Cycles: Implement an area preserving parameterization sampling for area lamps
Replace old code for area lamps which was more like incorrect with more correct one using the following paper as a reference: Carlos Urena et al. An Area-Preserving Parametrization for Spherical Rectangles. https://www.solidangle.com/research/egsr2013_spherical_rectangle.pdf Implementation is straight from the paper, currently the rectangle constants are calculated for each of the samples. Ideally we need to pre-calculate them. Some comparison images are available there http://wiki.blender.org/index.php/Dev:Ref/Release_Notes/2.73/Cycles Reviewers: brecht, juicyfruit Subscribers: dingto, ton Differential Revision: https://developer.blender.org/D823
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@ -167,12 +167,137 @@ ccl_device float3 sphere_light_sample(float3 P, float3 center, float radius, flo
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return disk_light_sample(normalize(P - center), randu, randv)*radius;
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}
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ccl_device float3 area_light_sample(float3 axisu, float3 axisv, float randu, float randv)
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/* Uses the following paper:
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*
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* Carlos Urena et al.
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* An Area-Preserving Parametrization for Spherical Rectangles.
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*
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* https://www.solidangle.com/research/egsr2013_spherical_rectangle.pdf
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*/
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ccl_device float3 area_light_sample(float3 P,
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float3 light_p,
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float3 axisu, float3 axisv,
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float randu, float randv,
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float *pdf)
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{
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randu = randu - 0.5f;
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randv = randv - 0.5f;
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/* In our name system we're using P for the center,
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* which is o in the paper.
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*/
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return axisu*randu + axisv*randv;
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float3 corner = light_p - axisu * 0.5f - axisv * 0.5f;
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float axisu_len, axisv_len;
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/* Compute local reference system R. */
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float3 x = normalize_len(axisu, &axisu_len);
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float3 y = normalize_len(axisv, &axisv_len);
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float3 z = cross(x, y);
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/* Compute rectangle coords in local reference system. */
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float3 dir = corner - P;
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float z0 = dot(dir, z);
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/* Flip 'z' to make it point against Q. */
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if(z0 > 0.0f) {
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z *= -1.0f;
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z0 *= -1.0f;
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}
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float z0sq = z0 * z0;
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float x0 = dot(dir, x);
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float y0 = dot(dir, y);
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float x1 = x0 + axisu_len;
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float y1 = y0 + axisv_len;
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float y0sq = y0 * y0;
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float y1sq = y1 * y1;
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/* Create vectors to four vertices. */
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float3 v00 = make_float3(x0, y0, z0);
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float3 v01 = make_float3(x0, y1, z0);
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float3 v10 = make_float3(x1, y0, z0);
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float3 v11 = make_float3(x1, y1, z0);
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/* Compute normals to edges. */
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float3 n0 = normalize(cross(v00, v10));
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float3 n1 = normalize(cross(v10, v11));
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float3 n2 = normalize(cross(v11, v01));
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float3 n3 = normalize(cross(v01, v00));
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/* Compute internal angles (gamma_i). */
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float g0 = acosf(-dot(n0, n1));
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float g1 = acosf(-dot(n1, n2));
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float g2 = acosf(-dot(n2, n3));
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float g3 = acosf(-dot(n3, n0));
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/* Compute predefined constants. */
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float b0 = n0.z;
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float b1 = n2.z;
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float b0sq = b0 * b0;
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float k = M_2PI_F - g2 - g3;
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/* Compute solid angle from internal angles. */
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float S = g0 + g1 - k;
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/* Compute cu. */
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float au = randu * S + k;
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float fu = (cosf(au) * b0 - b1) / sinf(au);
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float cu = 1.0f / sqrtf(fu * fu + b0sq) * (fu > 0.0f ? 1.0f : -1.0f);
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cu = clamp(cu, -1.0f, 1.0f);
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/* Compute xu. */
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float xu = -(cu * z0) / sqrtf(1.0f - cu * cu);
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xu = clamp(xu, x0, x1);
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/* Compute yv. */
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float d = sqrtf(xu * xu + z0sq);
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float h0 = y0 / sqrtf(d * d + y0sq);
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float h1 = y1 / sqrtf(d * d + y1sq);
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float hv = h0 + randv * (h1 - h0), hv2 = hv * hv;
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float yv = (hv2 < 1.0f - 1e-6f) ? (hv * d) / sqrtf(1.0f - hv2) : y1;
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*pdf = 1.0f / S;
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/* Transform (xu, yv, z0) to world coords. */
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return P + xu * x + yv * y + z0 * z;
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}
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/* TODO(sergey): This is actually a duplicated code from above, but how to avoid
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* this without having some nasty function with loads of parameters?
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*/
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ccl_device float area_light_pdf(float3 P,
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float3 light_p,
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float3 axisu, float3 axisv)
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{
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/* In our name system we're using P for the center,
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* which is o in the paper.
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*/
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float3 corner = light_p - axisu * 0.5f - axisv * 0.5f;
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float axisu_len, axisv_len;
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/* Compute local reference system R. */
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float3 x = normalize_len(axisu, &axisu_len);
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float3 y = normalize_len(axisv, &axisv_len);
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float3 z = cross(x, y);
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/* Compute rectangle coords in local reference system. */
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float3 dir = corner - P;
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float z0 = dot(dir, z);
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/* Flip 'z' to make it point against Q. */
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if(z0 > 0.0f) {
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z *= -1.0f;
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z0 *= -1.0f;
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}
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float x0 = dot(dir, x);
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float y0 = dot(dir, y);
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float x1 = x0 + axisu_len;
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float y1 = y0 + axisv_len;
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/* Create vectors to four vertices. */
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float3 v00 = make_float3(x0, y0, z0);
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float3 v01 = make_float3(x0, y1, z0);
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float3 v10 = make_float3(x1, y0, z0);
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float3 v11 = make_float3(x1, y1, z0);
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/* Compute normals to edges. */
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float3 n0 = normalize(cross(v00, v10));
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float3 n1 = normalize(cross(v10, v11));
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float3 n2 = normalize(cross(v11, v01));
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float3 n3 = normalize(cross(v01, v00));
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/* Compute internal angles (gamma_i). */
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float g0 = acosf(-dot(n0, n1));
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float g1 = acosf(-dot(n1, n2));
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float g2 = acosf(-dot(n2, n3));
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float g3 = acosf(-dot(n3, n0));
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/* Compute predefined constants. */
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float k = M_2PI_F - g2 - g3;
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/* Compute solid angle from internal angles. */
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float S = g0 + g1 - k;
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return 1.0f / S;
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}
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ccl_device float spot_light_attenuation(float4 data1, float4 data2, LightSample *ls)
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@ -276,6 +401,7 @@ ccl_device void lamp_light_sample(KernelGlobals *kg, int lamp,
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float4 data2 = kernel_tex_fetch(__light_data, lamp*LIGHT_SIZE + 2);
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ls->eval_fac *= spot_light_attenuation(data1, data2, ls);
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}
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ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
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}
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else {
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/* area light */
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@ -286,18 +412,22 @@ ccl_device void lamp_light_sample(KernelGlobals *kg, int lamp,
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float3 axisv = make_float3(data2.y, data2.z, data2.w);
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float3 D = make_float3(data3.y, data3.z, data3.w);
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ls->P += area_light_sample(axisu, axisv, randu, randv);
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ls->P = area_light_sample(P, ls->P,
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axisu, axisv,
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randu, randv,
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&ls->pdf);
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ls->Ng = D;
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ls->D = normalize_len(ls->P - P, &ls->t);
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float invarea = data2.x;
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ls->eval_fac = 0.25f*invarea;
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ls->pdf = invarea;
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if(dot(ls->D, D) > 0.0f)
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ls->pdf = 0.0f;
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}
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ls->eval_fac *= kernel_data.integrator.inv_pdf_lights;
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ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
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}
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}
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@ -355,8 +485,12 @@ ccl_device bool lamp_light_eval(KernelGlobals *kg, int lamp, float3 P, float3 D,
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ls->D = D;
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ls->t = FLT_MAX;
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/* compute pdf */
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float invarea = data1.w;
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ls->pdf = invarea/(costheta*costheta*costheta);
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if(ls->t != FLT_MAX)
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ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
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ls->eval_fac = ls->pdf;
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}
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else if(type == LIGHT_POINT || type == LIGHT_SPOT) {
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@ -386,6 +520,10 @@ ccl_device bool lamp_light_eval(KernelGlobals *kg, int lamp, float3 P, float3 D,
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if(ls->eval_fac == 0.0f)
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return false;
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}
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/* compute pdf */
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if(ls->t != FLT_MAX)
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ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
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}
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else if(type == LIGHT_AREA) {
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/* area light */
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@ -412,16 +550,12 @@ ccl_device bool lamp_light_eval(KernelGlobals *kg, int lamp, float3 P, float3 D,
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ls->D = D;
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ls->Ng = Ng;
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ls->pdf = invarea;
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ls->eval_fac = 0.25f*ls->pdf;
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ls->pdf = area_light_pdf(P, ls->P, axisu, axisv);
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ls->eval_fac = 0.25f*invarea;
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}
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else
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return false;
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/* compute pdf */
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if(ls->t != FLT_MAX)
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ls->pdf *= lamp_light_pdf(kg, ls->Ng, -ls->D, ls->t);
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return true;
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}
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