CS计算机代考程序代写 ///////////////////////////////////////////////////////////////////////////////////

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 – 2015 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
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/// 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.
///
/// Restrictions:
/// By making use of the Software for military purposes, you choose to make
/// a Bunny unhappy.
///
/// 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{
namespace gtc
{
template
GLM_FUNC_QUALIFIER tvec4 grad4(T const & j, tvec4 const & ip)
{
tvec3 pXYZ = floor(fract(tvec3(j) * tvec3(ip)) * T(7)) * ip[2] – T(1);
T pW = static_cast(1.5) – dot(abs(pXYZ), tvec3(1));
tvec4 s = tvec4(lessThan(tvec4(pXYZ, pW), tvec4(0.0)));
pXYZ = pXYZ + (tvec3(s) * T(2) – T(1)) * s.w;
return tvec4(pXYZ, pW);
}
}//namespace gtc

// Classic Perlin noise
template
GLM_FUNC_QUALIFIER T perlin(tvec2 const & Position)
{
tvec4 Pi = glm::floor(tvec4(Position.x, Position.y, Position.x, Position.y)) + tvec4(0.0, 0.0, 1.0, 1.0);
tvec4 Pf = glm::fract(tvec4(Position.x, Position.y, Position.x, Position.y)) – tvec4(0.0, 0.0, 1.0, 1.0);
Pi = mod(Pi, tvec4(289)); // To avoid truncation effects in permutation
tvec4 ix(Pi.x, Pi.z, Pi.x, Pi.z);
tvec4 iy(Pi.y, Pi.y, Pi.w, Pi.w);
tvec4 fx(Pf.x, Pf.z, Pf.x, Pf.z);
tvec4 fy(Pf.y, Pf.y, Pf.w, Pf.w);

tvec4 i = detail::permute(detail::permute(ix) + iy);

tvec4 gx = static_cast(2) * glm::fract(i / T(41)) – T(1);
tvec4 gy = glm::abs(gx) – T(0.5);
tvec4 tx = glm::floor(gx + T(0.5));
gx = gx – tx;

tvec2 g00(gx.x, gy.x);
tvec2 g10(gx.y, gy.y);
tvec2 g01(gx.z, gy.z);
tvec2 g11(gx.w, gy.w);

tvec4 norm = detail::taylorInvSqrt(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, tvec2(fx.x, fy.x));
T n10 = dot(g10, tvec2(fx.y, fy.y));
T n01 = dot(g01, tvec2(fx.z, fy.z));
T n11 = dot(g11, tvec2(fx.w, fy.w));

tvec2 fade_xy = detail::fade(tvec2(Pf.x, Pf.y));
tvec2 n_x = mix(tvec2(n00, n01), 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
GLM_FUNC_QUALIFIER T perlin(tvec3 const & Position)
{
tvec3 Pi0 = floor(Position); // Integer part for indexing
tvec3 Pi1 = Pi0 + T(1); // Integer part + 1
Pi0 = detail::mod289(Pi0);
Pi1 = detail::mod289(Pi1);
tvec3 Pf0 = fract(Position); // Fractional part for interpolation
tvec3 Pf1 = Pf0 – T(1); // Fractional part – 1.0
tvec4 ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
tvec4 iy = tvec4(tvec2(Pi0.y), tvec2(Pi1.y));
tvec4 iz0(Pi0.z);
tvec4 iz1(Pi1.z);

tvec4 ixy = detail::permute(detail::permute(ix) + iy);
tvec4 ixy0 = detail::permute(ixy + iz0);
tvec4 ixy1 = detail::permute(ixy + iz1);

tvec4 gx0 = ixy0 * T(1.0 / 7.0);
tvec4 gy0 = fract(floor(gx0) * T(1.0 / 7.0)) – T(0.5);
gx0 = fract(gx0);
tvec4 gz0 = tvec4(0.5) – abs(gx0) – abs(gy0);
tvec4 sz0 = step(gz0, tvec4(0.0));
gx0 -= sz0 * (step(T(0), gx0) – T(0.5));
gy0 -= sz0 * (step(T(0), gy0) – T(0.5));

tvec4 gx1 = ixy1 * T(1.0 / 7.0);
tvec4 gy1 = fract(floor(gx1) * T(1.0 / 7.0)) – T(0.5);
gx1 = fract(gx1);
tvec4 gz1 = tvec4(0.5) – abs(gx1) – abs(gy1);
tvec4 sz1 = step(gz1, tvec4(0.0));
gx1 -= sz1 * (step(T(0), gx1) – T(0.5));
gy1 -= sz1 * (step(T(0), gy1) – T(0.5));

tvec3 g000(gx0.x, gy0.x, gz0.x);
tvec3 g100(gx0.y, gy0.y, gz0.y);
tvec3 g010(gx0.z, gy0.z, gz0.z);
tvec3 g110(gx0.w, gy0.w, gz0.w);
tvec3 g001(gx1.x, gy1.x, gz1.x);
tvec3 g101(gx1.y, gy1.y, gz1.y);
tvec3 g011(gx1.z, gy1.z, gz1.z);
tvec3 g111(gx1.w, gy1.w, gz1.w);

tvec4 norm0 = detail::taylorInvSqrt(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;
tvec4 norm1 = detail::taylorInvSqrt(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, tvec3(Pf1.x, Pf0.y, Pf0.z));
T n010 = dot(g010, tvec3(Pf0.x, Pf1.y, Pf0.z));
T n110 = dot(g110, tvec3(Pf1.x, Pf1.y, Pf0.z));
T n001 = dot(g001, tvec3(Pf0.x, Pf0.y, Pf1.z));
T n101 = dot(g101, tvec3(Pf1.x, Pf0.y, Pf1.z));
T n011 = dot(g011, tvec3(Pf0.x, Pf1.y, Pf1.z));
T n111 = dot(g111, Pf1);

tvec3 fade_xyz = detail::fade(Pf0);
tvec4 n_z = mix(tvec4(n000, n100, n010, n110), tvec4(n001, n101, n011, n111), fade_xyz.z);
tvec2 n_yz = mix(tvec2(n_z.x, n_z.y), tvec2(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
GLM_FUNC_QUALIFIER T perlin(tvec3 const & P)
{
tvec3 Pi0 = floor(P); // Integer part for indexing
tvec3 Pi1 = Pi0 + T(1); // Integer part + 1
Pi0 = mod(Pi0, T(289));
Pi1 = mod(Pi1, T(289));
tvec3 Pf0 = fract(P); // Fractional part for interpolation
tvec3 Pf1 = Pf0 – T(1); // Fractional part – 1.0
tvec4 ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
tvec4 iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
tvec4 iz0(Pi0.z);
tvec4 iz1(Pi1.z);

tvec4 ixy = permute(permute(ix) + iy);
tvec4 ixy0 = permute(ixy + iz0);
tvec4 ixy1 = permute(ixy + iz1);

tvec4 gx0 = ixy0 / T(7);
tvec4 gy0 = fract(floor(gx0) / T(7)) – T(0.5);
gx0 = fract(gx0);
tvec4 gz0 = tvec4(0.5) – abs(gx0) – abs(gy0);
tvec4 sz0 = step(gz0, tvec4(0.0));
gx0 -= sz0 * (step(0.0, gx0) – T(0.5));
gy0 -= sz0 * (step(0.0, gy0) – T(0.5));

tvec4 gx1 = ixy1 / T(7);
tvec4 gy1 = fract(floor(gx1) / T(7)) – T(0.5);
gx1 = fract(gx1);
tvec4 gz1 = tvec4(0.5) – abs(gx1) – abs(gy1);
tvec4 sz1 = step(gz1, tvec4(0.0));
gx1 -= sz1 * (step(T(0), gx1) – T(0.5));
gy1 -= sz1 * (step(T(0), gy1) – T(0.5));

tvec4 norm0 = taylorInvSqrt(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;
tvec4 norm1 = taylorInvSqrt(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;

tvec3 fade_xyz = fade(Pf0);
tvec4 n_z = mix(tvec4(n000, n100, n010, n110), tvec4(n001, n101, n011, n111), fade_xyz.z);
tvec2 n_yz = mix(
tvec2(n_z.x, n_z.y),
tvec2(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
GLM_FUNC_QUALIFIER T perlin(tvec4 const & Position)
{
tvec4 Pi0 = floor(Position); // Integer part for indexing
tvec4 Pi1 = Pi0 + T(1); // Integer part + 1
Pi0 = mod(Pi0, tvec4(289));
Pi1 = mod(Pi1, tvec4(289));
tvec4 Pf0 = fract(Position); // Fractional part for interpolation
tvec4 Pf1 = Pf0 – T(1); // Fractional part – 1.0
tvec4 ix(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
tvec4 iy(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
tvec4 iz0(Pi0.z);
tvec4 iz1(Pi1.z);
tvec4 iw0(Pi0.w);
tvec4 iw1(Pi1.w);

tvec4 ixy = detail::permute(detail::permute(ix) + iy);
tvec4 ixy0 = detail::permute(ixy + iz0);
tvec4 ixy1 = detail::permute(ixy + iz1);
tvec4 ixy00 = detail::permute(ixy0 + iw0);
tvec4 ixy01 = detail::permute(ixy0 + iw1);
tvec4 ixy10 = detail::permute(ixy1 + iw0);
tvec4 ixy11 = detail::permute(ixy1 + iw1);

tvec4 gx00 = ixy00 / T(7);
tvec4 gy00 = floor(gx00) / T(7);
tvec4 gz00 = floor(gy00) / T(6);
gx00 = fract(gx00) – T(0.5);
gy00 = fract(gy00) – T(0.5);
gz00 = fract(gz00) – T(0.5);
tvec4 gw00 = tvec4(0.75) – abs(gx00) – abs(gy00) – abs(gz00);
tvec4 sw00 = step(gw00, tvec4(0.0));
gx00 -= sw00 * (step(T(0), gx00) – T(0.5));
gy00 -= sw00 * (step(T(0), gy00) – T(0.5));

tvec4 gx01 = ixy01 / T(7);
tvec4 gy01 = floor(gx01) / T(7);
tvec4 gz01 = floor(gy01) / T(6);
gx01 = fract(gx01) – T(0.5);
gy01 = fract(gy01) – T(0.5);
gz01 = fract(gz01) – T(0.5);
tvec4 gw01 = tvec4(0.75) – abs(gx01) – abs(gy01) – abs(gz01);
tvec4 sw01 = step(gw01, tvec4(0.0));
gx01 -= sw01 * (step(T(0), gx01) – T(0.5));
gy01 -= sw01 * (step(T(0), gy01) – T(0.5));

tvec4 gx10 = ixy10 / T(7);
tvec4 gy10 = floor(gx10) / T(7);
tvec4 gz10 = floor(gy10) / T(6);
gx10 = fract(gx10) – T(0.5);
gy10 = fract(gy10) – T(0.5);
gz10 = fract(gz10) – T(0.5);
tvec4 gw10 = tvec4(0.75) – abs(gx10) – abs(gy10) – abs(gz10);
tvec4 sw10 = step(gw10, tvec4(0));
gx10 -= sw10 * (step(T(0), gx10) – T(0.5));
gy10 -= sw10 * (step(T(0), gy10) – T(0.5));

tvec4 gx11 = ixy11 / T(7);
tvec4 gy11 = floor(gx11) / T(7);
tvec4 gz11 = floor(gy11) / T(6);
gx11 = fract(gx11) – T(0.5);
gy11 = fract(gy11) – T(0.5);
gz11 = fract(gz11) – T(0.5);
tvec4 gw11 = tvec4(0.75) – abs(gx11) – abs(gy11) – abs(gz11);
tvec4 sw11 = step(gw11, tvec4(0.0));
gx11 -= sw11 * (step(T(0), gx11) – T(0.5));
gy11 -= sw11 * (step(T(0), gy11) – T(0.5));

tvec4 g0000(gx00.x, gy00.x, gz00.x, gw00.x);
tvec4 g1000(gx00.y, gy00.y, gz00.y, gw00.y);
tvec4 g0100(gx00.z, gy00.z, gz00.z, gw00.z);
tvec4 g1100(gx00.w, gy00.w, gz00.w, gw00.w);
tvec4 g0010(gx10.x, gy10.x, gz10.x, gw10.x);
tvec4 g1010(gx10.y, gy10.y, gz10.y, gw10.y);
tvec4 g0110(gx10.z, gy10.z, gz10.z, gw10.z);
tvec4 g1110(gx10.w, gy10.w, gz10.w, gw10.w);
tvec4 g0001(gx01.x, gy01.x, gz01.x, gw01.x);
tvec4 g1001(gx01.y, gy01.y, gz01.y, gw01.y);
tvec4 g0101(gx01.z, gy01.z, gz01.z, gw01.z);
tvec4 g1101(gx01.w, gy01.w, gz01.w, gw01.w);
tvec4 g0011(gx11.x, gy11.x, gz11.x, gw11.x);
tvec4 g1011(gx11.y, gy11.y, gz11.y, gw11.y);
tvec4 g0111(gx11.z, gy11.z, gz11.z, gw11.z);
tvec4 g1111(gx11.w, gy11.w, gz11.w, gw11.w);

tvec4 norm00 = detail::taylorInvSqrt(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;

tvec4 norm01 = detail::taylorInvSqrt(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;

tvec4 norm10 = detail::taylorInvSqrt(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;

tvec4 norm11 = detail::taylorInvSqrt(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, tvec4(Pf1.x, Pf0.y, Pf0.z, Pf0.w));
T n0100 = dot(g0100, tvec4(Pf0.x, Pf1.y, Pf0.z, Pf0.w));
T n1100 = dot(g1100, tvec4(Pf1.x, Pf1.y, Pf0.z, Pf0.w));
T n0010 = dot(g0010, tvec4(Pf0.x, Pf0.y, Pf1.z, Pf0.w));
T n1010 = dot(g1010, tvec4(Pf1.x, Pf0.y, Pf1.z, Pf0.w));
T n0110 = dot(g0110, tvec4(Pf0.x, Pf1.y, Pf1.z, Pf0.w));
T n1110 = dot(g1110, tvec4(Pf1.x, Pf1.y, Pf1.z, Pf0.w));
T n0001 = dot(g0001, tvec4(Pf0.x, Pf0.y, Pf0.z, Pf1.w));
T n1001 = dot(g1001, tvec4(Pf1.x, Pf0.y, Pf0.z, Pf1.w));
T n0101 = dot(g0101, tvec4(Pf0.x, Pf1.y, Pf0.z, Pf1.w));
T n1101 = dot(g1101, tvec4(Pf1.x, Pf1.y, Pf0.z, Pf1.w));
T n0011 = dot(g0011, tvec4(Pf0.x, Pf0.y, Pf1.z, Pf1.w));
T n1011 = dot(g1011, tvec4(Pf1.x, Pf0.y, Pf1.z, Pf1.w));
T n0111 = dot(g0111, tvec4(Pf0.x, Pf1.y, Pf1.z, Pf1.w));
T n1111 = dot(g1111, Pf1);

tvec4 fade_xyzw = detail::fade(Pf0);
tvec4 n_0w = mix(tvec4(n0000, n1000, n0100, n1100), tvec4(n0001, n1001, n0101, n1101), fade_xyzw.w);
tvec4 n_1w = mix(tvec4(n0010, n1010, n0110, n1110), tvec4(n0011, n1011, n0111, n1111), fade_xyzw.w);
tvec4 n_zw = mix(n_0w, n_1w, fade_xyzw.z);
tvec2 n_yzw = mix(tvec2(n_zw.x, n_zw.y), tvec2(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
GLM_FUNC_QUALIFIER T perlin(tvec2 const & Position, tvec2 const & rep)
{
tvec4 Pi = floor(tvec4(Position.x, Position.y, Position.x, Position.y)) + tvec4(0.0, 0.0, 1.0, 1.0);
tvec4 Pf = fract(tvec4(Position.x, Position.y, Position.x, Position.y)) – tvec4(0.0, 0.0, 1.0, 1.0);
Pi = mod(Pi, tvec4(rep.x, rep.y, rep.x, rep.y)); // To create noise with explicit period
Pi = mod(Pi, tvec4(289)); // To avoid truncation effects in permutation
tvec4 ix(Pi.x, Pi.z, Pi.x, Pi.z);
tvec4 iy(Pi.y, Pi.y, Pi.w, Pi.w);
tvec4 fx(Pf.x, Pf.z, Pf.x, Pf.z);
tvec4 fy(Pf.y, Pf.y, Pf.w, Pf.w);

tvec4 i = detail::permute(detail::permute(ix) + iy);

tvec4 gx = static_cast(2) * fract(i / T(41)) – T(1);
tvec4 gy = abs(gx) – T(0.5);
tvec4 tx = floor(gx + T(0.5));
gx = gx – tx;

tvec2 g00(gx.x, gy.x);
tvec2 g10(gx.y, gy.y);
tvec2 g01(gx.z, gy.z);
tvec2 g11(gx.w, gy.w);

tvec4 norm = detail::taylorInvSqrt(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, tvec2(fx.x, fy.x));
T n10 = dot(g10, tvec2(fx.y, fy.y));
T n01 = dot(g01, tvec2(fx.z, fy.z));
T n11 = dot(g11, tvec2(fx.w, fy.w));

tvec2 fade_xy = detail::fade(tvec2(Pf.x, Pf.y));
tvec2 n_x = mix(tvec2(n00, n01), 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
GLM_FUNC_QUALIFIER T perlin(tvec3 const & Position, tvec3 const & rep)
{
tvec3 Pi0 = mod(floor(Position), rep); // Integer part, modulo period
tvec3 Pi1 = mod(Pi0 + tvec3(T(1)), rep); // Integer part + 1, mod period
Pi0 = mod(Pi0, tvec3(289));
Pi1 = mod(Pi1, tvec3(289));
tvec3 Pf0 = fract(Position); // Fractional part for interpolation
tvec3 Pf1 = Pf0 – tvec3(T(1)); // Fractional part – 1.0
tvec4 ix = tvec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
tvec4 iy = tvec4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
tvec4 iz0(Pi0.z);
tvec4 iz1(Pi1.z);

tvec4 ixy = detail::permute(detail::permute(ix) + iy);
tvec4 ixy0 = detail::permute(ixy + iz0);
tvec4 ixy1 = detail::permute(ixy + iz1);

tvec4 gx0 = ixy0 / T(7);
tvec4 gy0 = fract(floor(gx0) / T(7)) – T(0.5);
gx0 = fract(gx0);
tvec4 gz0 = tvec4(0.5) – abs(gx0) – abs(gy0);
tvec4 sz0 = step(gz0, tvec4(0));
gx0 -= sz0 * (step(T(0), gx0) – T(0.5));
gy0 -= sz0 * (step(T(0), gy0) – T(0.5));

tvec4 gx1 = ixy1 / T(7);
tvec4 gy1 = fract(floor(gx1) / T(7)) – T(0.5);
gx1 = fract(gx1);
tvec4 gz1 = tvec4(0.5) – abs(gx1) – abs(gy1);
tvec4 sz1 = step(gz1, tvec4(T(0)));
gx1 -= sz1 * (step(T(0), gx1) – T(0.5));
gy1 -= sz1 * (step(T(0), gy1) – T(0.5));

tvec3 g000 = tvec3(gx0.x, gy0.x, gz0.x);
tvec3 g100 = tvec3(gx0.y, gy0.y, gz0.y);
tvec3 g010 = tvec3(gx0.z, gy0.z, gz0.z);
tvec3 g110 = tvec3(gx0.w, gy0.w, gz0.w);
tvec3 g001 = tvec3(gx1.x, gy1.x, gz1.x);
tvec3 g101 = tvec3(gx1.y, gy1.y, gz1.y);
tvec3 g011 = tvec3(gx1.z, gy1.z, gz1.z);
tvec3 g111 = tvec3(gx1.w, gy1.w, gz1.w);

// Classic Perlin noise, periodic version
template
GLM_FUNC_QUALIFIER T perlin(tvec4 const & Position, tvec4 const & rep)
{
tvec4 Pi0 = mod(floor(Position), rep); // Integer part modulo rep
tvec4 Pi1 = mod(Pi0 + T(1), rep); // Integer part + 1 mod rep
tvec4 Pf0 = fract(Position); // Fractional part for interpolation
tvec4 Pf1 = Pf0 – T(1); // Fractional part – 1.0
tvec4 ix = tvec4(Pi0.x, Pi1.x, Pi0.x, Pi1.x);
tvec4 iy = tvec4(Pi0.y, Pi0.y, Pi1.y, Pi1.y);
tvec4 iz0(Pi0.z);
tvec4 iz1(Pi1.z);
tvec4 iw0(Pi0.w);
tvec4 iw1(Pi1.w);

tvec4 gx00 = ixy00 / T(7);
tvec4 gy00 = floor(gx00) / T(7);
tvec4 gz00 = floor(gy00) / T(6);
gx00 = fract(gx00) – T(0.5);
gy00 = fract(gy00) – T(0.5);
gz00 = fract(gz00) – T(0.5);
tvec4 gw00 = tvec4(0.75) – abs(gx00) – abs(gy00) – abs(gz00);
tvec4 sw00 = step(gw00, tvec4(0));
gx00 -= sw00 * (step(T(0), gx00) – T(0.5));
gy00 -= sw00 * (step(T(0), gy00) – T(0.5));

tvec4 gx10 = ixy10 / T(7);
tvec4 gy10 = floor(gx10) / T(7);
tvec4 gz10 = floor(gy10) / T(6);
gx10 = fract(gx10) – T(0.5);
gy10 = fract(gy10) – T(0.5);
gz10 = fract(gz10) – T(0.5);
tvec4 gw10 = tvec4(0.75) – abs(gx10) – abs(gy10) – abs(gz10);
tvec4 sw10 = step(gw10, tvec4(0.0));
gx10 -= sw10 * (step(T(0), gx10) – T(0.5));
gy10 -= sw10 * (step(T(0), gy10) – T(0.5));

tvec4 gx11 = ixy11 / T(7);
tvec4 gy11 = floor(gx11) / T(7);
tvec4 gz11 = floor(gy11) / T(6);
gx11 = fract(gx11) – T(0.5);
gy11 = fract(gy11) – T(0.5);
gz11 = fract(gz11) – T(0.5);
tvec4 gw11 = tvec4(0.75) – abs(gx11) – abs(gy11) – abs(gz11);
tvec4 sw11 = step(gw11, tvec4(T(0)));
gx11 -= sw11 * (step(T(0), gx11) – T(0.5));
gy11 -= sw11 * (step(T(0), gy11) – T(0.5));

tvec4 norm00 = detail::taylorInvSqrt(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;

tvec4 norm01 = detail::taylorInvSqrt(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;

tvec4 norm10 = detail::taylorInvSqrt(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;

tvec4 norm11 = detail::taylorInvSqrt(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;

template
GLM_FUNC_QUALIFIER T simplex(glm::tvec2 const & v)
{
tvec4 const C = tvec4(
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 i = floor(v + dot(v, tvec2(C[1])));
tvec2 x0 = v – i + dot(i, tvec2(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 i1 = (x0.x > x0.y) ? tvec2(1, 0) : tvec2(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 x12 = tvec4(x0.x, x0.y, x0.x, x0.y) + tvec4(C.x, C.x, C.z, C.z);
x12 = tvec4(tvec2(x12) – i1, x12.z, x12.w);

// Permutations
i = mod(i, tvec2(289)); // Avoid truncation effects in permutation
tvec3 p = detail::permute(
detail::permute(i.y + tvec3(T(0), i1.y, T(1)))
+ i.x + tvec3(T(0), i1.x, T(1)));

tvec3 m = max(tvec3(0.5) – tvec3(
dot(x0, x0),
dot(tvec2(x12.x, x12.y), tvec2(x12.x, x12.y)),
dot(tvec2(x12.z, x12.w), tvec2(x12.z, x12.w))), tvec3(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 x = static_cast(2) * fract(p * C.w) – T(1);
tvec3 h = abs(x) – T(0.5);
tvec3 ox = floor(x + T(0.5));
tvec3 a0 = x – ox;

// Normalise gradients implicitly by scaling m
// Inlined for speed: m *= taylorInvSqrt( a0*a0 + h*h );
m *= static_cast(1.79284291400159) – T(0.85373472095314) * (a0 * a0 + h * h);

// Compute final noise value at P
tvec3 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
GLM_FUNC_QUALIFIER T simplex(tvec3 const & v)
{
tvec2 const C(1.0 / 6.0, 1.0 / 3.0);
tvec4 const D(0.0, 0.5, 1.0, 2.0);

// First corner
tvec3 i(floor(v + dot(v, tvec3(C.y))));
tvec3 x0(v – i + dot(i, tvec3(C.x)));

// Other corners
tvec3 g(step(tvec3(x0.y, x0.z, x0.x), x0));
tvec3 l(T(1) – g);
tvec3 i1(min(g, tvec3(l.z, l.x, l.y)));
tvec3 i2(max(g, tvec3(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 x1(x0 – i1 + C.x);
tvec3 x2(x0 – i2 + C.y); // 2.0*C.x = 1/3 = C.y
tvec3 x3(x0 – D.y); // -1.0+3.0*C.x = -0.5 = -D.y

// Permutations
i = detail::mod289(i);
tvec4 p(detail::permute(detail::permute(detail::permute(
i.z + tvec4(T(0), i1.z, i2.z, T(1))) +
i.y + tvec4(T(0), i1.y, i2.y, T(1))) +
i.x + tvec4(T(0), i1.x, i2.x, T(1))));

// Gradients: 7×7 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(0.142857142857); // 1.0/7.0
tvec3 ns(n_ * tvec3(D.w, D.y, D.z) – tvec3(D.x, D.z, D.x));

tvec4 j(p – T(49) * floor(p * ns.z * ns.z)); // mod(p,7*7)

tvec4 x_(floor(j * ns.z));
tvec4 y_(floor(j – T(7) * x_)); // mod(j,N)

tvec4 x(x_ * ns.x + ns.y);
tvec4 y(y_ * ns.x + ns.y);
tvec4 h(T(1) – abs(x) – abs(y));

tvec4 b0(x.x, x.y, y.x, y.y);
tvec4 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 s0(floor(b0) * T(2) + T(1));
tvec4 s1(floor(b1) * T(2) + T(1));
tvec4 sh(-step(h, tvec4(0.0)));

tvec4 a0 = tvec4(b0.x, b0.z, b0.y, b0.w) + tvec4(s0.x, s0.z, s0.y, s0.w) * tvec4(sh.x, sh.x, sh.y, sh.y);
tvec4 a1 = tvec4(b1.x, b1.z, b1.y, b1.w) + tvec4(s1.x, s1.z, s1.y, s1.w) * tvec4(sh.z, sh.z, sh.w, sh.w);

tvec3 p0(a0.x, a0.y, h.x);
tvec3 p1(a0.z, a0.w, h.y);
tvec3 p2(a1.x, a1.y, h.z);
tvec3 p3(a1.z, a1.w, h.w);

// Normalise gradients
tvec4 norm = detail::taylorInvSqrt(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;

// Mix final noise value
tvec4 m = max(T(0.6) – tvec4(dot(x0, x0), dot(x1, x1), dot(x2, x2), dot(x3, x3)), tvec4(0));
m = m * m;
return T(42) * dot(m * m, tvec4(dot(p0, x0), dot(p1, x1), dot(p2, x2), dot(p3, x3)));
}

template
GLM_FUNC_QUALIFIER T simplex(tvec4 const & v)
{
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 = static_cast(0.309016994374947451);

// First corner
tvec4 i = floor(v + dot(v, vec4(F4)));
tvec4 x0 = v – i + dot(i, vec4(C.x));

// Other corners

// Rank sorting originally contributed by Bill Licea-Kane, AMD (formerly ATI)
tvec4 i0;
tvec3 isX = step(tvec3(x0.y, x0.z, x0.w), tvec3(x0.x));
tvec3 isYZ = step(tvec3(x0.z, x0.w, x0.w), tvec3(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(1) – isX;
i0 = tvec4(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(isYZ.x, isYZ.y);
i0.z += static_cast(1) – isYZ.x;
i0.w += static_cast(1) – isYZ.y;
i0.z += isYZ.z;
i0.w += static_cast(1) – isYZ.z;

// i0 now contains the unique values 0,1,2,3 in each channel
tvec4 i3 = clamp(i0, T(0), T(1));
tvec4 i2 = clamp(i0 – T(1), T(0), T(1));
tvec4 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 x1 = x0 – i1 + C.x;
tvec4 x2 = x0 – i2 + C.y;
tvec4 x3 = x0 – i3 + C.z;
tvec4 x4 = x0 + C.w;

// Permutations
i = mod(i, tvec4(289));
T j0 = detail::permute(detail::permute(detail::permute(detail::permute(i.w) + i.z) + i.y) + i.x);
tvec4 j1 = detail::permute(detail::permute(detail::permute(detail::permute(
i.w + tvec4(i1.w, i2.w, i3.w, T(1))) +
i.z + tvec4(i1.z, i2.z, i3.z, T(1))) +
i.y + tvec4(i1.y, i2.y, i3.y, T(1))) +
i.x + 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.
tvec4 ip = tvec4(T(1) / T(294), T(1) / T(49), T(1) / T(7), T(0));

tvec4 p0 = gtc::grad4(j0, ip);
tvec4 p1 = gtc::grad4(j1.x, ip);
tvec4 p2 = gtc::grad4(j1.y, ip);
tvec4 p3 = gtc::grad4(j1.z, ip);
tvec4 p4 = gtc::grad4(j1.w, ip);

// Normalise gradients
tvec4 norm = detail::taylorInvSqrt(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 *= detail::taylorInvSqrt(dot(p4, p4));

// Mix contributions from the five corners
tvec3 m0 = max(T(0.6) – tvec3(dot(x0, x0), dot(x1, x1), dot(x2, x2)), tvec3(0));
tvec2 m1 = max(T(0.6) – tvec2(dot(x3, x3), dot(x4, x4) ), tvec2(0));
m0 = m0 * m0;
m1 = m1 * m1;
return T(49) *
(dot(m0 * m0, tvec3(dot(p0, x0), dot(p1, x1), dot(p2, x2))) +
dot(m1 * m1, tvec2(dot(p3, x3), dot(p4, x4))));
}
}//namespace glm

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