n0110, n1110), tvec4<T, P>(n0011, n1011, n0111, n1111), fade_xyzw.w); tvec4<T, P> n_zw = mix(n_0w, n_1w, fade_xyzw.z); tvec2<T, P> n_yzw = mix(tvec2<T, P>(n_zw.x, n_zw.y), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec2<T, P> const & Position, tvec2<T, P> const & rep) { tvec4<T, P> Pi = floor(tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) + tvec4<T, P>(0.0, 0.0, 1.0, 1.0); tvec4<T, P> Pf = fract(tvec4<T, P>(Position.x, Position.y, Position.x, Position.y)) - tvec4<T, P>(0.0, 0.0, 1.0, 1.0); Pi = mod(Pi, tvec4<T, P>(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period Pi = mod(Pi, tvec4<T, P>(289)); // To avoid truncation effects in permutation tvec4<T, P> ix(Pi.x, Pi.z, Pi.x, Pi.z); tvec4<T, P> iy(Pi.y, Pi.y, Pi.w, Pi.w); tvec4<T, P> fx(Pf.x, Pf.z, Pf.x, Pf.z); tvec4<T, P> fy(Pf.y, Pf.y, Pf.w, Pf.w); tvec4<T, P> i = detail::permute(detail::permute(ix) + iy); tvec4<T, P> gx = static_cast<T>(2) * fract(i / T(41)) - T(1); tvec4<T, P> gy = abs(gx) - T(0.5); tvec4<T, P> tx = floor(gx + T(0.5)); gx = gx - tx; tvec2<T, P> g00(gx.x, gy.x); tvec2<T, P> g10(gx.y, gy.y); tvec2<T, P> g01(gx.z, gy.z); tvec2<T, P> g11(gx.w, gy.w); tvec4<T, P> norm = detail::taylorInvSqrt(tvec4<T, P>(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, tvec2<T, P>(fx.x, fy.x)); T n10 = dot(g10, tvec2<T, P>(fx.y, fy.y)); T n01 = dot(g01, tvec2<T, P>(fx.z, fy.z)); T n11 = dot(g11, tvec2<T, P>(fx.w, fy.w)); tvec2<T, P> fade_xy = detail::fade(tvec2<T, P>(Pf.x, Pf.y)); tvec2<T, P> n_x = mix(tvec2<T, P>(n00, n01), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec3<T, P> const & Position, tvec3<T, P> const & rep) { tvec3<T, P> Pi0 = mod(floor(Position), rep); // Integer part, modulo period tvec3<T, P> Pi1 = mod(Pi0 + tvec3<T, P>(T(1)), rep); // Integer part + 1, mod period Pi0 = mod(Pi0, tvec3<T, P>(289)); Pi1 = mod(Pi1, tvec3<T, P>(289)); tvec3<T, P> Pf0 = fract(Position); // Fractional part for interpolation tvec3<T, P> Pf1 = Pf0 - tvec3<T, P>(T(1)); // Fractional part - 1.0 tvec4<T, P> ix = tvec4<T, P>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); tvec4<T, P> iy = tvec4<T, P>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); tvec4<T, P> iz0(Pi0.z); tvec4<T, P> iz1(Pi1.z); tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); tvec4<T, P> ixy0 = detail::permute(ixy + iz0); tvec4<T, P> ixy1 = detail::permute(ixy + iz1); tvec4<T, P> gx0 = ixy0 / T(7); tvec4<T, P> gy0 = fract(floor(gx0) / T(7)) - T(0.5); gx0 = fract(gx0); tvec4<T, P> gz0 = tvec4<T, P>(0.5) - abs(gx0) - abs(gy0); tvec4<T, P> sz0 = step(gz0, tvec4<T, P>(0)); gx0 -= sz0 * (step(T(0), gx0) - T(0.5)); gy0 -= sz0 * (step(T(0), gy0) - T(0.5)); tvec4<T, P> gx1 = ixy1 / T(7); tvec4<T, P> gy1 = fract(floor(gx1) / T(7)) - T(0.5); gx1 = fract(gx1); tvec4<T, P> gz1 = tvec4<T, P>(0.5) - abs(gx1) - abs(gy1); tvec4<T, P> sz1 = step(gz1, tvec4<T, P>(T(0))); gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); tvec3<T, P> g000 = tvec3<T, P>(gx0.x, gy0.x, gz0.x); tvec3<T, P> g100 = tvec3<T, P>(gx0.y, gy0.y, gz0.y); tvec3<T, P> g010 = tvec3<T, P>(gx0.z, gy0.z, gz0.z); tvec3<T, P> g110 = tvec3<T, P>(gx0.w, gy0.w, gz0.w); tvec3<T, P> g001 = tvec3<T, P>(gx1.x, gy1.x, gz1.x); tvec3<T, P> g101 = tvec3<T, P>(gx1.y, gy1.y, gz1.y); tvec3<T, P> g011 = tvec3<T, P>(gx1.z, gy1.z, gz1.z); tvec3<T, P> g111 = tvec3<T, P>(gx1.w, gy1.w, gz1.w); tvec4<T, P> norm0 = detail::taylorInvSqrt(tvec4<T, P>(dot(g000, g000), dot(g010, g010), dot(g100, g100), dot(g110, g110))); g000 *= norm0.x; g010 *= norm0.y; g100 *= norm0.z; g110 *= norm0.w; tvec4<T, P> norm1 = detail::taylorInvSqrt(tvec4<T, P>(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, tvec3<T, P>(Pf1.x, Pf0.y, Pf0.z)); T n010 = dot(g010, tvec3<T, P>(Pf0.x, Pf1.y, Pf0.z)); T n110 = dot(g110, tvec3<T, P>(Pf1.x, Pf1.y, Pf0.z)); T n001 = dot(g001, tvec3<T, P>(Pf0.x, Pf0.y, Pf1.z)); T n101 = dot(g101, tvec3<T, P>(Pf1.x, Pf0.y, Pf1.z)); T n011 = dot(g011, tvec3<T, P>(Pf0.x, Pf1.y, Pf1.z)); T n111 = dot(g111, Pf1); tvec3<T, P> fade_xyz = detail::fade(Pf0); tvec4<T, P> n_z = mix(tvec4<T, P>(n000, n100, n010, n110), tvec4<T, P>(n001, n101, n011, n111), fade_xyz.z); tvec2<T, P> n_yz = mix(tvec2<T, P>(n_z.x, n_z.y), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T perlin(tvec4<T, P> const & Position, tvec4<T, P> const & rep) { tvec4<T, P> Pi0 = mod(floor(Position), rep); // Integer part modulo rep tvec4<T, P> Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep tvec4<T, P> Pf0 = fract(Position); // Fractional part for interpolation tvec4<T, P> Pf1 = Pf0 - T(1); // Fractional part - 1.0 tvec4<T, P> ix = tvec4<T, P>(Pi0.x, Pi1.x, Pi0.x, Pi1.x); tvec4<T, P> iy = tvec4<T, P>(Pi0.y, Pi0.y, Pi1.y, Pi1.y); tvec4<T, P> iz0(Pi0.z); tvec4<T, P> iz1(Pi1.z); tvec4<T, P> iw0(Pi0.w); tvec4<T, P> iw1(Pi1.w); tvec4<T, P> ixy = detail::permute(detail::permute(ix) + iy); tvec4<T, P> ixy0 = detail::permute(ixy + iz0); tvec4<T, P> ixy1 = detail::permute(ixy + iz1); tvec4<T, P> ixy00 = detail::permute(ixy0 + iw0); tvec4<T, P> ixy01 = detail::permute(ixy0 + iw1); tvec4<T, P> ixy10 = detail::permute(ixy1 + iw0); tvec4<T, P> ixy11 = detail::permute(ixy1 + iw1); tvec4<T, P> gx00 = ixy00 / T(7); tvec4<T, P> gy00 = floor(gx00) / T(7); tvec4<T, P> gz00 = floor(gy00) / T(6); gx00 = fract(gx00) - T(0.5); gy00 = fract(gy00) - T(0.5); gz00 = fract(gz00) - T(0.5); tvec4<T, P> gw00 = tvec4<T, P>(0.75) - abs(gx00) - abs(gy00) - abs(gz00); tvec4<T, P> sw00 = step(gw00, tvec4<T, P>(0)); gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); tvec4<T, P> gx01 = ixy01 / T(7); tvec4<T, P> gy01 = floor(gx01) / T(7); tvec4<T, P> gz01 = floor(gy01) / T(6); gx01 = fract(gx01) - T(0.5); gy01 = fract(gy01) - T(0.5); gz01 = fract(gz01) - T(0.5); tvec4<T, P> gw01 = tvec4<T, P>(0.75) - abs(gx01) - abs(gy01) - abs(gz01); tvec4<T, P> sw01 = step(gw01, tvec4<T, P>(0.0)); gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); tvec4<T, P> gx10 = ixy10 / T(7); tvec4<T, P> gy10 = floor(gx10) / T(7); tvec4<T, P> gz10 = floor(gy10) / T(6); gx10 = fract(gx10) - T(0.5); gy10 = fract(gy10) - T(0.5); gz10 = fract(gz10) - T(0.5); tvec4<T, P> gw10 = tvec4<T, P>(0.75) - abs(gx10) - abs(gy10) - abs(gz10); tvec4<T, P> sw10 = step(gw10, tvec4<T, P>(0.0)); gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); tvec4<T, P> gx11 = ixy11 / T(7); tvec4<T, P> gy11 = floor(gx11) / T(7); tvec4<T, P> gz11 = floor(gy11) / T(6); gx11 = fract(gx11) - T(0.5); gy11 = fract(gy11) - T(0.5); gz11 = fract(gz11) - T(0.5); tvec4<T, P> gw11 = tvec4<T, P>(0.75) - abs(gx11) - abs(gy11) - abs(gz11); tvec4<T, P> sw11 = step(gw11, tvec4<T, P>(T(0))); gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); tvec4<T, P> g0000(gx00.x, gy00.x, gz00.x, gw00.x); tvec4<T, P> g1000(gx00.y, gy00.y, gz00.y, gw00.y); tvec4<T, P> g0100(gx00.z, gy00.z, gz00.z, gw00.z); tvec4<T, P> g1100(gx00.w, gy00.w, gz00.w, gw00.w); tvec4<T, P> g0010(gx10.x, gy10.x, gz10.x, gw10.x); tvec4<T, P> g1010(gx10.y, gy10.y, gz10.y, gw10.y); tvec4<T, P> g0110(gx10.z, gy10.z, gz10.z, gw10.z); tvec4<T, P> g1110(gx10.w, gy10.w, gz10.w, gw10.w); tvec4<T, P> g0001(gx01.x, gy01.x, gz01.x, gw01.x); tvec4<T, P> g1001(gx01.y, gy01.y, gz01.y, gw01.y); tvec4<T, P> g0101(gx01.z, gy01.z, gz01.z, gw01.z); tvec4<T, P> g1101(gx01.w, gy01.w, gz01.w, gw01.w); tvec4<T, P> g0011(gx11.x, gy11.x, gz11.x, gw11.x); tvec4<T, P> g1011(gx11.y, gy11.y, gz11.y, gw11.y); tvec4<T, P> g0111(gx11.z, gy11.z, gz11.z, gw11.z); tvec4<T, P> g1111(gx11.w, gy11.w, gz11.w, gw11.w); tvec4<T, P> norm00 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0000, g0000), dot(g0100, g0100), dot(g1000, g1000), dot(g1100, g1100))); g0000 *= norm00.x; g0100 *= norm00.y; g1000 *= norm00.z; g1100 *= norm00.w; tvec4<T, P> norm01 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0001, g0001), dot(g0101, g0101), dot(g1001, g1001), dot(g1101, g1101))); g0001 *= norm01.x; g0101 *= norm01.y; g1001 *= norm01.z; g1101 *= norm01.w; tvec4<T, P> norm10 = detail::taylorInvSqrt(tvec4<T, P>(dot(g0010, g0010), dot(g0110, g0110), dot(g1010, g1010), dot(g1110, g1110))); g0010 *= norm10.x; g0110 *= norm10.y; g1010 *= norm10.z; g1110 *= norm10.w; tvec4<T, P> norm11 = detail::taylorInvSqrt(tvec4<T, P>(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, tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf0.w)); T n0100 = dot(g0100, tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf0.w)); T n1100 = dot(g1100, tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf0.w)); T n0010 = dot(g0010, tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf0.w)); T n1010 = dot(g1010, tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); T n0110 = dot(g0110, tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf0.w)); T n1110 = dot(g1110, tvec4<T, P>(Pf1.x, Pf1.y, Pf1.z, Pf0.w)); T n0001 = dot(g0001, tvec4<T, P>(Pf0.x, Pf0.y, Pf0.z, Pf1.w)); T n1001 = dot(g1001, tvec4<T, P>(Pf1.x, Pf0.y, Pf0.z, Pf1.w)); T n0101 = dot(g0101, tvec4<T, P>(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); T n1101 = dot(g1101, tvec4<T, P>(Pf1.x, Pf1.y, Pf0.z, Pf1.w)); T n0011 = dot(g0011, tvec4<T, P>(Pf0.x, Pf0.y, Pf1.z, Pf1.w)); T n1011 = dot(g1011, tvec4<T, P>(Pf1.x, Pf0.y, Pf1.z, Pf1.w)); T n0111 = dot(g0111, tvec4<T, P>(Pf0.x, Pf1.y, Pf1.z, Pf1.w)); T n1111 = dot(g1111, Pf1); tvec4<T, P> fade_xyzw = detail::fade(Pf0); tvec4<T, P> n_0w = mix(tvec4<T, P>(n0000, n1000, n0100, n1100), tvec4<T, P>(n0001, n1001, n0101, n1101), fade_xyzw.w); tvec4<T, P> n_1w = mix(tvec4<T, P>(n0010, n1010, n0110, n1110), tvec4<T, P>(n0011, n1011, n0111, n1111), fade_xyzw.w); tvec4<T, P> n_zw = mix(n_0w, n_1w, fade_xyzw.z); tvec2<T, P> n_yzw = mix(tvec2<T, P>(n_zw.x, n_zw.y), tvec2<T, P>(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, precision P> GLM_FUNC_QUALIFIER T simplex(glm::tvec2<T, P> const & v) { tvec4<T, P> const C = tvec4<T, P>( 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 tvec2<T, P> i = floor(v + dot(v, tvec2<T, P>(C[1]))); tvec2<T, P> x0 = v - i + dot(i, tvec2<T, P>(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; tvec2<T, P> i1 = (x0.x > x0.y) ? tvec2<T, P>(1, 0) : tvec2<T, P>(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 ; tvec4<T, P> x12 = tvec4<T, P>(x0.x, x0.y, x0.x, x0.y) + tvec4<T, P>(C.x, C.x, C.z, C.z); x12 = tvec4<T, P>(tvec2<T, P>(x12) - i1, x12.z, x12.w); // Permutations i = mod(i, tvec2<T, P>(289)); // Avoid truncation effects in permutation tvec3<T, P> p = detail::permute( detail::permute(i.y + tvec3<T, P>(T(0), i1.y, T(1))) + i.x + tvec3<T, P>(T(0), i1.x, T(1))); tvec3<T, P> m = max(tvec3<T, P>(0.5) - tvec3<T, P>( dot(x0, x0), dot(tvec2<T, P>(x12.x, x12.y), tvec2<T, P>(x12.x, x12.y)), dot(tvec2<T, P>(x12.z, x12.w), tvec2<T, P>(x12.z, x12.w))), tvec3<T, P>(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) tvec3<T, P> x = static_cast<T>(2) * fract(p * C.w) - T(1); tvec3<T, P> h = abs(x) - T(0.5); tvec3<T, P> ox = floor(x + T(0.5)); tvec3<T, P> a0 = x - ox; // Normalise gradients implicitly by scaling m // Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h ); m *= static_cast<T>(1.79284291400159) - T(0.85373472095314) * (a0 * a0 + h * h); // Compute final noise value at P tvec3<T, P> 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, precision P> GLM_FUNC_QUALIFIER T simplex(tvec3<T, P> const & v) { tvec2<T, P> const C(1.0 / 6.0, 1.0 / 3.0); tvec4<T, P> const D(0.0, 0.5, 1.0, 2.0); // First corner tvec3<T, P> i(floor(v + dot(v, tvec3<T, P>(C.y)))); tvec3<T, P> x0(v - i + dot(i, tvec3<T, P>(C.x))); // Other corners tvec3<T, P> g(step(tvec3<T, P>(x0.y, x0.z, x0.x), x0)); tvec3<T, P> l(T(1) - g); tvec3<T, P> i1(min(g, tvec3<T, P>(l.z, l.x, l.y))); tvec3<T, P> i2(max(g, tvec3<T, P>(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; tvec3<T, P> x1(x0 - i1 + C.x); tvec3<T, P> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y tvec3<T, P> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y // Permutations i = detail::mod289(i); tvec4<T, P> p(detail::permute(detail::permute(detail::permute( i.z + tvec4<T, P>(T(0), i1.z, i2.z, T(1))) + i.y + tvec4<T, P>(T(0), i1.y, i2.y, T(1))) + i.x + tvec4<T, P>(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_ = static_cast<T>(0.142857142857); // 1.0/7.0 tvec3<T, P> ns(n_ * tvec3<T, P>(D.w, D.y, D.z) - tvec3<T, P>(D.x, D.z, D.x)); tvec4<T, P> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7) tvec4<T, P> x_(floor(j * ns.z)); tvec4<T, P> y_(floor(j - T(7) * x_)); // mod(j,N) tvec4<T, P> x(x_ * ns.x + ns.y); tvec4<T, P> y(y_ * ns.x + ns.y); tvec4<T, P> h(T(1) - abs(x) - abs(y)); tvec4<T, P> b0(x.x, x.y, y.x, y.y); tvec4<T, P> 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; tvec4<T, P> s0(floor(b0) * T(2) + T(1)); tvec4<T, P> s1(floor(b1) * T(2) + T(1)); tvec4<T, P> sh(-step(h, tvec4<T, P>(0.0))); tvec4<T, P> a0 = tvec4<T, P>(b0.x, b0.z, b0.y, b0.w) + tvec4<T, P>(s0.x, s0.z, s0.y, s0.w) * tvec4<T, P>(sh.x, sh.x, sh.y, sh.y); tvec4<T, P> a1 = tvec4<T, P>(b1.x, b1.z, b1.y, b1.w) + tvec4<T, P>(s1.x, s1.z, s1.y, s1.w) * tvec4<T, P>(sh.z, sh.z, sh.w, sh.w); tvec3<T, P> p0(a0.x, a0.y, h.x); tvec3<T, P> p1(a0.z, a0.w, h.y); tvec3<T, P> p2(a1.x, a1.y, h.z); tvec3<T, P> p3(a1.z, a1.w, h.w); // Normalise gradients tvec4<T, P> norm = detail::taylorInvSqrt(tvec4<T, P>(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 tvec4<T, P> m = max(T(0.6) - tvec4<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), tvec4<T, P>(0)); m = m * m; return T(42) * dot(m * m, tvec4<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); } template <typename T, precision P> GLM_FUNC_QUALIFIER T simplex(tvec4<T, P> const & v) { tvec4<T, P> 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 = static_cast<T>(0.309016994374947451); // First corner tvec4<T, P> i = floor(v + dot(v, vec4(F4))); tvec4<T, P> x0 = v - i + dot(i, vec4(C.x)); // Other corners // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) tvec4<T, P> i0; tvec3<T, P> isX = step(tvec3<T, P>(x0.y, x0.z, x0.w), tvec3<T, P>(x0.x)); tvec3<T, P> isYZ = step(tvec3<T, P>(x0.z, x0.w, x0.w), tvec3<T, P>(x0.y, x0.y, x0.z)); // i0.x = dot(isX, vec3(1.0)); //i0.x = isX.x + isX.y + isX.z; //i0.yzw = static_cast<T>(1) - isX; i0 = tvec4<T, P>(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 - tvec2<T, P>(isYZ.x, isYZ.y); i0.z += static_cast<T>(1) - isYZ.x; i0.w += static_cast<T>(1) - isYZ.y; i0.z += isYZ.z; i0.w += static_cast<T>(1) - isYZ.z; // i0 now contains the unique values 0,1,2,3 in each channel tvec4<T, P> i3 = clamp(i0, T(0), T(1)); tvec4<T, P> i2 = clamp(i0 - T(1), T(0), T(1)); tvec4<T, P> i1 = clamp(i0 - T(2), T(0), T(1)); // 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 tvec4<T, P> x1 = x0 - i1 + C.x; tvec4<T, P> x2 = x0 - i2 + C.y; tvec4<T, P> x3 = x0 - i3 + C.z; tvec4<T, P> x4 = x0 + C.w; // Permutations i = mod(i, tvec4<T, P>(289)); T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x); tvec4<T, P> j1 = detail::permute(detail::permute(detail::permute(detail::permute( i.w + tvec4<T, P>(i1.w, i2.w, i3.w, T(1))) + i.z + tvec4<T, P>(i1.z, i2.z, i3.z, T(1))) + i.y + tvec4<T, P>(i1.y, i2.y, i3.y, T(1))) + i.x + tvec4<T, P>(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. tvec4<T, P> ip = tvec4<T, P>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); tvec4<T, P> p0 = gtc::grad4(j0, ip); tvec4<T, P> p1 = gtc::grad4(j1.x, ip); tvec4<T, P> p2 = gtc::grad4(j1.y, ip); tvec4<T, P> p3 = gtc::grad4(j1.z, ip); tvec4<T, P> p4 = gtc::grad4(j1.w, ip); // Normalise gradients tvec4<T, P> norm = detail::taylorInvSqrt(tvec4<T, P>(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 *= detail::taylorInvSqrt(dot(p4, p4)); // Mix contributions from the five corners tvec3<T, P> m0 = max(T(0.6) - tvec3<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), tvec3<T, P>(0)); tvec2<T, P> m1 = max(T(0.6) - tvec2<T, P>(dot(x3, x3), dot(x4, x4) ), tvec2<T, P>(0)); m0 = m0 * m0; m1 = m1 * m1; return T(49) * (dot(m0 * m0, tvec3<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + dot(m1 * m1, tvec2<T, P>(dot(p3, x3), dot(p4, x4)))); } }//namespace glm