diff options
Diffstat (limited to 'intern/cycles/kernel/kernel_montecarlo.h')
-rw-r--r-- | intern/cycles/kernel/kernel_montecarlo.h | 117 |
1 files changed, 97 insertions, 20 deletions
diff --git a/intern/cycles/kernel/kernel_montecarlo.h b/intern/cycles/kernel/kernel_montecarlo.h index ba25c0e24e4..ce37bd0b15e 100644 --- a/intern/cycles/kernel/kernel_montecarlo.h +++ b/intern/cycles/kernel/kernel_montecarlo.h @@ -195,31 +195,108 @@ ccl_device float2 regular_polygon_sample(float corners, float rotation, float u, ccl_device float3 ensure_valid_reflection(float3 Ng, float3 I, float3 N) { - float3 R; - float NI = dot(N, I); - float NgR, threshold; - - /* Check if the incident ray is coming from behind normal N. */ - if (NI > 0) { - /* Normal reflection */ - R = (2 * NI) * N - I; - NgR = dot(Ng, R); - - /* Reflection rays may always be at least as shallow as the incoming ray. */ - threshold = min(0.9f * dot(Ng, I), 0.01f); - if (NgR >= threshold) { - return N; + float3 R = 2 * dot(N, I) * N - I; + + /* Reflection rays may always be at least as shallow as the incoming ray. */ + float threshold = min(0.9f * dot(Ng, I), 0.01f); + if (dot(Ng, R) >= threshold) { + return N; + } + + /* Form coordinate system with Ng as the Z axis and N inside the X-Z-plane. + * The X axis is found by normalizing the component of N that's orthogonal to Ng. + * The Y axis isn't actually needed. + */ + float NdotNg = dot(N, Ng); + float3 X = normalize(N - NdotNg * Ng); + + /* Keep math expressions. */ + /* clang-format off */ + /* Calculate N.z and N.x in the local coordinate system. + * + * The goal of this computation is to find a N' that is rotated towards Ng just enough + * to lift R' above the threshold (here called t), therefore dot(R', Ng) = t. + * + * According to the standard reflection equation, + * this means that we want dot(2*dot(N', I)*N' - I, Ng) = t. + * + * Since the Z axis of our local coordinate system is Ng, dot(x, Ng) is just x.z, so we get + * 2*dot(N', I)*N'.z - I.z = t. + * + * The rotation is simple to express in the coordinate system we formed - + * since N lies in the X-Z-plane, we know that N' will also lie in the X-Z-plane, + * so N'.y = 0 and therefore dot(N', I) = N'.x*I.x + N'.z*I.z . + * + * Furthermore, we want N' to be normalized, so N'.x = sqrt(1 - N'.z^2). + * + * With these simplifications, + * we get the final equation 2*(sqrt(1 - N'.z^2)*I.x + N'.z*I.z)*N'.z - I.z = t. + * + * The only unknown here is N'.z, so we can solve for that. + * + * The equation has four solutions in general: + * + * 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)) + * We can simplify this expression a bit by grouping terms: + * + * a = I.x^2 + I.z^2 + * b = sqrt(I.x^2 * (a - t^2)) + * c = I.z*t + a + * N'.z = +-sqrt(0.5*(+-b + c)/a) + * + * Two solutions can immediately be discarded because they're negative so N' would lie in the + * lower hemisphere. + */ + /* clang-format on */ + + float Ix = dot(I, X), Iz = dot(I, Ng); + float Ix2 = sqr(Ix), Iz2 = sqr(Iz); + float a = Ix2 + Iz2; + + float b = safe_sqrtf(Ix2 * (a - sqr(threshold))); + float c = Iz * threshold + a; + + /* Evaluate both solutions. + * In many cases one can be immediately discarded (if N'.z would be imaginary or larger than + * one), so check for that first. If no option is viable (might happen in extreme cases like N + * being in the wrong hemisphere), give up and return Ng. */ + float fac = 0.5f / a; + float N1_z2 = fac * (b + c), N2_z2 = fac * (-b + c); + bool valid1 = (N1_z2 > 1e-5f) && (N1_z2 <= (1.0f + 1e-5f)); + bool valid2 = (N2_z2 > 1e-5f) && (N2_z2 <= (1.0f + 1e-5f)); + + float2 N_new; + if (valid1 && valid2) { + /* If both are possible, do the expensive reflection-based check. */ + float2 N1 = make_float2(safe_sqrtf(1.0f - N1_z2), safe_sqrtf(N1_z2)); + float2 N2 = make_float2(safe_sqrtf(1.0f - N2_z2), safe_sqrtf(N2_z2)); + + float R1 = 2 * (N1.x * Ix + N1.y * Iz) * N1.y - Iz; + float R2 = 2 * (N2.x * Ix + N2.y * Iz) * N2.y - Iz; + + valid1 = (R1 >= 1e-5f); + valid2 = (R2 >= 1e-5f); + if (valid1 && valid2) { + /* If both solutions are valid, return the one with the shallower reflection since it will be + * closer to the input (if the original reflection wasn't shallow, we would not be in this + * part of the function). */ + N_new = (R1 < R2) ? N1 : N2; } + else { + /* If only one reflection is valid (= positive), pick that one. */ + N_new = (R1 > R2) ? N1 : N2; + } + } + else if (valid1 || valid2) { + /* Only one solution passes the N'.z criterium, so pick that one. */ + float Nz2 = valid1 ? N1_z2 : N2_z2; + N_new = make_float2(safe_sqrtf(1.0f - Nz2), safe_sqrtf(Nz2)); } else { - /* Bad incident */ - R = -I; - NgR = dot(Ng, R); - threshold = 0.01f; + return Ng; } - R = R + Ng * (threshold - NgR); /* Lift the reflection above the threshold. */ - return normalize(I * len(R) + R * len(I)); /* Find a bisector. */ + return N_new.x * X + N_new.y * Ng; } CCL_NAMESPACE_END |