diff options
Diffstat (limited to 'intern/cycles/kernel/closure/bsdf_microfacet.h')
| -rw-r--r-- | intern/cycles/kernel/closure/bsdf_microfacet.h | 193 |
1 files changed, 64 insertions, 129 deletions
diff --git a/intern/cycles/kernel/closure/bsdf_microfacet.h b/intern/cycles/kernel/closure/bsdf_microfacet.h index 71086f2e764..6a50bbed3b3 100644 --- a/intern/cycles/kernel/closure/bsdf_microfacet.h +++ b/intern/cycles/kernel/closure/bsdf_microfacet.h @@ -35,79 +35,7 @@ CCL_NAMESPACE_BEGIN -/* Approximate erf and erfinv implementations. - * Implementation comes straight from Wikipedia: - * - * http://en.wikipedia.org/wiki/Error_function - * - * Some constants are baked into the code. - */ - -ccl_device_inline float approx_erff_do(float x) -{ - /* Such a clamp doesn't give much distortion to the output value - * and gives quite a few of the speedup. - */ - if(x > 3.0f) { - return 1.0f; - } - float t = 1.0f / (1.0f + 0.47047f*x); - return (1.0f - - t*(0.3480242f + t*(-0.0958798f + t*0.7478556f)) * expf(-x*x)); -} - -ccl_device_inline float approx_erff(float x) -{ - if(x >= 0.0f) { - return approx_erff_do(x); - } - else { - return -approx_erff_do(-x); - } -} - -ccl_device_inline float approx_erfinvf_do(float x) -{ - if(x <= 0.7f) { - const float x2 = x * x; - const float a1 = 0.886226899f; - const float a2 = -1.645349621f; - const float a3 = 0.914624893f; - const float a4 = -0.140543331f; - const float b1 = -2.118377725f; - const float b2 = 1.442710462f; - const float b3 = -0.329097515f; - const float b4 = 0.012229801f; - return x * (((a4 * x2 + a3) * x2 + a2) * x2 + a1) / - ((((b4 * x2 + b3) * x2 + b2) * x2 + b1) * x2 + 1.0f); - } - else { - const float c1 = -1.970840454f; - const float c2 = -1.624906493f; - const float c3 = 3.429567803f; - const float c4 = 1.641345311f; - const float d1 = 3.543889200f; - const float d2 = 1.637067800f; - const float z = sqrtf(-logf((1.0f - x) * 0.5f)); - return (((c4 * z + c3) * z + c2) * z + c1) / - ((d2 * z + d1) * z + 1.0f); - } -} - -ccl_device_inline float approx_erfinvf(float x) -{ - if(x >= 0.0f) { - return approx_erfinvf_do(x); - } - else { - return -approx_erfinvf_do(-x); - } -} - -/* Beckmann and GGX microfacet importance sampling from: - * - * Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals. - * E. Heitz and E. d'Eon, EGSR 2014 */ +/* Beckmann and GGX microfacet importance sampling. */ ccl_device_inline void microfacet_beckmann_sample_slopes( KernelGlobals *kg, @@ -128,64 +56,71 @@ ccl_device_inline void microfacet_beckmann_sample_slopes( /* precomputations */ const float tan_theta_i = sin_theta_i/cos_theta_i; const float inv_a = tan_theta_i; - const float a = 1.0f/inv_a; - const float erf_a = approx_erff(a); - const float exp_a2 = expf(-a*a); + const float cot_theta_i = 1.0f/tan_theta_i; + const float erf_a = fast_erff(cot_theta_i); + const float exp_a2 = expf(-cot_theta_i*cot_theta_i); const float SQRT_PI_INV = 0.56418958354f; const float Lambda = 0.5f*(erf_a - 1.0f) + (0.5f*SQRT_PI_INV)*(exp_a2*inv_a); const float G1 = 1.0f/(1.0f + Lambda); /* masking */ *G1i = G1; -#if 0 - const float C = 1.0f - G1 * erf_a; - - /* sample slope X */ - if(randu < C) { - /* rescale randu */ - randu = randu / C; - const float w_1 = 0.5f * SQRT_PI_INV * sin_theta_i * exp_a2; - const float w_2 = cos_theta_i * (0.5f - 0.5f*erf_a); - const float p = w_1 / (w_1 + w_2); +#if defined(__KERNEL_GPU__) + /* Based on paper from Wenzel Jakob + * An Improved Visible Normal Sampling Routine for the Beckmann Distribution + * + * http://www.mitsuba-renderer.org/~wenzel/files/visnormal.pdf + * + * Reformulation from OpenShadingLanguage which avoids using inverse + * trigonometric functions. + */ - if(randu < p) { - randu = randu / p; - *slope_x = -sqrtf(-logf(randu*exp_a2)); - } - else { - randu = (randu - p) / (1.0f - p); - *slope_x = approx_erfinvf(randu - 1.0f - randu*erf_a); - } + /* Sample slope X. + * + * Compute a coarse approximation using the approximation: + * exp(-ierf(x)^2) ~= 1 - x * x + * solve y = 1 + b + K * (1 - b * b) + */ + float K = tan_theta_i * SQRT_PI_INV; + float y_approx = randu * (1.0f + erf_a + K * (1 - erf_a * erf_a)); + float y_exact = randu * (1.0f + erf_a + K * exp_a2); + float b = K > 0 ? (0.5f - sqrtf(K * (K - y_approx + 1.0f) + 0.25f)) / K : y_approx - 1.0f; + + /* Perform newton step to refine toward the true root. */ + float inv_erf = fast_ierff(b); + float value = 1.0f + b + K * expf(-inv_erf * inv_erf) - y_exact; + /* Check if we are close enough already, + * this also avoids NaNs as we get close to the root. + */ + if(fabsf(value) > 1e-6f) { + b -= value / (1.0f - inv_erf * tan_theta_i); /* newton step 1. */ + inv_erf = fast_ierff(b); + value = 1.0f + b + K * expf(-inv_erf * inv_erf) - y_exact; + b -= value / (1.0f - inv_erf * tan_theta_i); /* newton step 2. */ + /* Compute the slope from the refined value. */ + *slope_x = fast_ierff(b); } else { - /* rescale randu */ - randu = (randu - C) / (1.0f - C); - *slope_x = approx_erfinvf((-1.0f + 2.0f*randu)*erf_a); - - const float p = (-(*slope_x)*sin_theta_i + cos_theta_i) / (2.0f*cos_theta_i); - - if(randv > p) { - *slope_x = -(*slope_x); - randv = (randv - p) / (1.0f - p); - } - else - randv = randv / p; + /* We are close enough already. */ + *slope_x = inv_erf; } - - /* sample slope Y */ - *slope_y = approx_erfinvf(2.0f*randv - 1.0f); + *slope_y = fast_ierff(2.0f*randv - 1.0f); #else - /* use precomputed table, because it better preserves stratification - * of the random number pattern */ + /* Use precomputed table on CPU, it gives better perfomance. */ int beckmann_table_offset = kernel_data.tables.beckmann_offset; *slope_x = lookup_table_read_2D(kg, randu, cos_theta_i, beckmann_table_offset, BECKMANN_TABLE_SIZE, BECKMANN_TABLE_SIZE); - *slope_y = approx_erfinvf(2.0f*randv - 1.0f); + *slope_y = fast_ierff(2.0f*randv - 1.0f); #endif - } +/* GGX microfacet importance sampling from: + * + * Importance Sampling Microfacet-Based BSDFs using the Distribution of Visible Normals. + * E. Heitz and E. d'Eon, EGSR 2014 + */ + ccl_device_inline void microfacet_ggx_sample_slopes( const float cos_theta_i, const float sin_theta_i, float randu, float randv, float *slope_x, float *slope_y, @@ -300,7 +235,7 @@ ccl_device_inline float3 microfacet_sample_stretched( ccl_device int bsdf_microfacet_ggx_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ + sc->data0 = saturate(sc->data0); /* alpha_x */ sc->data1 = sc->data0; /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_GGX_ID; @@ -310,8 +245,8 @@ ccl_device int bsdf_microfacet_ggx_setup(ShaderClosure *sc) ccl_device int bsdf_microfacet_ggx_aniso_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ - sc->data1 = clamp(sc->data1, 0.0f, 1.0f); /* alpha_y */ + sc->data0 = saturate(sc->data0); /* alpha_x */ + sc->data1 = saturate(sc->data1); /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_GGX_ANISO_ID; @@ -320,7 +255,7 @@ ccl_device int bsdf_microfacet_ggx_aniso_setup(ShaderClosure *sc) ccl_device int bsdf_microfacet_ggx_refraction_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ + sc->data0 = saturate(sc->data0); /* alpha_x */ sc->data1 = sc->data0; /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_GGX_REFRACTION_ID; @@ -342,7 +277,7 @@ ccl_device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderClosure *sc, cons float3 N = sc->N; if(m_refractive || fmaxf(alpha_x, alpha_y) <= 1e-4f) - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); float cosNO = dot(N, I); float cosNI = dot(N, omega_in); @@ -421,7 +356,7 @@ ccl_device float3 bsdf_microfacet_ggx_eval_reflect(const ShaderClosure *sc, cons return make_float3(out, out, out); } - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); } ccl_device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf) @@ -433,13 +368,13 @@ ccl_device float3 bsdf_microfacet_ggx_eval_transmit(const ShaderClosure *sc, con float3 N = sc->N; if(!m_refractive || fmaxf(alpha_x, alpha_y) <= 1e-4f) - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); float cosNO = dot(N, I); float cosNI = dot(N, omega_in); if(cosNO <= 0 || cosNI >= 0) - return make_float3(0, 0, 0); /* vectors on same side -- not possible */ + return make_float3(0.0f, 0.0f, 0.0f); /* vectors on same side -- not possible */ /* compute half-vector of the refraction (eq. 16) */ float3 ht = -(m_eta * omega_in + I); @@ -653,7 +588,7 @@ ccl_device int bsdf_microfacet_ggx_sample(KernelGlobals *kg, const ShaderClosure ccl_device int bsdf_microfacet_beckmann_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ + sc->data0 = saturate(sc->data0); /* alpha_x */ sc->data1 = sc->data0; /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ID; @@ -662,8 +597,8 @@ ccl_device int bsdf_microfacet_beckmann_setup(ShaderClosure *sc) ccl_device int bsdf_microfacet_beckmann_aniso_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ - sc->data1 = clamp(sc->data1, 0.0f, 1.0f); /* alpha_y */ + sc->data0 = saturate(sc->data0); /* alpha_x */ + sc->data1 = saturate(sc->data1); /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_ANISO_ID; return SD_BSDF|SD_BSDF_HAS_EVAL; @@ -671,7 +606,7 @@ ccl_device int bsdf_microfacet_beckmann_aniso_setup(ShaderClosure *sc) ccl_device int bsdf_microfacet_beckmann_refraction_setup(ShaderClosure *sc) { - sc->data0 = clamp(sc->data0, 0.0f, 1.0f); /* alpha_x */ + sc->data0 = saturate(sc->data0); /* alpha_x */ sc->data1 = sc->data0; /* alpha_y */ sc->type = CLOSURE_BSDF_MICROFACET_BECKMANN_REFRACTION_ID; @@ -692,7 +627,7 @@ ccl_device float3 bsdf_microfacet_beckmann_eval_reflect(const ShaderClosure *sc, float3 N = sc->N; if(m_refractive || fmaxf(alpha_x, alpha_y) <= 1e-4f) - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); float cosNO = dot(N, I); float cosNI = dot(N, omega_in); @@ -774,7 +709,7 @@ ccl_device float3 bsdf_microfacet_beckmann_eval_reflect(const ShaderClosure *sc, return make_float3(out, out, out); } - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); } ccl_device float3 bsdf_microfacet_beckmann_eval_transmit(const ShaderClosure *sc, const float3 I, const float3 omega_in, float *pdf) @@ -786,13 +721,13 @@ ccl_device float3 bsdf_microfacet_beckmann_eval_transmit(const ShaderClosure *sc float3 N = sc->N; if(!m_refractive || fmaxf(alpha_x, alpha_y) <= 1e-4f) - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); float cosNO = dot(N, I); float cosNI = dot(N, omega_in); if(cosNO <= 0 || cosNI >= 0) - return make_float3(0, 0, 0); + return make_float3(0.0f, 0.0f, 0.0f); /* compute half-vector of the refraction (eq. 16) */ float3 ht = -(m_eta * omega_in + I); |