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stegustegu
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Updated to version 2021-12-02 across all variants
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‎src/psrddnoise2.glsl

+99-100
Original file line numberDiff line numberDiff line change
@@ -3,7 +3,7 @@
33
//
44
// Authors: Stefan Gustavson ([email protected])
55
// and Ian McEwan ([email protected])
6-
// Version 2021-11-04, published under the MIT license (see below)
6+
// Version 2021-12-02, published under the MIT license (see below)
77
//
88
// Copyright (c) 2021 Stefan Gustavson and Ian McEwan.
99
//
@@ -56,10 +56,9 @@
5656
// and "out vec3 dg" returns the second order derivatives as
5757
// dg = (dn2/dx2, dn2/dy2, dn2/dxy)
5858
//
59-
// Setting both periods to 0.0 or a negative value will skip the periodic
60-
// wrap and make the function execute 10% faster. If you want periodicity
61-
// for one dimensions but not the other, set the period to 0.0 only for
62-
// one of the dimensions. In that case, there is no significant speedup.
59+
// Setting either period to 0.0 or a negative value will skip the wrapping
60+
// along that dimension. Setting both periods to 0.0 makes the function
61+
// execute about 10% faster.
6362
//
6463
// Not using the return value for some or all of the first or second order
6564
// derivatives will make the compiler eliminate the code for computing them.
@@ -70,99 +69,99 @@
7069
// of psrddnoise(), setting alpha == 0.0 gives no speedup.
7170
//
7271
float psrddnoise(vec2 x, vec2 period, float alpha, out vec2 gradient,
73-
out vec3 dg) {
74-
75-
// Transform to simplex space (axis-aligned hexagonal grid)
76-
vec2 uv = vec2(x.x + x.y*0.5, x.y);
77-
78-
// Determine which simplex we're in, with i0 being the "base"
79-
vec2 i0 = floor(uv);
80-
vec2 f0 = fract(uv);
81-
// o1 is the offset in simplex space to the second corner
82-
float cmp = step(f0.y, f0.x);
83-
vec2 o1 = vec2(cmp, 1.0-cmp);
84-
85-
// Enumerate the remaining simplex corners
86-
vec2 i1 = i0 + o1;
87-
vec2 i2 = i0 + vec2(1.0, 1.0);
88-
89-
// Transform corners back to texture space
90-
vec2 v0 = vec2(i0.x - i0.y * 0.5, i0.y);
91-
vec2 v1 = vec2(v0.x + o1.x - o1.y * 0.5, v0.y + o1.y);
92-
vec2 v2 = vec2(v0.x + 0.5, v0.y + 1.0);
93-
94-
// Compute vectors from v to each of the simplex corners
95-
vec2 x0 = x - v0;
96-
vec2 x1 = x - v1;
97-
vec2 x2 = x - v2;
98-
99-
vec3 iu, iv;
100-
vec3 xw, yw;
101-
102-
// Wrap to periods, if desired
103-
if(any(greaterThan(period, vec2(0.0)))) {
104-
xw = vec3(v0.x, v1.x, v2.x);
105-
yw = vec3(v0.y, v1.y, v2.y);
106-
if(period.x > 0.0)
107-
xw = mod(vec3(v0.x, v1.x, v2.x), period.x);
108-
if(period.y > 0.0)
109-
yw = mod(vec3(v0.y, v1.y, v2.y), period.y);
110-
// Transform back to simplex space and fix rounding errors
111-
iu = floor(xw + 0.5*yw + 0.5);
112-
iv = floor(yw + 0.5);
113-
} else { // Shortcut if neither x nor y periods are specified
114-
iu = vec3(i0.x, i1.x, i2.x);
115-
iv = vec3(i0.y, i1.y, i2.y);
116-
}
117-
118-
// Compute one pseudo-random hash value for each corner
119-
vec3 hash = mod(iu, 289.0);
120-
hash = mod((hash*51.0 + 2.0)*hash + iv, 289.0);
121-
hash = mod((hash*34.0 + 10.0)*hash, 289.0);
122-
123-
// Pick a pseudo-random angle and add the desired rotation
124-
vec3 psi = hash * 0.07482 + alpha;
125-
vec3 gx = cos(psi);
126-
vec3 gy = sin(psi);
127-
128-
// Reorganize for dot products below
129-
vec2 g0 = vec2(gx.x,gy.x);
130-
vec2 g1 = vec2(gx.y,gy.y);
131-
vec2 g2 = vec2(gx.z,gy.z);
132-
133-
// Radial decay with distance from each simplex corner
134-
vec3 w = 0.8 - vec3(dot(x0, x0), dot(x1, x1), dot(x2, x2));
135-
w = max(w, 0.0);
136-
vec3 w2 = w * w;
137-
vec3 w4 = w2 * w2;
138-
139-
// The value of the linear ramp from each of the corners
140-
vec3 gdotx = vec3(dot(g0, x0), dot(g1, x1), dot(g2, x2));
141-
142-
// Multiply by the radial decay and sum up the noise value
143-
float n = dot(w4, gdotx);
144-
145-
// Compute the first order partial derivatives
146-
vec3 w3 = w2 * w;
147-
vec3 dw = -8.0 * w3 * gdotx;
148-
vec2 dn0 = w4.x * g0 + dw.x * x0;
149-
vec2 dn1 = w4.y * g1 + dw.y * x1;
150-
vec2 dn2 = w4.z * g2 + dw.z * x2;
151-
gradient = 10.9 * (dn0 + dn1 + dn2);
152-
153-
// Compute the second order partial derivatives
154-
vec3 dg0, dg1, dg2;
155-
vec3 dw2 = 48.0 * w2 * gdotx;
156-
// d2n/dx2 and d2n/dy2
157-
dg0.xy = dw2.x * x0 * x0 - 8.0 * w3.x * (2.0 * g0 * x0 + gdotx.x);
158-
dg1.xy = dw2.y * x1 * x1 - 8.0 * w3.y * (2.0 * g1 * x1 + gdotx.y);
159-
dg2.xy = dw2.z * x2 * x2 - 8.0 * w3.z * (2.0 * g2 * x2 + gdotx.z);
160-
// d2n/dxy
161-
dg0.z = dw2.x * x0.x * x0.y - 8.0 * w3.x * dot(g0, x0.yx);
162-
dg1.z = dw2.y * x1.x * x1.y - 8.0 * w3.y * dot(g1, x1.yx);
163-
dg2.z = dw2.z * x2.x * x2.y - 8.0 * w3.z * dot(g2, x2.yx);
164-
dg = 10.9 * (dg0 + dg1 + dg2);
165-
166-
// Scale the return value to fit nicely into the range [-1,1]
167-
return 10.9 * n;
72+
out vec3 dg) {
73+
74+
// Transform to simplex space (axis-aligned hexagonal grid)
75+
vec2 uv = vec2(x.x + x.y*0.5, x.y);
76+
77+
// Determine which simplex we're in, with i0 being the "base"
78+
vec2 i0 = floor(uv);
79+
vec2 f0 = fract(uv);
80+
// o1 is the offset in simplex space to the second corner
81+
float cmp = step(f0.y, f0.x);
82+
vec2 o1 = vec2(cmp, 1.0-cmp);
83+
84+
// Enumerate the remaining simplex corners
85+
vec2 i1 = i0 + o1;
86+
vec2 i2 = i0 + vec2(1.0, 1.0);
87+
88+
// Transform corners back to texture space
89+
vec2 v0 = vec2(i0.x - i0.y * 0.5, i0.y);
90+
vec2 v1 = vec2(v0.x + o1.x - o1.y * 0.5, v0.y + o1.y);
91+
vec2 v2 = vec2(v0.x + 0.5, v0.y + 1.0);
92+
93+
// Compute vectors from v to each of the simplex corners
94+
vec2 x0 = x - v0;
95+
vec2 x1 = x - v1;
96+
vec2 x2 = x - v2;
97+
98+
vec3 iu, iv;
99+
vec3 xw, yw;
100+
101+
// Wrap to periods, if desired
102+
if(any(greaterThan(period, vec2(0.0)))) {
103+
xw = vec3(v0.x, v1.x, v2.x);
104+
yw = vec3(v0.y, v1.y, v2.y);
105+
if(period.x > 0.0)
106+
xw = mod(vec3(v0.x, v1.x, v2.x), period.x);
107+
if(period.y > 0.0)
108+
yw = mod(vec3(v0.y, v1.y, v2.y), period.y);
109+
// Transform back to simplex space and fix rounding errors
110+
iu = floor(xw + 0.5*yw + 0.5);
111+
iv = floor(yw + 0.5);
112+
} else { // Shortcut if neither x nor y periods are specified
113+
iu = vec3(i0.x, i1.x, i2.x);
114+
iv = vec3(i0.y, i1.y, i2.y);
115+
}
116+
117+
// Compute one pseudo-random hash value for each corner
118+
vec3 hash = mod(iu, 289.0);
119+
hash = mod((hash*51.0 + 2.0)*hash + iv, 289.0);
120+
hash = mod((hash*34.0 + 10.0)*hash, 289.0);
121+
122+
// Pick a pseudo-random angle and add the desired rotation
123+
vec3 psi = hash * 0.07482 + alpha;
124+
vec3 gx = cos(psi);
125+
vec3 gy = sin(psi);
126+
127+
// Reorganize for dot products below
128+
vec2 g0 = vec2(gx.x,gy.x);
129+
vec2 g1 = vec2(gx.y,gy.y);
130+
vec2 g2 = vec2(gx.z,gy.z);
131+
132+
// Radial decay with distance from each simplex corner
133+
vec3 w = 0.8 - vec3(dot(x0, x0), dot(x1, x1), dot(x2, x2));
134+
w = max(w, 0.0);
135+
vec3 w2 = w * w;
136+
vec3 w4 = w2 * w2;
137+
138+
// The value of the linear ramp from each of the corners
139+
vec3 gdotx = vec3(dot(g0, x0), dot(g1, x1), dot(g2, x2));
140+
141+
// Multiply by the radial decay and sum up the noise value
142+
float n = dot(w4, gdotx);
143+
144+
// Compute the first order partial derivatives
145+
vec3 w3 = w2 * w;
146+
vec3 dw = -8.0 * w3 * gdotx;
147+
vec2 dn0 = w4.x * g0 + dw.x * x0;
148+
vec2 dn1 = w4.y * g1 + dw.y * x1;
149+
vec2 dn2 = w4.z * g2 + dw.z * x2;
150+
gradient = 10.9 * (dn0 + dn1 + dn2);
151+
152+
// Compute the second order partial derivatives
153+
vec3 dg0, dg1, dg2;
154+
vec3 dw2 = 48.0 * w2 * gdotx;
155+
// d2n/dx2 and d2n/dy2
156+
dg0.xy = dw2.x * x0 * x0 - 8.0 * w3.x * (2.0 * g0 * x0 + gdotx.x);
157+
dg1.xy = dw2.y * x1 * x1 - 8.0 * w3.y * (2.0 * g1 * x1 + gdotx.y);
158+
dg2.xy = dw2.z * x2 * x2 - 8.0 * w3.z * (2.0 * g2 * x2 + gdotx.z);
159+
// d2n/dxy
160+
dg0.z = dw2.x * x0.x * x0.y - 8.0 * w3.x * dot(g0, x0.yx);
161+
dg1.z = dw2.y * x1.x * x1.y - 8.0 * w3.y * dot(g1, x1.yx);
162+
dg2.z = dw2.z * x2.x * x2.y - 8.0 * w3.z * dot(g2, x2.yx);
163+
dg = 10.9 * (dg0 + dg1 + dg2);
164+
165+
// Scale the return value to fit nicely into the range [-1,1]
166+
return 10.9 * n;
168167
}

‎src/psrddnoise3.glsl

+22-17
Original file line numberDiff line numberDiff line change
@@ -3,7 +3,7 @@
33
//
44
// Authors: Stefan Gustavson ([email protected])
55
// and Ian McEwan ([email protected])
6-
// Version 2021-11-04, published under the MIT license (see below)
6+
// Version 2021-12-02, published under the MIT license (see below)
77
//
88
// Copyright (c) 2021 Stefan Gustavson and Ian McEwan.
99
//
@@ -84,12 +84,9 @@ vec4 permute(vec4 i) {
8484
// (This speedup will not happen if FASTROTATION is enabled. Do not specify
8585
// FASTROTATION if you are not actually going to use the rotation.)
8686
//
87-
// Setting any period to 0.0 or a negative value will skip the wrapping
88-
// and make the function execute about 10% faster. If you want periodicity
89-
// for some dimensions but not others, set the period to 289.0 (288.0
90-
// if using the "Perlin" grid orientation) rather than 0.0 for the
91-
// dimensions where you don't want any specific periodicity. In that
92-
// case, there is no speedup.
87+
// Setting any period to 0.0 or a negative value will skip the periodic
88+
// wrap for that dimension. Setting all periods to 0.0 makes the function
89+
// execute about 10% faster.
9390
//
9491
// Not using the return values for the first or second order derivatives
9592
// will make the compiler eliminate the code for computing that value.
@@ -165,25 +162,33 @@ float psrddnoise(vec3 x, vec3 period, float alpha, out vec3 gradient,
165162
vec3 x2 = x - v2;
166163
vec3 x3 = x - v3;
167164

168-
if(all(greaterThan(period, vec3(0.0)))) {
165+
if(any(greaterThan(period, vec3(0.0)))) {
169166
// Wrap to periods and transform back to simplex space
167+
vec4 vx = vec4(v0.x, v1.x, v2.x, v3.x);
168+
vec4 vy = vec4(v0.y, v1.y, v2.y, v3.y);
169+
vec4 vz = vec4(v0.z, v1.z, v2.z, v3.z);
170+
// Wrap to periods where specified
171+
if(period.x > 0.0) vx = mod(vx, period.x);
172+
if(period.y > 0.0) vy = mod(vy, period.y);
173+
if(period.z > 0.0) vz = mod(vz, period.z);
174+
// Transform back
170175
#ifndef PERLINGRID
171-
i0 = M * mod(v0, period);
172-
i1 = M * mod(v1, period);
173-
i2 = M * mod(v2, period);
174-
i3 = M * mod(v3, period);
176+
i0 = M * vec3(vx.x, vy.x, vz.x);
177+
i1 = M * vec3(vx.y, vy.y, vz.y);
178+
i2 = M * vec3(vx.z, vy.z, vz.z);
179+
i3 = M * vec3(vx.w, vy.w, vz.w);
175180
#else
176-
v0 = mod(v0, period);
177-
v1 = mod(v1, period);
178-
v2 = mod(v2, period);
179-
v3 = mod(v3, period);
181+
v0 = vec3(vx.x, vy.x, vz.x);
182+
v1 = vec3(vx.y, vy.y, vz.y);
183+
v2 = vec3(vx.z, vy.z, vz.z);
184+
v3 = vec3(vx.w, vy.w, vz.w);
180185
// Transform wrapped coordinates back to uvw
181186
i0 = v0 + dot(v0, vec3(1.0/3.0));
182187
i1 = v1 + dot(v1, vec3(1.0/3.0));
183188
i2 = v2 + dot(v2, vec3(1.0/3.0));
184189
i3 = v3 + dot(v3, vec3(1.0/3.0));
185190
#endif
186-
// Fix any rounding errors in the transformations
191+
// Fix rounding errors
187192
i0 = floor(i0 + 0.5);
188193
i1 = floor(i1 + 0.5);
189194
i2 = floor(i2 + 0.5);

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