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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 core/// @file glm/core/func_noise.inl/// @date 2008-08-01 / 2011-09-27/// @author Christophe Riccio///////////////////////////////////////////////////////////////////////////////////
namespace glm{ template <typename T> GLM_FUNC_QUALIFIER T noise1(T const & x) { return noise1(glm::detail::tvec2<T>(x, T(0))); }
template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec2<T> noise2(T const & x) { return glm::detail::tvec2<T>( noise1(x + T(0.0)), noise1(x + T(1.0))); }
template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec3<T> noise3(T const & x) { return glm::detail::tvec3<T>( noise1(x - T(1.0)), noise1(x + T(0.0)), noise1(x + T(1.0))); }
template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec4<T> noise4(T const & x) { return glm::detail::tvec4<T>( noise1(x - T(1.0)), noise1(x + T(0.0)), noise1(x + T(1.0)), noise1(x + T(2.0))); } template <typename T> GLM_FUNC_QUALIFIER T noise1(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 noise1(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 noise1(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)))); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec2<T> noise2(glm::detail::tvec2<T> const & x) { return glm::detail::tvec2<T>( noise1(x + glm::detail::tvec2<T>(0.0)), noise1(glm::detail::tvec2<T>(0.0) - x)); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec2<T> noise2(glm::detail::tvec3<T> const & x) { return glm::detail::tvec2<T>( noise1(x + glm::detail::tvec3<T>(0.0)), noise1(glm::detail::tvec3<T>(0.0) - x)); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec2<T> noise2(glm::detail::tvec4<T> const & x) { return glm::detail::tvec2<T>( noise1(x + glm::detail::tvec4<T>(0.0)), noise1(glm::detail::tvec4<T>(0.0) - x)); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec3<T> noise3(glm::detail::tvec2<T> const & x) { return glm::detail::tvec3<T>( noise1(x - glm::detail::tvec2<T>(1.0)), noise1(x + glm::detail::tvec2<T>(0.0)), noise1(x + glm::detail::tvec2<T>(1.0))); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec3<T> noise3(glm::detail::tvec3<T> const & x) { return glm::detail::tvec3<T>( noise1(x - glm::detail::tvec3<T>(1.0)), noise1(x + glm::detail::tvec3<T>(0.0)), noise1(x + glm::detail::tvec3<T>(1.0))); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec3<T> noise3(glm::detail::tvec4<T> const & x) { return glm::detail::tvec3<T>( noise1(x - glm::detail::tvec4<T>(1.0)), noise1(x + glm::detail::tvec4<T>(0.0)), noise1(x + glm::detail::tvec4<T>(1.0))); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec4<T> noise4(glm::detail::tvec2<T> const & x) { return glm::detail::tvec4<T>( noise1(x - glm::detail::tvec2<T>(1.0)), noise1(x + glm::detail::tvec2<T>(0.0)), noise1(x + glm::detail::tvec2<T>(1.0)), noise1(x + glm::detail::tvec2<T>(2.0))); }
template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec4<T> noise4(glm::detail::tvec3<T> const & x) { return glm::detail::tvec4<T>( noise1(x - glm::detail::tvec3<T>(1.0)), noise1(x + glm::detail::tvec3<T>(0.0)), noise1(x + glm::detail::tvec3<T>(1.0)), noise1(x + glm::detail::tvec3<T>(2.0))); } template <typename T> GLM_FUNC_QUALIFIER glm::detail::tvec4<T> noise4(glm::detail::tvec4<T> const & x) { return glm::detail::tvec4<T>( noise1(x - glm::detail::tvec4<T>(1.0)), noise1(x + glm::detail::tvec4<T>(0.0)), noise1(x + glm::detail::tvec4<T>(1.0)), noise1(x + glm::detail::tvec4<T>(2.0))); } }//namespace glm
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