test2/intern/cycles/kernel/closure/bsdf_util.h

/* SPDX-License-Identifier: BSD-3-Clause
 *
 * Adapted from Open Shading Language
 * Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
 * All Rights Reserved.
 *
 * Modifications Copyright 2011-2022 Blender Foundation. */

#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