| /////////////////////////////////////////////////////////////////////////////////// |
| /// OpenGL Mathematics (glm.g-truc.net) |
| /// |
| /// Copyright (c) 2005 - 2014 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 |
| /////////////////////////////////////////////////////////////////////////////////// |
| |
| #include "../detail/_noise.hpp" |
| #include "./func_common.hpp" |
| |
| namespace glm{ |
| namespace detail |
| { |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> grad4(T const & j, detail::tvec4<T, P> const & ip) |
| { |
| detail::tvec3<T, P> pXYZ = floor(fract(detail::tvec3<T, P>(j) * detail::tvec3<T, P>(ip)) * T(7)) * ip[2] - T(1); |
| T pW = static_cast<T>(1.5) - dot(abs(pXYZ), detail::tvec3<T, P>(1)); |
| detail::tvec4<T, P> s = detail::tvec4<T, P>(lessThan(detail::tvec4<T, P>(pXYZ, pW), detail::tvec4<T, P>(0.0))); |
| pXYZ = pXYZ + (detail::tvec3<T, P>(s) * T(2) - T(1)) * s.w; |
| return detail::tvec4<T, P>(pXYZ, pW); |
| } |
| }//namespace detail |
| |
| template <typename T> |
| GLM_FUNC_QUALIFIER T noise1(T const & x) |
| { |
| return noise1(detail::tvec2<T, defaultp>(x, T(0))); |
| } |
| |
| template <typename T> |
| GLM_FUNC_QUALIFIER detail::tvec2<T, defaultp> noise2(T const & x) |
| { |
| return detail::tvec2<T, defaultp>( |
| noise1(x + T(0.0)), |
| noise1(x + T(1.0))); |
| } |
| |
| template <typename T> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, defaultp> noise3(T const & x) |
| { |
| return detail::tvec3<T, defaultp>( |
| noise1(x - T(1.0)), |
| noise1(x + T(0.0)), |
| noise1(x + T(1.0))); |
| } |
| |
| template <typename T> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, defaultp> noise4(T const & x) |
| { |
| return detail::tvec4<T, defaultp>( |
| noise1(x - T(1.0)), |
| noise1(x + T(0.0)), |
| noise1(x + T(1.0)), |
| noise1(x + T(2.0))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T noise1(detail::tvec2<T, P> const & v) |
| { |
| detail::tvec4<T, P> const C = detail::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 |
| detail::tvec2<T, P> i = floor(v + dot(v, detail::tvec2<T, P>(C[1]))); |
| detail::tvec2<T, P> x0 = v - i + dot(i, detail::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; |
| detail::tvec2<T, P> i1 = (x0.x > x0.y) ? detail::tvec2<T, P>(1, 0) : detail::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 ; |
| detail::tvec4<T, P> x12 = detail::tvec4<T, P>(x0.x, x0.y, x0.x, x0.y) + detail::tvec4<T, P>(C.x, C.x, C.z, C.z); |
| x12 = detail::tvec4<T, P>(detail::tvec2<T, P>(x12) - i1, x12.z, x12.w); |
| |
| // Permutations |
| i = mod(i, T(289)); // Avoid truncation effects in permutation |
| detail::tvec3<T, P> p = detail::permute( |
| detail::permute(i.y + detail::tvec3<T, P>(T(0), i1.y, T(1))) + i.x + detail::tvec3<T, P>(T(0), i1.x, T(1))); |
| |
| detail::tvec3<T, P> m = max(T(0.5) - detail::tvec3<T, P>( |
| dot(x0, x0), |
| dot(detail::tvec2<T, P>(x12.x, x12.y), detail::tvec2<T, P>(x12.x, x12.y)), |
| dot(detail::tvec2<T, P>(x12.z, x12.w), detail::tvec2<T, P>(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, P> x = static_cast<T>(2) * fract(p * C.w) - T(1); |
| detail::tvec3<T, P> h = abs(x) - T(0.5); |
| detail::tvec3<T, P> ox = floor(x + T(0.5)); |
| detail::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 |
| detail::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 noise1(detail::tvec3<T, P> const & v) |
| { |
| detail::tvec2<T, P> const C(1.0 / 6.0, 1.0 / 3.0); |
| detail::tvec4<T, P> const D(0.0, 0.5, 1.0, 2.0); |
| |
| // First corner |
| detail::tvec3<T, P> i(floor(v + dot(v, detail::tvec3<T, P>(C.y)))); |
| detail::tvec3<T, P> x0(v - i + dot(i, detail::tvec3<T, P>(C.x))); |
| |
| // Other corners |
| detail::tvec3<T, P> g(step(detail::tvec3<T, P>(x0.y, x0.z, x0.x), x0)); |
| detail::tvec3<T, P> l(T(1) - g); |
| detail::tvec3<T, P> i1(min(g, detail::tvec3<T, P>(l.z, l.x, l.y))); |
| detail::tvec3<T, P> i2(max(g, detail::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; |
| detail::tvec3<T, P> x1(x0 - i1 + C.x); |
| detail::tvec3<T, P> x2(x0 - i2 + C.y); // 2.0*C.x = 1/3 = C.y |
| detail::tvec3<T, P> x3(x0 - D.y); // -1.0+3.0*C.x = -0.5 = -D.y |
| |
| // Permutations |
| i = mod289(i); |
| detail::tvec4<T, P> p(detail::permute(detail::permute(detail::permute( |
| i.z + detail::tvec4<T, P>(T(0), i1.z, i2.z, T(1))) + |
| i.y + detail::tvec4<T, P>(T(0), i1.y, i2.y, T(1))) + |
| i.x + detail::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 |
| detail::tvec3<T, P> ns(n_ * detail::tvec3<T, P>(D.w, D.y, D.z) - detail::tvec3<T, P>(D.x, D.z, D.x)); |
| |
| detail::tvec4<T, P> j(p - T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7) |
| |
| detail::tvec4<T, P> x_(floor(j * ns.z)); |
| detail::tvec4<T, P> y_(floor(j - T(7) * x_)); // mod(j,N) |
| |
| detail::tvec4<T, P> x(x_ * ns.x + ns.y); |
| detail::tvec4<T, P> y(y_ * ns.x + ns.y); |
| detail::tvec4<T, P> h(T(1) - abs(x) - abs(y)); |
| |
| detail::tvec4<T, P> b0(x.x, x.y, y.x, y.y); |
| detail::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; |
| detail::tvec4<T, P> s0(floor(b0) * T(2) + T(1)); |
| detail::tvec4<T, P> s1(floor(b1) * T(2) + T(1)); |
| detail::tvec4<T, P> sh(-step(h, detail::tvec4<T, P>(0.0))); |
| |
| detail::tvec4<T, P> a0 = detail::tvec4<T, P>(b0.x, b0.z, b0.y, b0.w) + detail::tvec4<T, P>(s0.x, s0.z, s0.y, s0.w) * detail::tvec4<T, P>(sh.x, sh.x, sh.y, sh.y); |
| detail::tvec4<T, P> a1 = detail::tvec4<T, P>(b1.x, b1.z, b1.y, b1.w) + detail::tvec4<T, P>(s1.x, s1.z, s1.y, s1.w) * detail::tvec4<T, P>(sh.z, sh.z, sh.w, sh.w); |
| |
| detail::tvec3<T, P> p0(a0.x, a0.y, h.x); |
| detail::tvec3<T, P> p1(a0.z, a0.w, h.y); |
| detail::tvec3<T, P> p2(a1.x, a1.y, h.z); |
| detail::tvec3<T, P> p3(a1.z, a1.w, h.w); |
| |
| // Normalise gradients |
| detail::tvec4<T, P> norm = taylorInvSqrt(detail::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 |
| detail::tvec4<T, P> m = max(T(0.6) - detail::tvec4<T, P>(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, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER T noise1(detail::tvec4<T, P> const & v) |
| { |
| detail::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 |
| detail::tvec4<T, P> i = floor(v + dot(v, detail::tvec4<T, P>(F4))); |
| detail::tvec4<T, P> x0 = v - i + dot(i, detail::tvec4<T, P>(C.x)); |
| |
| // Other corners |
| |
| // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) |
| detail::tvec4<T, P> i0; |
| detail::tvec3<T, P> isX = step(detail::tvec3<T, P>(x0.y, x0.z, x0.w), detail::tvec3<T, P>(x0.x)); |
| detail::tvec3<T, P> isYZ = step(detail::tvec3<T, P>(x0.z, x0.w, x0.w), detail::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 = detail::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 - detail::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 |
| detail::tvec4<T, P> i3 = clamp(i0, T(0), T(1)); |
| detail::tvec4<T, P> i2 = clamp(i0 - T(1), T(0), T(1)); |
| detail::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 |
| detail::tvec4<T, P> x1 = x0 - i1 + C.x; |
| detail::tvec4<T, P> x2 = x0 - i2 + C.y; |
| detail::tvec4<T, P> x3 = x0 - i3 + C.z; |
| detail::tvec4<T, P> x4 = x0 + C.w; |
| |
| // Permutations |
| i = mod(i, T(289)); |
| T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x); |
| detail::tvec4<T, P> j1 = detail::permute(detail::permute(detail::permute(detail::permute( |
| i.w + detail::tvec4<T, P>(i1.w, i2.w, i3.w, T(1))) + |
| i.z + detail::tvec4<T, P>(i1.z, i2.z, i3.z, T(1))) + |
| i.y + detail::tvec4<T, P>(i1.y, i2.y, i3.y, T(1))) + |
| i.x + detail::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. |
| detail::tvec4<T, P> ip = detail::tvec4<T, P>(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); |
| |
| detail::tvec4<T, P> p0 = detail::grad4(j0, ip); |
| detail::tvec4<T, P> p1 = detail::grad4(j1.x, ip); |
| detail::tvec4<T, P> p2 = detail::grad4(j1.y, ip); |
| detail::tvec4<T, P> p3 = detail::grad4(j1.z, ip); |
| detail::tvec4<T, P> p4 = detail::grad4(j1.w, ip); |
| |
| // Normalise gradients |
| detail::tvec4<T, P> norm = detail::taylorInvSqrt(detail::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 *= taylorInvSqrt(dot(p4, p4)); |
| |
| // Mix contributions from the five corners |
| detail::tvec3<T, P> m0 = max(T(0.6) - detail::tvec3<T, P>(dot(x0, x0), dot(x1, x1), dot(x2, x2)), T(0)); |
| detail::tvec2<T, P> m1 = max(T(0.6) - detail::tvec2<T, P>(dot(x3, x3), dot(x4, x4) ), T(0)); |
| m0 = m0 * m0; |
| m1 = m1 * m1; |
| |
| return T(49) * ( |
| dot(m0 * m0, detail::tvec3<T, P>(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + |
| dot(m1 * m1, detail::tvec2<T, P>(dot(p3, x3), dot(p4, x4)))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec2<T, P> const & x) |
| { |
| return detail::tvec2<T, P>( |
| noise1(x + detail::tvec2<T, P>(0.0)), |
| noise1(detail::tvec2<T, P>(0.0) - x)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec3<T, P> const & x) |
| { |
| return detail::tvec2<T, P>( |
| noise1(x + detail::tvec3<T, P>(0.0)), |
| noise1(detail::tvec3<T, P>(0.0) - x)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec2<T, P> noise2(detail::tvec4<T, P> const & x) |
| { |
| return detail::tvec2<T, P>( |
| noise1(x + detail::tvec4<T, P>(0)), |
| noise1(detail::tvec4<T, P>(0) - x)); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec2<T, P> const & x) |
| { |
| return detail::tvec3<T, P>( |
| noise1(x - detail::tvec2<T, P>(1.0)), |
| noise1(x + detail::tvec2<T, P>(0.0)), |
| noise1(x + detail::tvec2<T, P>(1.0))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec3<T, P> const & x) |
| { |
| return detail::tvec3<T, P>( |
| noise1(x - detail::tvec3<T, P>(1.0)), |
| noise1(x + detail::tvec3<T, P>(0.0)), |
| noise1(x + detail::tvec3<T, P>(1.0))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec3<T, P> noise3(detail::tvec4<T, P> const & x) |
| { |
| return detail::tvec3<T, P>( |
| noise1(x - detail::tvec4<T, P>(1)), |
| noise1(x + detail::tvec4<T, P>(0)), |
| noise1(x + detail::tvec4<T, P>(1))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec2<T, P> const & x) |
| { |
| return detail::tvec4<T, P>( |
| noise1(x - detail::tvec2<T, P>(1)), |
| noise1(x + detail::tvec2<T, P>(0)), |
| noise1(x + detail::tvec2<T, P>(1)), |
| noise1(x + detail::tvec2<T, P>(2))); |
| } |
| |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec3<T, P> const & x) |
| { |
| return detail::tvec4<T, P>( |
| noise1(x - detail::tvec3<T, P>(1)), |
| noise1(x + detail::tvec3<T, P>(0)), |
| noise1(x + detail::tvec3<T, P>(1)), |
| noise1(x + detail::tvec3<T, P>(2))); |
| } |
| |
| template <typename T, precision P> |
| GLM_FUNC_QUALIFIER detail::tvec4<T, P> noise4(detail::tvec4<T, P> const & x) |
| { |
| return detail::tvec4<T, P>( |
| noise1(x - detail::tvec4<T, P>(1)), |
| noise1(x + detail::tvec4<T, P>(0)), |
| noise1(x + detail::tvec4<T, P>(1)), |
| noise1(x + detail::tvec4<T, P>(2))); |
| } |
| |
| }//namespace glm |
