rendering-in-cgi/Framework/include/sampling.hpp

// Copyright 2009-2021 Intel Corporation
// SPDX-License-Identifier: Apache-2.0

#pragma once

/*! \brief utility library containing sampling functions */

// convention is to return the sample (Vec3fa) generated from given Vec2f 's'ample as last parameter
// sampling functions often come in pairs: sample and pdf (needed later for MIS)
// good reference is "Total Compendium" by Philip Dutre http://people.cs.kuleuven.be/~philip.dutre/GI/

#include <math/vec.h>
#include <math/linearspace3.h>

namespace embree {

struct Sample3f
{
  Vec3fa v;
  float pdf;
};

inline Sample3f make_Sample3f(const Vec3fa& v, const float pdf) {
  Sample3f s; s.v = v; s.pdf = pdf; return s;
}

#if defined(ISPC)
inline Sample3f make_Sample3f(const Vec3fa& v, const float pdf) {
  Sample3f s; s.v = v; s.pdf = pdf; return s;
}
#endif

inline Vec3fa cartesian(const float phi, const float sinTheta, const float cosTheta)
{
  const float sinPhi = sinf(phi);
  const float cosPhi = cosf(phi);
  //sincosf(phi, &sinPhi, &cosPhi);
  return Vec3fa(cosPhi * sinTheta,
                    sinPhi * sinTheta,
                    cosTheta);
}

inline Vec3fa cartesian(const float phi, const float cosTheta)
{
  return cartesian(phi, cos2sin(cosTheta), cosTheta);
}


/// cosine-weighted sampling of hemisphere oriented along the +z-axis
////////////////////////////////////////////////////////////////////////////////

inline Vec3fa cosineSampleHemisphere(const Vec2f s)
{
  const float phi = 2.0f * float(M_PI) * s.x;
  const float cosTheta = sqrt(s.y);
  const float sinTheta = sqrt(1.0f - s.y);
  return cartesian(phi, sinTheta, cosTheta);
}

inline float cosineSampleHemispherePDF(const Vec3fa &dir)
{
  return dir.z / float(M_PI);
}

inline float cosineSampleHemispherePDF(float cosTheta)
{
  return cosTheta / float(M_PI);
}

/*! Cosine weighted hemisphere sampling. Up direction is provided as argument. */
inline Sample3f cosineSampleHemisphere(const float  u, const float  v, const Vec3fa& N)
{
  Vec3fa localDir = cosineSampleHemisphere(Vec2f(u,v));
  Sample3f s;
  s.v = frame(N) * localDir;
  s.pdf = cosineSampleHemispherePDF(localDir);
  return s;
}

/// power cosine-weighted sampling of hemisphere oriented along the +z-axis
////////////////////////////////////////////////////////////////////////////////

inline Vec3fa powerCosineSampleHemisphere(const float n, const Vec2f &s)
{
  const float phi =float(two_pi) * s.x;
  const float cosTheta = pow(s.y, 1.0f / (n + 1.0f));
  return cartesian(phi, cosTheta);
}

inline float powerCosineSampleHemispherePDF(const float cosTheta, const float n) // TODO: order of arguments
{
  return (n + 1.0f) * (0.5f / float(M_PI)) * pow(cosTheta, n);
}

inline float powerCosineSampleHemispherePDF(const Vec3fa& dir, const float n) // TODO: order of arguments
{
  return (n + 1.0f) * (0.5f / float(M_PI)) * pow(dir.z, n);
}

/// sampling of cone of directions oriented along the +z-axis
////////////////////////////////////////////////////////////////////////////////

inline Vec3fa uniformSampleCone(const float cosAngle, const Vec2f &s)
{
  const float phi =float(two_pi) * s.x;
  const float cosTheta = 1.0f - s.y * (1.0f - cosAngle);
  return cartesian(phi, cosTheta);
}

inline float erfInv(float x) {
	float w, p;
	x = clamp(x, -.99999f, .99999f);
	w = -std::log((1 - x) * (1 + x));
	if (w < 5) {
		w = w - 2.5f;
		p = 2.81022636e-08f;
		p = 3.43273939e-07f + p * w;
		p = -3.5233877e-06f + p * w;
		p = -4.39150654e-06f + p * w;
		p = 0.00021858087f + p * w;
		p = -0.00125372503f + p * w;
		p = -0.00417768164f + p * w;
		p = 0.246640727f + p * w;
		p = 1.50140941f + p * w;
	}
	else {
		w = std::sqrt(w) - 3;
		p = -0.000200214257f;
		p = 0.000100950558f + p * w;
		p = 0.00134934322f + p * w;
		p = -0.00367342844f + p * w;
		p = 0.00573950773f + p * w;
		p = -0.0076224613f + p * w;
		p = 0.00943887047f + p * w;
		p = 1.00167406f + p * w;
		p = 2.83297682f + p * w;
	}
	return p * x;
}

inline float uniformSampleConePDF(const float cosAngle)
{
    return rcp(float(two_pi)*(1.0f - cosAngle));
}

inline float _uniformSampleConePDF(const float cosAngle)
{
    return rcp(float(two_pi)*(1.0f - cosAngle));
}


/// sampling of disk
////////////////////////////////////////////////////////////////////////////////

inline Vec3fa uniformSampleDisk(const float radius, const Vec2f &s)
{
  const float r = sqrtf(s.x) * radius;
  const float phi =float(two_pi) * s.y;
  const float sinPhi = sinf(phi);
  const float cosPhi = cosf(phi);
  //sincosf(phi, &sinPhi, &cosPhi);
  return Vec3fa(r * cosPhi, r * sinPhi, 0.f);
}

inline float uniformSampleDiskPDF(const float radius)
{
  return rcp(float(M_PI) * sqr(radius));
}

inline float _uniformSampleDiskPDF(const float radius)
{
  return rcp(float(M_PI) * sqr(radius));
}


/// sampling of triangle abc
////////////////////////////////////////////////////////////////////////////////

inline Vec3fa uniformSampleTriangle(const Vec3fa &a, const Vec3fa &b, const Vec3fa &c, const Vec2f &s)
{
  const float su = sqrtf(s.x);
  return c + (1.0f - su) * (a-c) + (s.y*su) * (b-c);
}

inline float uniformSampleTrianglePDF(const Vec3fa &a, const Vec3fa &b, const Vec3fa &c)
{
  return 2.0f * rcp(abs(length(cross(a-c, b-c))));
}

} // namespace embree