201 lines
6.9 KiB
C
201 lines
6.9 KiB
C
/* SPDX-FileCopyrightText: 2009-2010 Sony Pictures Imageworks Inc., et al. All Rights Reserved.
|
|
* SPDX-FileCopyrightText: 2011-2022 Blender Foundation
|
|
*
|
|
* SPDX-License-Identifier: BSD-3-Clause
|
|
*
|
|
* Adapted code from Open Shading Language. */
|
|
|
|
#pragma once
|
|
|
|
CCL_NAMESPACE_BEGIN
|
|
|
|
ccl_device float fresnel_dielectric(
|
|
float eta, const float3 N, const float3 I, ccl_private float3 *T, ccl_private bool *is_inside)
|
|
{
|
|
float cos = dot(N, I), neta;
|
|
float3 Nn;
|
|
|
|
// check which side of the surface we are on
|
|
if (cos > 0) {
|
|
// we are on the outside of the surface, going in
|
|
neta = 1 / eta;
|
|
Nn = N;
|
|
*is_inside = false;
|
|
}
|
|
else {
|
|
// we are inside the surface
|
|
cos = -cos;
|
|
neta = eta;
|
|
Nn = -N;
|
|
*is_inside = true;
|
|
}
|
|
|
|
float arg = 1 - (neta * neta * (1 - (cos * cos)));
|
|
if (arg < 0) {
|
|
*T = make_float3(0.0f, 0.0f, 0.0f);
|
|
return 1; // total internal reflection
|
|
}
|
|
else {
|
|
float dnp = max(sqrtf(arg), 1e-7f);
|
|
float nK = (neta * cos) - dnp;
|
|
*T = -(neta * I) + (nK * Nn);
|
|
// compute Fresnel terms
|
|
float cosTheta1 = cos; // N.R
|
|
float cosTheta2 = -dot(Nn, *T);
|
|
float pPara = (cosTheta1 - eta * cosTheta2) / (cosTheta1 + eta * cosTheta2);
|
|
float pPerp = (eta * cosTheta1 - cosTheta2) / (eta * cosTheta1 + cosTheta2);
|
|
return 0.5f * (pPara * pPara + pPerp * pPerp);
|
|
}
|
|
}
|
|
|
|
ccl_device float fresnel_dielectric_cos(float cosi, float eta)
|
|
{
|
|
// compute fresnel reflectance without explicitly computing
|
|
// the refracted direction
|
|
float c = fabsf(cosi);
|
|
float g = eta * eta - 1 + c * c;
|
|
if (g > 0) {
|
|
g = sqrtf(g);
|
|
float A = (g - c) / (g + c);
|
|
float B = (c * (g + c) - 1) / (c * (g - c) + 1);
|
|
return 0.5f * A * A * (1 + B * B);
|
|
}
|
|
return 1.0f; // TIR(no refracted component)
|
|
}
|
|
|
|
ccl_device Spectrum fresnel_conductor(float cosi, const Spectrum eta, const Spectrum k)
|
|
{
|
|
Spectrum cosi2 = make_spectrum(cosi * cosi);
|
|
Spectrum one = make_spectrum(1.0f);
|
|
Spectrum tmp_f = eta * eta + k * k;
|
|
Spectrum tmp = tmp_f * cosi2;
|
|
Spectrum Rparl2 = (tmp - (2.0f * eta * cosi) + one) / (tmp + (2.0f * eta * cosi) + one);
|
|
Spectrum Rperp2 = (tmp_f - (2.0f * eta * cosi) + cosi2) / (tmp_f + (2.0f * eta * cosi) + cosi2);
|
|
return (Rparl2 + Rperp2) * 0.5f;
|
|
}
|
|
|
|
ccl_device float ior_from_F0(float f0)
|
|
{
|
|
const float sqrt_f0 = sqrtf(clamp(f0, 0.0f, 0.99f));
|
|
return (1.0f + sqrt_f0) / (1.0f - sqrt_f0);
|
|
}
|
|
|
|
ccl_device float F0_from_ior(float ior)
|
|
{
|
|
return sqr((ior - 1.0f) / (ior + 1.0f));
|
|
}
|
|
|
|
ccl_device float schlick_fresnel(float u)
|
|
{
|
|
float m = clamp(1.0f - u, 0.0f, 1.0f);
|
|
float m2 = m * m;
|
|
return m2 * m2 * m; // pow(m, 5)
|
|
}
|
|
|
|
/* Calculate the fresnel color, which is a blend between white and the F0 color */
|
|
ccl_device_forceinline Spectrum interpolate_fresnel_color(float3 L,
|
|
float3 H,
|
|
float ior,
|
|
Spectrum F0)
|
|
{
|
|
/* Compute the real Fresnel term and remap it from real_F0..1 to F0..1.
|
|
* The reason why we use this remapping instead of directly doing the
|
|
* Schlick approximation mix(F0, 1.0, (1.0-cosLH)^5) is that for cases
|
|
* with similar IORs (e.g. ice in water), the relative IOR can be close
|
|
* enough to 1.0 that the Schlick approximation becomes inaccurate. */
|
|
float real_F = fresnel_dielectric_cos(dot(L, H), ior);
|
|
float real_F0 = fresnel_dielectric_cos(1.0f, ior);
|
|
|
|
return mix(F0, one_spectrum(), inverse_lerp(real_F0, 1.0f, real_F));
|
|
}
|
|
|
|
/* If the shading normal results in specular reflection in the lower hemisphere, raise the shading
|
|
* normal towards the geometry normal so that the specular reflection is just above the surface.
|
|
* Only used for glossy materials. */
|
|
ccl_device float3 ensure_valid_specular_reflection(float3 Ng, float3 I, float3 N)
|
|
{
|
|
const float3 R = 2 * dot(N, I) * N - I;
|
|
|
|
const float Iz = dot(I, Ng);
|
|
kernel_assert(Iz > 0);
|
|
|
|
/* Reflection rays may always be at least as shallow as the incoming ray. */
|
|
const float threshold = min(0.9f * Iz, 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.
|
|
*/
|
|
const float3 X = normalize(N - dot(N, Ng) * Ng);
|
|
|
|
/* 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 equation
|
|
* 2*(sqrt(1 - N'.z^2)*I.x + N'.z*I.z)*N'.z - I.z = t,
|
|
* or
|
|
* 2*sqrt(1 - N'.z^2)*I.x*N'.z = t + I.z * (1 - 2*N'.z^2),
|
|
* after rearranging terms.
|
|
* Raise both sides to the power of two and substitute terms with
|
|
* a = I.x^2 + I.z^2,
|
|
* b = 2*(a + Iz*t),
|
|
* c = (Iz + t)^2,
|
|
* we obtain
|
|
* 4*a*N'.z^4 - 2*b*N'.z^2 + c = 0.
|
|
*
|
|
* The only unknown here is N'.z, so we can solve for that.
|
|
*
|
|
* The equation has four solutions in general, two can immediately be discarded because they're
|
|
* negative so N' would lie in the lower hemisphere; one solves
|
|
* 2*sqrt(1 - N'.z^2)*I.x*N'.z = -(t + I.z * (1 - 2*N'.z^2))
|
|
* instead of the original equation (before squaring both sides).
|
|
* Therefore only one root is valid.
|
|
*/
|
|
|
|
const float Ix = dot(I, X);
|
|
|
|
const float a = sqr(Ix) + sqr(Iz);
|
|
const float b = 2.0f * (a + Iz * threshold);
|
|
const float c = sqr(threshold + Iz);
|
|
|
|
/* In order that the root formula solves 2*sqrt(1 - N'.z^2)*I.x*N'.z = t + I.z - 2*I.z*N'.z^2,
|
|
* Ix and (t + I.z * (1 - 2*N'.z^2)) must have the same sign (the rest terms are non-negative by
|
|
* definition). */
|
|
const float Nz2 = (Ix < 0) ? 0.25f * (b + safe_sqrtf(sqr(b) - 4.0f * a * c)) / a :
|
|
0.25f * (b - safe_sqrtf(sqr(b) - 4.0f * a * c)) / a;
|
|
|
|
const float Nx = safe_sqrtf(1.0f - Nz2);
|
|
const float Nz = safe_sqrtf(Nz2);
|
|
|
|
return Nx * X + Nz * Ng;
|
|
}
|
|
|
|
/* Do not call #ensure_valid_specular_reflection if the primitive type is curve or if the geometry
|
|
* normal and the shading normal is the same. */
|
|
ccl_device float3 maybe_ensure_valid_specular_reflection(ccl_private ShaderData *sd, float3 N)
|
|
{
|
|
if ((sd->type & PRIMITIVE_CURVE) || isequal(sd->Ng, N)) {
|
|
return N;
|
|
}
|
|
return ensure_valid_specular_reflection(sd->Ng, sd->wi, N);
|
|
}
|
|
|
|
CCL_NAMESPACE_END
|