216 lines
7.3 KiB
C++
216 lines
7.3 KiB
C++
/* SPDX-License-Identifier: BSD-3-Clause
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*
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* Adapted from Open Shading Language
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* Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
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* All Rights Reserved.
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*
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* Modifications Copyright 2011-2022 Blender Foundation. */
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#pragma once
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CCL_NAMESPACE_BEGIN
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ccl_device float fresnel_dielectric(float eta,
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const float3 N,
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const float3 I,
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ccl_private float3 *R,
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ccl_private float3 *T,
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ccl_private bool *is_inside)
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{
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float cos = dot(N, I), neta;
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float3 Nn;
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// check which side of the surface we are on
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if (cos > 0) {
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// we are on the outside of the surface, going in
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neta = 1 / eta;
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Nn = N;
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*is_inside = false;
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}
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else {
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// we are inside the surface
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cos = -cos;
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neta = eta;
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Nn = -N;
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*is_inside = true;
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}
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// compute reflection
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*R = (2 * cos) * Nn - I;
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float arg = 1 - (neta * neta * (1 - (cos * cos)));
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if (arg < 0) {
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*T = make_float3(0.0f, 0.0f, 0.0f);
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return 1; // total internal reflection
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}
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else {
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float dnp = max(sqrtf(arg), 1e-7f);
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float nK = (neta * cos) - dnp;
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*T = -(neta * I) + (nK * Nn);
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// compute Fresnel terms
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float cosTheta1 = cos; // N.R
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float cosTheta2 = -dot(Nn, *T);
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float pPara = (cosTheta1 - eta * cosTheta2) / (cosTheta1 + eta * cosTheta2);
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float pPerp = (eta * cosTheta1 - cosTheta2) / (eta * cosTheta1 + cosTheta2);
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return 0.5f * (pPara * pPara + pPerp * pPerp);
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}
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}
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ccl_device float fresnel_dielectric_cos(float cosi, float eta)
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{
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// compute fresnel reflectance without explicitly computing
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// the refracted direction
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float c = fabsf(cosi);
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float g = eta * eta - 1 + c * c;
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if (g > 0) {
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g = sqrtf(g);
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float A = (g - c) / (g + c);
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float B = (c * (g + c) - 1) / (c * (g - c) + 1);
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return 0.5f * A * A * (1 + B * B);
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}
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return 1.0f; // TIR(no refracted component)
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}
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ccl_device float3 fresnel_conductor(float cosi, const float3 eta, const float3 k)
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{
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float3 cosi2 = make_float3(cosi * cosi, cosi * cosi, cosi * cosi);
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float3 one = make_float3(1.0f, 1.0f, 1.0f);
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float3 tmp_f = eta * eta + k * k;
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float3 tmp = tmp_f * cosi2;
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float3 Rparl2 = (tmp - (2.0f * eta * cosi) + one) / (tmp + (2.0f * eta * cosi) + one);
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float3 Rperp2 = (tmp_f - (2.0f * eta * cosi) + cosi2) / (tmp_f + (2.0f * eta * cosi) + cosi2);
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return (Rparl2 + Rperp2) * 0.5f;
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}
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ccl_device float schlick_fresnel(float u)
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{
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float m = clamp(1.0f - u, 0.0f, 1.0f);
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float m2 = m * m;
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return m2 * m2 * m; // pow(m, 5)
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}
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/* Calculate the fresnel color, which is a blend between white and the F0 color */
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ccl_device_forceinline Spectrum interpolate_fresnel_color(float3 L,
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float3 H,
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float ior,
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Spectrum F0)
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{
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/* Compute the real Fresnel term and remap it from real_F0..1 to F0..1.
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* The reason why we use this remapping instead of directly doing the
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* Schlick approximation lerp(F0, 1.0, (1.0-cosLH)^5) is that for cases
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* with similar IORs (e.g. ice in water), the relative IOR can be close
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* enough to 1.0 that the Schlick approximation becomes inaccurate. */
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float real_F = fresnel_dielectric_cos(dot(L, H), ior);
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float real_F0 = fresnel_dielectric_cos(1.0f, ior);
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return mix(F0, one_spectrum(), inverse_lerp(real_F0, 1.0f, real_F));
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}
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ccl_device float3 ensure_valid_reflection(float3 Ng, float3 I, float3 N)
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{
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float3 R = 2 * dot(N, I) * N - I;
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/* Reflection rays may always be at least as shallow as the incoming ray. */
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float threshold = min(0.9f * dot(Ng, I), 0.01f);
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if (dot(Ng, R) >= threshold) {
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return N;
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}
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/* Form coordinate system with Ng as the Z axis and N inside the X-Z-plane.
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* The X axis is found by normalizing the component of N that's orthogonal to Ng.
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* The Y axis isn't actually needed.
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*/
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float NdotNg = dot(N, Ng);
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float3 X = normalize(N - NdotNg * Ng);
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/* Keep math expressions. */
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/* clang-format off */
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/* Calculate N.z and N.x in the local coordinate system.
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*
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* The goal of this computation is to find a N' that is rotated towards Ng just enough
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* to lift R' above the threshold (here called t), therefore dot(R', Ng) = t.
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*
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* According to the standard reflection equation,
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* this means that we want dot(2*dot(N', I)*N' - I, Ng) = t.
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*
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* Since the Z axis of our local coordinate system is Ng, dot(x, Ng) is just x.z, so we get
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* 2*dot(N', I)*N'.z - I.z = t.
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*
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* The rotation is simple to express in the coordinate system we formed -
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* since N lies in the X-Z-plane, we know that N' will also lie in the X-Z-plane,
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* so N'.y = 0 and therefore dot(N', I) = N'.x*I.x + N'.z*I.z .
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*
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* Furthermore, we want N' to be normalized, so N'.x = sqrt(1 - N'.z^2).
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*
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* With these simplifications,
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* we get the final equation 2*(sqrt(1 - N'.z^2)*I.x + N'.z*I.z)*N'.z - I.z = t.
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*
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* The only unknown here is N'.z, so we can solve for that.
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*
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* The equation has four solutions in general:
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*
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* 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))
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* We can simplify this expression a bit by grouping terms:
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*
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* a = I.x^2 + I.z^2
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* b = sqrt(I.x^2 * (a - t^2))
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* c = I.z*t + a
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* N'.z = +-sqrt(0.5*(+-b + c)/a)
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*
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* Two solutions can immediately be discarded because they're negative so N' would lie in the
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* lower hemisphere.
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*/
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/* clang-format on */
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float Ix = dot(I, X), Iz = dot(I, Ng);
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float Ix2 = sqr(Ix), Iz2 = sqr(Iz);
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float a = Ix2 + Iz2;
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float b = safe_sqrtf(Ix2 * (a - sqr(threshold)));
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float c = Iz * threshold + a;
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/* Evaluate both solutions.
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* In many cases one can be immediately discarded (if N'.z would be imaginary or larger than
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* one), so check for that first. If no option is viable (might happen in extreme cases like N
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* being in the wrong hemisphere), give up and return Ng. */
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float fac = 0.5f / a;
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float N1_z2 = fac * (b + c), N2_z2 = fac * (-b + c);
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bool valid1 = (N1_z2 > 1e-5f) && (N1_z2 <= (1.0f + 1e-5f));
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bool valid2 = (N2_z2 > 1e-5f) && (N2_z2 <= (1.0f + 1e-5f));
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float2 N_new;
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if (valid1 && valid2) {
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/* If both are possible, do the expensive reflection-based check. */
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float2 N1 = make_float2(safe_sqrtf(1.0f - N1_z2), safe_sqrtf(N1_z2));
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float2 N2 = make_float2(safe_sqrtf(1.0f - N2_z2), safe_sqrtf(N2_z2));
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float R1 = 2 * (N1.x * Ix + N1.y * Iz) * N1.y - Iz;
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float R2 = 2 * (N2.x * Ix + N2.y * Iz) * N2.y - Iz;
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valid1 = (R1 >= 1e-5f);
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valid2 = (R2 >= 1e-5f);
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if (valid1 && valid2) {
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/* If both solutions are valid, return the one with the shallower reflection since it will be
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* closer to the input (if the original reflection wasn't shallow, we would not be in this
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* part of the function). */
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N_new = (R1 < R2) ? N1 : N2;
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}
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else {
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/* If only one reflection is valid (= positive), pick that one. */
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N_new = (R1 > R2) ? N1 : N2;
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}
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}
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else if (valid1 || valid2) {
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/* Only one solution passes the N'.z criterium, so pick that one. */
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float Nz2 = valid1 ? N1_z2 : N2_z2;
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N_new = make_float2(safe_sqrtf(1.0f - Nz2), safe_sqrtf(Nz2));
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}
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else {
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return Ng;
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}
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return N_new.x * X + N_new.y * Ng;
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}
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CCL_NAMESPACE_END
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