diff --git a/glm/gtx/noise.inl b/glm/gtx/noise.inl index 6e926133..9d7982c5 100644 --- a/glm/gtx/noise.inl +++ b/glm/gtx/noise.inl @@ -176,6 +176,584 @@ namespace noise dot(p3, x3))); } + template + inline T snoise(detail::tvec4 const & v) + { + detail::tvec4 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(0.309016994374947451); + + // First corner + detail::tvec4 i = floor(v + dot(v, vec4(F4))); + detail::tvec4 x0 = v - i + dot(i, vec4(C.x)); + + // Other corners + + // Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI) + detail::tvec4 i0; + detail::tvec3 isX = step(x0.yzw, x0.xxx); + detail::tvec3 isYZ = step(x0.zww, x0.yyz); + // i0.x = dot( isX, vec3( 1.0 ) ); + i0.x = isX.x + isX.y + isX.z; + i0.yzw = 1.0 - isX; + // i0.y += dot( isYZ.xy, vec2( 1.0 ) ); + i0.y += isYZ.x + isYZ.y; + i0.zw += 1.0 - isYZ.xy; + i0.z += isYZ.z; + i0.w += 1.0 - isYZ.z; + + // i0 now contains the unique values 0,1,2,3 in each channel + detail::tvec4 i3 = clamp(i0, 0.0, 1.0); + detail::tvec4 i2 = clamp(i0 - 1.0, 0.0, 1.0); + detail::tvec4 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 x1 = x0 - i1 + C.x; + detail::tvec4 x2 = x0 - i2 + C.y; + detail::tvec4 x3 = x0 - i3 + C.z; + detail::tvec4 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 j1 = permute(permute(permute(permute( + i.w + detail::tvec4(i1.w, i2.w, i3.w, T(1))) + + i.z + detail::tvec4(i1.z, i2.z, i3.z, T(1))) + + i.y + detail::tvec4(i1.y, i2.y, i3.y, T(1))) + + i.x + detail::tvec4(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 ip = detail::tvec4(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0)); + + detail::tvec4 p0 = grad4(j0, ip); + detail::tvec4 p1 = grad4(j1.x, ip); + detail::tvec4 p2 = grad4(j1.y, ip); + detail::tvec4 p3 = grad4(j1.z, ip); + detail::tvec4 p4 = grad4(j1.w, ip); + + // Normalise gradients + detail::tvec4 norm = taylorInvSqrt(detail::tvec4(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 m0 = max(T(0.6) - detail::tvec3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), T(0)); + detail::tvec2 m1 = max(T(0.6) - detail::tvec2(dot(x3, x3), dot(x4, x4) ), T(0)); + m0 = m0 * m0; + m1 = m1 * m1; + return T(49) * + (dot(m0 * m0, detail::tvec3(dot(p0, x0), dot(p1, x1), dot(p2, x2))) + + dot(m1 * m1, detail::tvec2(dot(p3, x3), dot(p4, x4)))); + } + + + // Classic Perlin noise + template + inline T cnoise(detail::tvec2 const & P) + { + detail::tvec4 Pi = floor(P.xyxy) + detail::tvec4(0.0, 0.0, 1.0, 1.0); + detail::tvec4 Pf = fract(P.xyxy) - detail::tvec4(0.0, 0.0, 1.0, 1.0); + Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation + detail::tvec4 ix = Pi.xzxz; + detail::tvec4 iy = Pi.yyww; + detail::tvec4 fx = Pf.xzxz; + detail::tvec4 fy = Pf.yyww; + + detail::tvec4 i = permute(permute(ix) + iy); + + detail::tvec4 gx = T(2) * fract(i / T(41)) - T(1); + detail::tvec4 gy = abs(gx) - T(0.5); + detail::tvec4 tx = floor(gx + T(0.5)); + gx = gx - tx; + + detail::tvec2 g00 = detail::tvec2(gx.x,gy.x); + detail::tvec2 g10 = detail::tvec2(gx.y,gy.y); + detail::tvec2 g01 = detail::tvec2(gx.z,gy.z); + detail::tvec2 g11 = detail::tvec2(gx.w,gy.w); + + detail::tvec4 norm = taylorInvSqrt(detail::tvec4(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(fx.x, fy.x)); + T n10 = dot(g10, detail::tvec2(fx.y, fy.y)); + T n01 = dot(g01, detail::tvec2(fx.z, fy.z)); + T n11 = dot(g11, detail::tvec2(fx.w, fy.w)); + + detail::tvec2 fade_xy = fade(Pf.xy); + detail::tvec2 n_x = mix(detail::tvec2(n00, n01), detail::tvec2(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 + inline T pnoise(detail::tvec2 const & P, detail::tvec2 const & rep) + { + detail::tvec4 Pi = floor(P.xyxy) + detail::tvec4(0.0, 0.0, 1.0, 1.0); + detail::tvec4 Pf = fract(P.xyxy) - detail::tvec4(0.0, 0.0, 1.0, 1.0); + Pi = mod(Pi, rep.xyxy); // To create noise with explicit period + Pi = mod(Pi, T(289)); // To avoid truncation effects in permutation + detail::tvec4 ix = Pi.xzxz; + detail::tvec4 iy = Pi.yyww; + detail::tvec4 fx = Pf.xzxz; + detail::tvec4 fy = Pf.yyww; + + detail::tvec4 i = permute(permute(ix) + iy); + + detail::tvec4 gx = T(2) * fract(i / T(41)) - T(1); + detail::tvec4 gy = abs(gx) - T(0.5); + detail::tvec4 tx = floor(gx + T(0.5)); + gx = gx - tx; + + detail::tvec2 g00(gx.x,gy.x); + detail::tvec2 g10(gx.y,gy.y); + detail::tvec2 g01(gx.z,gy.z); + detail::tvec2 g11(gx.w,gy.w); + + detail::tvec4 norm = taylorInvSqrt(detail::tvec4(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(fx.x, fy.x)); + T n10 = dot(g10, detail::tvec2(fx.y, fy.y)); + T n01 = dot(g01, detail::tvec2(fx.z, fy.z)); + T n11 = dot(g11, detail::tvec2(fx.w, fy.w)); + + detail::tvec2 fade_xy = fade(Pf.xy); + detail::tvec2 n_x = mix(detail::tvec2(n00, n01), detail::tvec2(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 + inline T cnoise(detail::tvec3 const & P) + { + detail::tvec3 Pi0 = floor(P); // Integer part for indexing + detail::tvec3 Pi1 = Pi0 + T(1); // Integer part + 1 + Pi0 = mod(Pi0, T(289)); + Pi1 = mod(Pi1, T(289)); + detail::tvec3 Pf0 = fract(P); // Fractional part for interpolation + detail::tvec3 Pf1 = Pf0 - T(1); // Fractional part - 1.0 + detail::tvec4 ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); + detail::tvec4 iy(Pi0.yy, Pi1.yy); + detail::tvec4 iz0(Pi0.z); + detail::tvec4 iz1(Pi1.z); + + detail::tvec4 ixy = permute(permute(ix) + iy); + detail::tvec4 ixy0 = permute(ixy + iz0); + detail::tvec4 ixy1 = permute(ixy + iz1); + + detail::tvec4 gx0 = ixy0 / T(7); + detail::tvec4 gy0 = fract(floor(gx0) / T(7)) - T(0.5); + gx0 = fract(gx0); + detail::tvec4 gz0 = detail::tvec4(0.5) - abs(gx0) - abs(gy0); + detail::tvec4 sz0 = step(gz0, detail::tvec4(0.0)); + gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); + gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); + + detail::tvec4 gx1 = ixy1 / T(7); + detail::tvec4 gy1 = fract(floor(gx1) / T(7)) - T(0.5); + gx1 = fract(gx1); + detail::tvec4 gz1 = detail::tvec4(0.5) - abs(gx1) - abs(gy1); + detail::tvec4 sz1 = step(gz1, detail::tvec4(0.0)); + gx1 -= sz1 * (step(T(0), gx1) - T(0.5)); + gy1 -= sz1 * (step(T(0), gy1) - T(0.5)); + + detail::tvec3 g000(gx0.x,gy0.x,gz0.x); + detail::tvec3 g100(gx0.y,gy0.y,gz0.y); + detail::tvec3 g010(gx0.z,gy0.z,gz0.z); + detail::tvec3 g110(gx0.w,gy0.w,gz0.w); + detail::tvec3 g001(gx1.x,gy1.x,gz1.x); + detail::tvec3 g101(gx1.y,gy1.y,gz1.y); + detail::tvec3 g011(gx1.z,gy1.z,gz1.z); + detail::tvec3 g111(gx1.w,gy1.w,gz1.w); + + detail::tvec4 norm0 = taylorInvSqrt(detail::tvec4(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 norm1 = taylorInvSqrt(detail::tvec4(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(Pf1.x, Pf0.yz)); + T n010 = dot(g010, detail::tvec3(Pf0.x, Pf1.y, Pf0.z)); + T n110 = dot(g110, detail::tvec3(Pf1.xy, Pf0.z)); + T n001 = dot(g001, detail::tvec3(Pf0.xy, Pf1.z)); + T n101 = dot(g101, detail::tvec3(Pf1.x, Pf0.y, Pf1.z)); + T n011 = dot(g011, detail::tvec3(Pf0.x, Pf1.yz)); + T n111 = dot(g111, Pf1); + + detail::tvec3 fade_xyz = fade(Pf0); + detail::tvec4 n_z = mix(detail::tvec4(n000, n100, n010, n110), detail::tvec4(n001, n101, n011, n111), fade_xyz.z); + detail::tvec2 n_yz = mix(n_z.xy, n_z.zw, 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 variant + template + inline T pnoise(detail::tvec3 const & P, detail::tvec3 const & rep) + { + detail::tvec3 Pi0 = mod(floor(P), rep); // Integer part, modulo period + detail::tvec3 Pi1 = mod(Pi0 + detail::tvec3(1.0), rep); // Integer part + 1, mod period + Pi0 = mod(Pi0, T(289)); + Pi1 = mod(Pi1, T(289)); + detail::tvec3 Pf0 = fract(P); // Fractional part for interpolation + detail::tvec3 Pf1 = Pf0 - detail::tvec3(1.0); // Fractional part - 1.0 + detail::tvec4 ix = detail::tvec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x); + detail::tvec4 iy = detail::tvec4(Pi0.yy, Pi1.yy); + detail::tvec4 iz0(Pi0.z); + detail::tvec4 iz1(Pi1.z); + + detail::tvec4 ixy = permute(permute(ix) + iy); + detail::tvec4 ixy0 = permute(ixy + iz0); + detail::tvec4 ixy1 = permute(ixy + iz1); + + detail::tvec4 gx0 = ixy0 / T(7); + detail::tvec4 gy0 = fract(floor(gx0) / T(7)) - T(0.5); + gx0 = fract(gx0); + detail::tvec4 gz0 = detail::tvec4(0.5) - abs(gx0) - abs(gy0); + detail::tvec4 sz0 = step(gz0, detail::tvec4(0)); + gx0 -= sz0 * (step(0.0, gx0) - T(0.5)); + gy0 -= sz0 * (step(0.0, gy0) - T(0.5)); + + detail::tvec4 gx1 = ixy1 / T(7); + detail::tvec4 gy1 = fract(floor(gx1) / T(7)) - T(0.5); + gx1 = fract(gx1); + detail::tvec4 gz1 = detail::tvec4(0.5) - abs(gx1) - abs(gy1); + detail::tvec4 sz1 = step(gz1, detail::tvec4(0.0)); + gx1 -= sz1 * (step(0.0, gx1) - T(0.5)); + gy1 -= sz1 * (step(0.0, gy1) - T(0.5)); + + detail::tvec3 g000 = detail::tvec3(gx0.x, gy0.x, gz0.x); + detail::tvec3 g100 = detail::tvec3(gx0.y, gy0.y, gz0.y); + detail::tvec3 g010 = detail::tvec3(gx0.z, gy0.z, gz0.z); + detail::tvec3 g110 = detail::tvec3(gx0.w, gy0.w, gz0.w); + detail::tvec3 g001 = detail::tvec3(gx1.x, gy1.x, gz1.x); + detail::tvec3 g101 = detail::tvec3(gx1.y, gy1.y, gz1.y); + detail::tvec3 g011 = detail::tvec3(gx1.z, gy1.z, gz1.z); + detail::tvec3 g111 = detail::tvec3(gx1.w, gy1.w, gz1.w); + + detail::tvec4 norm0 = taylorInvSqrt(detail::tvec4(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 norm1 = taylorInvSqrt(detail::tvec4(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(Pf1.x, Pf0.yz)); + T n010 = dot(g010, detail::tvec3(Pf0.x, Pf1.y, Pf0.z)); + T n110 = dot(g110, detail::tvec3(Pf1.xy, Pf0.z)); + T n001 = dot(g001, detail::tvec3(Pf0.xy, Pf1.z)); + T n101 = dot(g101, detail::tvec3(Pf1.x, Pf0.y, Pf1.z)); + T n011 = dot(g011, detail::tvec3(Pf0.x, Pf1.yz)); + T n111 = dot(g111, Pf1); + + detail::tvec3 fade_xyz = fade(Pf0); + detail::tvec4 n_z = mix(detail::tvec4(n000, n100, n010, n110), detail::tvec4(n001, n101, n011, n111), fade_xyz.z); + detail::tvec2 n_yz = mix(n_z.xy, n_z.zw, 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 + inline T cnoise(detail::tvec4 const & P) + { + detail::tvec4 Pi0 = floor(P); // Integer part for indexing + detail::tvec4 Pi1 = Pi0 + T(1); // Integer part + 1 + Pi0 = mod(Pi0, T(289)); + Pi1 = mod(Pi1, T(289)); + detail::tvec4 Pf0 = fract(P); // Fractional part for interpolation + detail::tvec4 Pf1 = Pf0 - T(1); // Fractional part - 1.0 + detail::tvec4 ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x); + detail::tvec4 iy(Pi0.yy, Pi1.yy); + detail::tvec4 iz0(Pi0.z); + detail::tvec4 iz1(Pi1.z); + detail::tvec4 iw0(Pi0.w); + detail::tvec4 iw1(Pi1.w); + + detail::tvec4 ixy = permute(permute(ix) + iy); + detail::tvec4 ixy0 = permute(ixy + iz0); + detail::tvec4 ixy1 = permute(ixy + iz1); + detail::tvec4 ixy00 = permute(ixy0 + iw0); + detail::tvec4 ixy01 = permute(ixy0 + iw1); + detail::tvec4 ixy10 = permute(ixy1 + iw0); + detail::tvec4 ixy11 = permute(ixy1 + iw1); + + detail::tvec4 gx00 = ixy00 / T(7); + detail::tvec4 gy00 = floor(gx00) / T(7); + detail::tvec4 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 gw00 = vec4(0.75) - abs(gx00) - abs(gy00) - abs(gz00); + detail::tvec4 sw00 = step(gw00, vec4(0.0)); + gx00 -= sw00 * (step(T(0), gx00) - T(0.5)); + gy00 -= sw00 * (step(T(0), gy00) - T(0.5)); + + detail::tvec4 gx01 = ixy01 / T(7); + detail::tvec4 gy01 = floor(gx01) / T(7); + detail::tvec4 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 gw01 = vec4(0.75) - abs(gx01) - abs(gy01) - abs(gz01); + detail::tvec4 sw01 = step(gw01, vec4(0.0)); + gx01 -= sw01 * (step(T(0), gx01) - T(0.5)); + gy01 -= sw01 * (step(T(0), gy01) - T(0.5)); + + detail::tvec4 gx10 = ixy10 / T(7); + detail::tvec4 gy10 = floor(gx10) / T(7); + detail::tvec4 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 gw10 = detail::tvec4(0.75) - abs(gx10) - abs(gy10) - abs(gz10); + detail::tvec4 sw10 = step(gw10, detail::tvec4(0)); + gx10 -= sw10 * (step(T(0), gx10) - T(0.5)); + gy10 -= sw10 * (step(T(0), gy10) - T(0.5)); + + detail::tvec4 gx11 = ixy11 / T(7); + detail::tvec4 gy11 = floor(gx11) / T(7); + detail::tvec4 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 gw11 = detail::tvec4(0.75) - abs(gx11) - abs(gy11) - abs(gz11); + detail::tvec4 sw11 = step(gw11, vec4(0.0)); + gx11 -= sw11 * (step(T(0), gx11) - T(0.5)); + gy11 -= sw11 * (step(T(0), gy11) - T(0.5)); + + detail::tvec4 g0000(gx00.x, gy00.x, gz00.x, gw00.x); + detail::tvec4 g1000(gx00.y, gy00.y, gz00.y, gw00.y); + detail::tvec4 g0100(gx00.z, gy00.z, gz00.z, gw00.z); + detail::tvec4 g1100(gx00.w, gy00.w, gz00.w, gw00.w); + detail::tvec4 g0010(gx10.x, gy10.x, gz10.x, gw10.x); + detail::tvec4 g1010(gx10.y, gy10.y, gz10.y, gw10.y); + detail::tvec4 g0110(gx10.z, gy10.z, gz10.z, gw10.z); + detail::tvec4 g1110(gx10.w, gy10.w, gz10.w, gw10.w); + detail::tvec4 g0001(gx01.x, gy01.x, gz01.x, gw01.x); + detail::tvec4 g1001(gx01.y, gy01.y, gz01.y, gw01.y); + detail::tvec4 g0101(gx01.z, gy01.z, gz01.z, gw01.z); + detail::tvec4 g1101(gx01.w, gy01.w, gz01.w, gw01.w); + detail::tvec4 g0011(gx11.x, gy11.x, gz11.x, gw11.x); + detail::tvec4 g1011(gx11.y, gy11.y, gz11.y, gw11.y); + detail::tvec4 g0111(gx11.z, gy11.z, gz11.z, gw11.z); + detail::tvec4 g1111(gx11.w, gy11.w, gz11.w, gw11.w); + + detail::tvec4 norm00 = taylorInvSqrt(detail::tvec4(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 norm01 = taylorInvSqrt(detail::tvec4(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 norm10 = taylorInvSqrt(detail::tvec4(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 norm11 = taylorInvSqrt(detail::tvec4(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(Pf1.x, Pf0.yzw)); + T n0100 = dot(g0100, detail::tvec4(Pf0.x, Pf1.y, Pf0.zw)); + T n1100 = dot(g1100, detail::tvec4(Pf1.xy, Pf0.zw)); + T n0010 = dot(g0010, detail::tvec4(Pf0.xy, Pf1.z, Pf0.w)); + T n1010 = dot(g1010, detail::tvec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); + T n0110 = dot(g0110, detail::tvec4(Pf0.x, Pf1.yz, Pf0.w)); + T n1110 = dot(g1110, detail::tvec4(Pf1.xyz, Pf0.w)); + T n0001 = dot(g0001, detail::tvec4(Pf0.xyz, Pf1.w)); + T n1001 = dot(g1001, detail::tvec4(Pf1.x, Pf0.yz, Pf1.w)); + T n0101 = dot(g0101, detail::tvec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); + T n1101 = dot(g1101, detail::tvec4(Pf1.xy, Pf0.z, Pf1.w)); + T n0011 = dot(g0011, detail::tvec4(Pf0.xy, Pf1.zw)); + T n1011 = dot(g1011, detail::tvec4(Pf1.x, Pf0.y, Pf1.zw)); + T n0111 = dot(g0111, detail::tvec4(Pf0.x, Pf1.yzw)); + T n1111 = dot(g1111, Pf1); + + detail::tvec4 fade_xyzw = fade(Pf0); + detail::tvec4 n_0w = mix(detail::tvec4(n0000, n1000, n0100, n1100), detail::tvec4(n0001, n1001, n0101, n1101), fade_xyzw.w); + detail::tvec4 n_1w = mix(detail::tvec4(n0010, n1010, n0110, n1110), detail::tvec4(n0011, n1011, n0111, n1111), fade_xyzw.w); + detail::tvec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z); + detail::tvec4 n_yzw = mix(n_zw.xy, n_zw.zw, 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 version + template + inline T pnoise(detail::tvec4 const & P, detail::tvec4 const & rep) + { + detail::tvec4 Pi0 = mod(floor(P), rep); // Integer part modulo rep + detail::tvec4 Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep + detail::tvec4 Pf0 = fract(P); // Fractional part for interpolation + detail::tvec4 Pf1 = Pf0 - T(1); // Fractional part - 1.0 + detail::tvec4 ix = detail::tvec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x); + detail::tvec4 iy = detail::tvec4(Pi0.yy, Pi1.yy); + detail::tvec4 iz0(Pi0.z); + detail::tvec4 iz1(Pi1.z); + detail::tvec4 iw0(Pi0.w); + detail::tvec4 iw1(Pi1.w); + + detail::tvec4 ixy = permute(permute(ix) + iy); + detail::tvec4 ixy0 = permute(ixy + iz0); + detail::tvec4 ixy1 = permute(ixy + iz1); + detail::tvec4 ixy00 = permute(ixy0 + iw0); + detail::tvec4 ixy01 = permute(ixy0 + iw1); + detail::tvec4 ixy10 = permute(ixy1 + iw0); + detail::tvec4 ixy11 = permute(ixy1 + iw1); + + detail::tvec4 gx00 = ixy00 / T(7); + detail::tvec4 gy00 = floor(gx00) / T(7); + detail::tvec4 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 gw00 = detail::tvec4(0.75) - abs(gx00) - abs(gy00) - abs(gz00); + detail::tvec4 sw00 = step(gw00, detail::tvec4(0)); + gx00 -= sw00 * (step(0.0, gx00) - T(0.5)); + gy00 -= sw00 * (step(0.0, gy00) - T(0.5)); + + detail::tvec4 gx01 = ixy01 / T(7); + detail::tvec4 gy01 = floor(gx01) / T(7); + detail::tvec4 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 gw01 = detail::tvec4(0.75) - abs(gx01) - abs(gy01) - abs(gz01); + detail::tvec4 sw01 = step(gw01, detail::tvec4(0.0)); + gx01 -= sw01 * (step(0.0, gx01) - T(0.5)); + gy01 -= sw01 * (step(0.0, gy01) - T(0.5)); + + detail::tvec4 gx10 = ixy10 / T(7); + detail::tvec4 gy10 = floor(gx10) / T(7); + detail::tvec4 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 gw10 = detail::tvec4(0.75) - abs(gx10) - abs(gy10) - abs(gz10); + detail::tvec4 sw10 = step(gw10, detail::tvec4(0.0)); + gx10 -= sw10 * (step(0.0, gx10) - T(0.5)); + gy10 -= sw10 * (step(0.0, gy10) - T(0.5)); + + detail::tvec4 gx11 = ixy11 / T(7); + detail::tvec4 gy11 = floor(gx11) / T(7); + detail::tvec4 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 gw11 = detail::tvec4(0.75) - abs(gx11) - abs(gy11) - abs(gz11); + detail::tvec4 sw11 = step(gw11, detail::tvec4(0.0)); + gx11 -= sw11 * (step(0.0, gx11) - T(0.5)); + gy11 -= sw11 * (step(0.0, gy11) - T(0.5)); + + detail::tvec4 g0000(gx00.x, gy00.x, gz00.x, gw00.x); + detail::tvec4 g1000(gx00.y, gy00.y, gz00.y, gw00.y); + detail::tvec4 g0100(gx00.z, gy00.z, gz00.z, gw00.z); + detail::tvec4 g1100(gx00.w, gy00.w, gz00.w, gw00.w); + detail::tvec4 g0010(gx10.x, gy10.x, gz10.x, gw10.x); + detail::tvec4 g1010(gx10.y, gy10.y, gz10.y, gw10.y); + detail::tvec4 g0110(gx10.z, gy10.z, gz10.z, gw10.z); + detail::tvec4 g1110(gx10.w, gy10.w, gz10.w, gw10.w); + detail::tvec4 g0001(gx01.x, gy01.x, gz01.x, gw01.x); + detail::tvec4 g1001(gx01.y, gy01.y, gz01.y, gw01.y); + detail::tvec4 g0101(gx01.z, gy01.z, gz01.z, gw01.z); + detail::tvec4 g1101(gx01.w, gy01.w, gz01.w, gw01.w); + detail::tvec4 g0011(gx11.x, gy11.x, gz11.x, gw11.x); + detail::tvec4 g1011(gx11.y, gy11.y, gz11.y, gw11.y); + detail::tvec4 g0111(gx11.z, gy11.z, gz11.z, gw11.z); + detail::tvec4 g1111(gx11.w, gy11.w, gz11.w, gw11.w); + + detail::tvec4 norm00 = taylorInvSqrt(detail::tvec4(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 norm01 = taylorInvSqrt(detail::tvec4(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 norm10 = taylorInvSqrt(detail::tvec4(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 norm11 = taylorInvSqrt(detail::tvec4(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(Pf1.x, Pf0.yzw)); + T n0100 = dot(g0100, detail::tvec4(Pf0.x, Pf1.y, Pf0.zw)); + T n1100 = dot(g1100, detail::tvec4(Pf1.xy, Pf0.zw)); + T n0010 = dot(g0010, detail::tvec4(Pf0.xy, Pf1.z, Pf0.w)); + T n1010 = dot(g1010, detail::tvec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w)); + T n0110 = dot(g0110, detail::tvec4(Pf0.x, Pf1.yz, Pf0.w)); + T n1110 = dot(g1110, detail::tvec4(Pf1.xyz, Pf0.w)); + T n0001 = dot(g0001, detail::tvec4(Pf0.xyz, Pf1.w)); + T n1001 = dot(g1001, detail::tvec4(Pf1.x, Pf0.yz, Pf1.w)); + T n0101 = dot(g0101, detail::tvec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w)); + T n1101 = dot(g1101, detail::tvec4(Pf1.xy, Pf0.z, Pf1.w)); + T n0011 = dot(g0011, detail::tvec4(Pf0.xy, Pf1.zw)); + T n1011 = dot(g1011, detail::tvec4(Pf1.x, Pf0.y, Pf1.zw)); + T n0111 = dot(g0111, detail::tvec4(Pf0.x, Pf1.yzw)); + T n1111 = dot(g1111, Pf1); + + detail::tvec4 fade_xyzw = fade(Pf0); + detail::tvec4 n_0w = mix(detail::tvec4(n0000, n1000, n0100, n1100), detail::tvec4(n0001, n1001, n0101, n1101), fade_xyzw.w); + detail::tvec4 n_1w = mix(detail::tvec4(n0010, n1010, n0110, n1110), detail::tvec4(n0011, n1011, n0111, n1111), fade_xyzw.w); + detail::tvec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z); + detail::tvec2 n_yzw = mix(n_zw.xy, n_zw.zw, fade_xyzw.y); + T n_xyzw = mix(n_yzw.x, n_yzw.y, fade_xyzw.x); + return T(2.2) * n_xyzw; + } }//namespace noise }//namespace gtx