1 /*
2 * Parts adapted from Open Shading Language with this license:
3 *
4 * Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
5 * All Rights Reserved.
6 *
7 * Modifications Copyright 2011, Blender Foundation.
8 *
9 * Redistribution and use in source and binary forms, with or without
10 * modification, are permitted provided that the following conditions are
11 * met:
12 * * Redistributions of source code must retain the above copyright
13 * notice, this list of conditions and the following disclaimer.
14 * * Redistributions in binary form must reproduce the above copyright
15 * notice, this list of conditions and the following disclaimer in the
16 * documentation and/or other materials provided with the distribution.
17 * * Neither the name of Sony Pictures Imageworks nor the names of its
18 * contributors may be used to endorse or promote products derived from
19 * this software without specific prior written permission.
20 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
21 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
22 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
23 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
24 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
25 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
26 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
27 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
28 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
29 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
30 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
31 */
32
33 #ifndef __KERNEL_MONTECARLO_CL__
34 #define __KERNEL_MONTECARLO_CL__
35
36 CCL_NAMESPACE_BEGIN
37
38 /* distribute uniform xy on [0,1] over unit disk [-1,1] */
to_unit_disk(float * x,float * y)39 ccl_device void to_unit_disk(float *x, float *y)
40 {
41 float phi = M_2PI_F * (*x);
42 float r = sqrtf(*y);
43
44 *x = r * cosf(phi);
45 *y = r * sinf(phi);
46 }
47
48 /* return an orthogonal tangent and bitangent given a normal and tangent that
49 * may not be exactly orthogonal */
make_orthonormals_tangent(const float3 N,const float3 T,float3 * a,float3 * b)50 ccl_device void make_orthonormals_tangent(const float3 N, const float3 T, float3 *a, float3 *b)
51 {
52 *b = normalize(cross(N, T));
53 *a = cross(*b, N);
54 }
55
56 /* sample direction with cosine weighted distributed in hemisphere */
sample_cos_hemisphere(const float3 N,float randu,float randv,float3 * omega_in,float * pdf)57 ccl_device_inline void sample_cos_hemisphere(
58 const float3 N, float randu, float randv, float3 *omega_in, float *pdf)
59 {
60 to_unit_disk(&randu, &randv);
61 float costheta = sqrtf(max(1.0f - randu * randu - randv * randv, 0.0f));
62 float3 T, B;
63 make_orthonormals(N, &T, &B);
64 *omega_in = randu * T + randv * B + costheta * N;
65 *pdf = costheta * M_1_PI_F;
66 }
67
68 /* sample direction uniformly distributed in hemisphere */
sample_uniform_hemisphere(const float3 N,float randu,float randv,float3 * omega_in,float * pdf)69 ccl_device_inline void sample_uniform_hemisphere(
70 const float3 N, float randu, float randv, float3 *omega_in, float *pdf)
71 {
72 float z = randu;
73 float r = sqrtf(max(0.0f, 1.0f - z * z));
74 float phi = M_2PI_F * randv;
75 float x = r * cosf(phi);
76 float y = r * sinf(phi);
77
78 float3 T, B;
79 make_orthonormals(N, &T, &B);
80 *omega_in = x * T + y * B + z * N;
81 *pdf = 0.5f * M_1_PI_F;
82 }
83
84 /* sample direction uniformly distributed in cone */
sample_uniform_cone(const float3 N,float angle,float randu,float randv,float3 * omega_in,float * pdf)85 ccl_device_inline void sample_uniform_cone(
86 const float3 N, float angle, float randu, float randv, float3 *omega_in, float *pdf)
87 {
88 float zMin = cosf(angle);
89 float z = zMin - zMin * randu + randu;
90 float r = safe_sqrtf(1.0f - sqr(z));
91 float phi = M_2PI_F * randv;
92 float x = r * cosf(phi);
93 float y = r * sinf(phi);
94
95 float3 T, B;
96 make_orthonormals(N, &T, &B);
97 *omega_in = x * T + y * B + z * N;
98 *pdf = M_1_2PI_F / (1.0f - zMin);
99 }
100
pdf_uniform_cone(const float3 N,float3 D,float angle)101 ccl_device_inline float pdf_uniform_cone(const float3 N, float3 D, float angle)
102 {
103 float zMin = cosf(angle);
104 float z = dot(N, D);
105 if (z > zMin) {
106 return M_1_2PI_F / (1.0f - zMin);
107 }
108 return 0.0f;
109 }
110
111 /* sample uniform point on the surface of a sphere */
sample_uniform_sphere(float u1,float u2)112 ccl_device float3 sample_uniform_sphere(float u1, float u2)
113 {
114 float z = 1.0f - 2.0f * u1;
115 float r = sqrtf(fmaxf(0.0f, 1.0f - z * z));
116 float phi = M_2PI_F * u2;
117 float x = r * cosf(phi);
118 float y = r * sinf(phi);
119
120 return make_float3(x, y, z);
121 }
122
balance_heuristic(float a,float b)123 ccl_device float balance_heuristic(float a, float b)
124 {
125 return (a) / (a + b);
126 }
127
balance_heuristic_3(float a,float b,float c)128 ccl_device float balance_heuristic_3(float a, float b, float c)
129 {
130 return (a) / (a + b + c);
131 }
132
power_heuristic(float a,float b)133 ccl_device float power_heuristic(float a, float b)
134 {
135 return (a * a) / (a * a + b * b);
136 }
137
power_heuristic_3(float a,float b,float c)138 ccl_device float power_heuristic_3(float a, float b, float c)
139 {
140 return (a * a) / (a * a + b * b + c * c);
141 }
142
max_heuristic(float a,float b)143 ccl_device float max_heuristic(float a, float b)
144 {
145 return (a > b) ? 1.0f : 0.0f;
146 }
147
148 /* distribute uniform xy on [0,1] over unit disk [-1,1], with concentric mapping
149 * to better preserve stratification for some RNG sequences */
concentric_sample_disk(float u1,float u2)150 ccl_device float2 concentric_sample_disk(float u1, float u2)
151 {
152 float phi, r;
153 float a = 2.0f * u1 - 1.0f;
154 float b = 2.0f * u2 - 1.0f;
155
156 if (a == 0.0f && b == 0.0f) {
157 return make_float2(0.0f, 0.0f);
158 }
159 else if (a * a > b * b) {
160 r = a;
161 phi = M_PI_4_F * (b / a);
162 }
163 else {
164 r = b;
165 phi = M_PI_2_F - M_PI_4_F * (a / b);
166 }
167
168 return make_float2(r * cosf(phi), r * sinf(phi));
169 }
170
171 /* sample point in unit polygon with given number of corners and rotation */
regular_polygon_sample(float corners,float rotation,float u,float v)172 ccl_device float2 regular_polygon_sample(float corners, float rotation, float u, float v)
173 {
174 /* sample corner number and reuse u */
175 float corner = floorf(u * corners);
176 u = u * corners - corner;
177
178 /* uniform sampled triangle weights */
179 u = sqrtf(u);
180 v = v * u;
181 u = 1.0f - u;
182
183 /* point in triangle */
184 float angle = M_PI_F / corners;
185 float2 p = make_float2((u + v) * cosf(angle), (u - v) * sinf(angle));
186
187 /* rotate */
188 rotation += corner * 2.0f * angle;
189
190 float cr = cosf(rotation);
191 float sr = sinf(rotation);
192
193 return make_float2(cr * p.x - sr * p.y, sr * p.x + cr * p.y);
194 }
195
ensure_valid_reflection(float3 Ng,float3 I,float3 N)196 ccl_device float3 ensure_valid_reflection(float3 Ng, float3 I, float3 N)
197 {
198 float3 R = 2 * dot(N, I) * N - I;
199
200 /* Reflection rays may always be at least as shallow as the incoming ray. */
201 float threshold = min(0.9f * dot(Ng, I), 0.01f);
202 if (dot(Ng, R) >= threshold) {
203 return N;
204 }
205
206 /* Form coordinate system with Ng as the Z axis and N inside the X-Z-plane.
207 * The X axis is found by normalizing the component of N that's orthogonal to Ng.
208 * The Y axis isn't actually needed.
209 */
210 float NdotNg = dot(N, Ng);
211 float3 X = normalize(N - NdotNg * Ng);
212
213 /* Keep math expressions. */
214 /* clang-format off */
215 /* Calculate N.z and N.x in the local coordinate system.
216 *
217 * The goal of this computation is to find a N' that is rotated towards Ng just enough
218 * to lift R' above the threshold (here called t), therefore dot(R', Ng) = t.
219 *
220 * According to the standard reflection equation,
221 * this means that we want dot(2*dot(N', I)*N' - I, Ng) = t.
222 *
223 * Since the Z axis of our local coordinate system is Ng, dot(x, Ng) is just x.z, so we get
224 * 2*dot(N', I)*N'.z - I.z = t.
225 *
226 * The rotation is simple to express in the coordinate system we formed -
227 * since N lies in the X-Z-plane, we know that N' will also lie in the X-Z-plane,
228 * so N'.y = 0 and therefore dot(N', I) = N'.x*I.x + N'.z*I.z .
229 *
230 * Furthermore, we want N' to be normalized, so N'.x = sqrt(1 - N'.z^2).
231 *
232 * With these simplifications,
233 * we get the final equation 2*(sqrt(1 - N'.z^2)*I.x + N'.z*I.z)*N'.z - I.z = t.
234 *
235 * The only unknown here is N'.z, so we can solve for that.
236 *
237 * The equation has four solutions in general:
238 *
239 * N'.z = +-sqrt(0.5*(+-sqrt(I.x^2*(I.x^2 + I.z^2 - t^2)) + t*I.z + I.x^2 + I.z^2)/(I.x^2 + I.z^2))
240 * We can simplify this expression a bit by grouping terms:
241 *
242 * a = I.x^2 + I.z^2
243 * b = sqrt(I.x^2 * (a - t^2))
244 * c = I.z*t + a
245 * N'.z = +-sqrt(0.5*(+-b + c)/a)
246 *
247 * Two solutions can immediately be discarded because they're negative so N' would lie in the
248 * lower hemisphere.
249 */
250 /* clang-format on */
251
252 float Ix = dot(I, X), Iz = dot(I, Ng);
253 float Ix2 = sqr(Ix), Iz2 = sqr(Iz);
254 float a = Ix2 + Iz2;
255
256 float b = safe_sqrtf(Ix2 * (a - sqr(threshold)));
257 float c = Iz * threshold + a;
258
259 /* Evaluate both solutions.
260 * In many cases one can be immediately discarded (if N'.z would be imaginary or larger than
261 * one), so check for that first. If no option is viable (might happen in extreme cases like N
262 * being in the wrong hemisphere), give up and return Ng. */
263 float fac = 0.5f / a;
264 float N1_z2 = fac * (b + c), N2_z2 = fac * (-b + c);
265 bool valid1 = (N1_z2 > 1e-5f) && (N1_z2 <= (1.0f + 1e-5f));
266 bool valid2 = (N2_z2 > 1e-5f) && (N2_z2 <= (1.0f + 1e-5f));
267
268 float2 N_new;
269 if (valid1 && valid2) {
270 /* If both are possible, do the expensive reflection-based check. */
271 float2 N1 = make_float2(safe_sqrtf(1.0f - N1_z2), safe_sqrtf(N1_z2));
272 float2 N2 = make_float2(safe_sqrtf(1.0f - N2_z2), safe_sqrtf(N2_z2));
273
274 float R1 = 2 * (N1.x * Ix + N1.y * Iz) * N1.y - Iz;
275 float R2 = 2 * (N2.x * Ix + N2.y * Iz) * N2.y - Iz;
276
277 valid1 = (R1 >= 1e-5f);
278 valid2 = (R2 >= 1e-5f);
279 if (valid1 && valid2) {
280 /* If both solutions are valid, return the one with the shallower reflection since it will be
281 * closer to the input (if the original reflection wasn't shallow, we would not be in this
282 * part of the function). */
283 N_new = (R1 < R2) ? N1 : N2;
284 }
285 else {
286 /* If only one reflection is valid (= positive), pick that one. */
287 N_new = (R1 > R2) ? N1 : N2;
288 }
289 }
290 else if (valid1 || valid2) {
291 /* Only one solution passes the N'.z criterium, so pick that one. */
292 float Nz2 = valid1 ? N1_z2 : N2_z2;
293 N_new = make_float2(safe_sqrtf(1.0f - Nz2), safe_sqrtf(Nz2));
294 }
295 else {
296 return Ng;
297 }
298
299 return N_new.x * X + N_new.y * Ng;
300 }
301
302 CCL_NAMESPACE_END
303
304 #endif /* __KERNEL_MONTECARLO_CL__ */
305