blender/intern/cycles/kernel/kernel_montecarlo.h

/*
 * Parts adapted from Open Shading Language with this license:
 *
 * Copyright (c) 2009-2010 Sony Pictures Imageworks Inc., et al.
 * All Rights Reserved.
 *
 * Modifications Copyright 2011, Blender Foundation.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 * * Redistributions of source code must retain the above copyright
 *   notice, this list of conditions and the following disclaimer.
 * * Redistributions in binary form must reproduce the above copyright
 *   notice, this list of conditions and the following disclaimer in the
 *   documentation and/or other materials provided with the distribution.
 * * Neither the name of Sony Pictures Imageworks nor the names of its
 *   contributors may be used to endorse or promote products derived from
 *   this software without specific prior written permission.
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#ifndef __KERNEL_MONTECARLO_CL__
#define __KERNEL_MONTECARLO_CL__

CCL_NAMESPACE_BEGIN

/* distribute uniform xy on [0,1] over unit disk [-1,1] */
ccl_device void to_unit_disk(float *x, float *y)
{
  float phi = M_2PI_F * (*x);
  float r = sqrtf(*y);

  *x = r * cosf(phi);
  *y = r * sinf(phi);
}

/* return an orthogonal tangent and bitangent given a normal and tangent that
 * may not be exactly orthogonal */
ccl_device void make_orthonormals_tangent(const float3 N, const float3 T, float3 *a, float3 *b)
{
  *b = normalize(cross(N, T));
  *a = cross(*b, N);
}

/* sample direction with cosine weighted distributed in hemisphere */
ccl_device_inline void sample_cos_hemisphere(
    const float3 N, float randu, float randv, float3 *omega_in, float *pdf)
{
  to_unit_disk(&randu, &randv);
  float costheta = sqrtf(max(1.0f - randu * randu - randv * randv, 0.0f));
  float3 T, B;
  make_orthonormals(N, &T, &B);
  *omega_in = randu * T + randv * B + costheta * N;
  *pdf = costheta * M_1_PI_F;
}

/* sample direction uniformly distributed in hemisphere */
ccl_device_inline void sample_uniform_hemisphere(
    const float3 N, float randu, float randv, float3 *omega_in, float *pdf)
{
  float z = randu;
  float r = sqrtf(max(0.0f, 1.0f - z * z));
  float phi = M_2PI_F * randv;
  float x = r * cosf(phi);
  float y = r * sinf(phi);

  float3 T, B;
  make_orthonormals(N, &T, &B);
  *omega_in = x * T + y * B + z * N;
  *pdf = 0.5f * M_1_PI_F;
}

/* sample direction uniformly distributed in cone */
ccl_device_inline void sample_uniform_cone(
    const float3 N, float angle, float randu, float randv, float3 *omega_in, float *pdf)
{
  float zMin = cosf(angle);
  float z = zMin - zMin * randu + randu;
  float r = safe_sqrtf(1.0f - sqr(z));
  float phi = M_2PI_F * randv;
  float x = r * cosf(phi);
  float y = r * sinf(phi);

  float3 T, B;
  make_orthonormals(N, &T, &B);
  *omega_in = x * T + y * B + z * N;
  *pdf = M_1_2PI_F / (1.0f - zMin);
}

ccl_device_inline float pdf_uniform_cone(const float3 N, float3 D, float angle)
{
  float zMin = cosf(angle);
  float z = dot(N, D);
  if (z > zMin) {
    return M_1_2PI_F / (1.0f - zMin);
  }
  return 0.0f;
}

/* sample uniform point on the surface of a sphere */
ccl_device float3 sample_uniform_sphere(float u1, float u2)
{
  float z = 1.0f - 2.0f * u1;
  float r = sqrtf(fmaxf(0.0f, 1.0f - z * z));
  float phi = M_2PI_F * u2;
  float x = r * cosf(phi);
  float y = r * sinf(phi);

  return make_float3(x, y, z);
}

ccl_device float balance_heuristic(float a, float b)
{
  return (a) / (a + b);
}

ccl_device float balance_heuristic_3(float a, float b, float c)
{
  return (a) / (a + b + c);
}

ccl_device float power_heuristic(float a, float b)
{
  return (a * a) / (a * a + b * b);
}

ccl_device float power_heuristic_3(float a, float b, float c)
{
  return (a * a) / (a * a + b * b + c * c);
}

ccl_device float max_heuristic(float a, float b)
{
  return (a > b) ? 1.0f : 0.0f;
}

/* distribute uniform xy on [0,1] over unit disk [-1,1], with concentric mapping
 * to better preserve stratification for some RNG sequences */
ccl_device float2 concentric_sample_disk(float u1, float u2)
{
  float phi, r;
  float a = 2.0f * u1 - 1.0f;
  float b = 2.0f * u2 - 1.0f;

  if (a == 0.0f && b == 0.0f) {
    return zero_float2();
  }
  else if (a * a > b * b) {
    r = a;
    phi = M_PI_4_F * (b / a);
  }
  else {
    r = b;
    phi = M_PI_2_F - M_PI_4_F * (a / b);
  }

  return make_float2(r * cosf(phi), r * sinf(phi));
}

/* sample point in unit polygon with given number of corners and rotation */
ccl_device float2 regular_polygon_sample(float corners, float rotation, float u, float v)
{
  /* sample corner number and reuse u */
  float corner = floorf(u * corners);
  u = u * corners - corner;

  /* uniform sampled triangle weights */
  u = sqrtf(u);
  v = v * u;
  u = 1.0f - u;

  /* point in triangle */
  float angle = M_PI_F / corners;
  float2 p = make_float2((u + v) * cosf(angle), (u - v) * sinf(angle));

  /* rotate */
  rotation += corner * 2.0f * angle;

  float cr = cosf(rotation);
  float sr = sinf(rotation);

  return make_float2(cr * p.x - sr * p.y, sr * p.x + cr * p.y);
}

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;
    }
  }
  else {
    /* Bad incident */
    R = -I;
    NgR = dot(Ng, R);
    threshold = 0.01f;
  }

  R = R + Ng * (threshold - NgR);            /* Lift the reflection above the threshold. */
  return normalize(I * len(R) + R * len(I)); /* Find a bisector. */
}

CCL_NAMESPACE_END

#endif /* __KERNEL_MONTECARLO_CL__ */