Sampling module

Random number generation, generation of points and directions, Monte Carlo utilities.

Functions

auto randf() -> float
Global random number generator that produces floats between [0,1)
auto random_in_unit_sphere() -> Vec3f
Sample a random point uniformly within a unit sphere (uses the global randf() RNG and rejection sampling)
auto random_in_unit_disk() -> Vec2f
Sample a random point uniformly within a unit disk (uses the global randf() RNG and rejection sampling)
auto sample_disk(const Vec2f& rv) -> Vec2f
Uniformly sample a vector on a 2D disk with radius 1, centered around the origin.
auto sample_disk_pdf(const Vec2f& p) -> float
Probability density of sample_disk()
auto sample_sphere(const Vec2f& rv) -> Vec3f
Uniformly sample a vector on the unit sphere with respect to solid angles.
auto sample_sphere_pdf() -> float
Probability density of sample_sphere()
auto sample_hemisphere(const Vec2f& rv) -> Vec3f
Uniformly sample a vector on the unit hemisphere around the pole (0,0,1) with respect to solid angles.
auto sample_hemisphere_pdf(const Vec3f& v) -> float
Probability density of sample_hemisphere()
auto sample_hemisphere_cosine(const Vec2f& rv) -> Vec3f
Uniformly sample a vector on the unit hemisphere around the pole (0,0,1) with respect to projected solid angles.
auto sample_hemisphere_cosine_pdf(const Vec3f& v) -> float
Probability density of sample_hemisphere_cosine()
auto sample_hemisphere_cosine_power(float exponent, const Vec2f& rv) -> Vec3f
Sample a vector on the unit hemisphere with a cosine-power density about the pole (0,0,1)
auto sample_hemisphere_cosine_power_pdf(float exponent, float cosine) -> float
Probability density of sample_hemisphere_cosine_power()
auto sample_sphere_cap(const Vec2f& rv, float cos_theta_max) -> Vec3f
Uniformly sample a vector on a spherical cap around (0, 0, 1)
auto sample_sphere_cap_pdf(float cos_theta, float cos_theta_max) -> float
Probability density of sample_sphere_cap()
auto sample_triangle(const Vec3f& v0, const Vec3f& v1, const Vec3f& v2, const Vec2f& rv) -> Vec3f
Sample a point uniformly on a triangle with vertices v0, v1, v2.
auto sample_triangle_pdf(const Vec3f& v0, const Vec3f& v1, const Vec3f& v2) -> float
Sampling density of sample_triangle()

Function documentation

float randf()
#include <darts/sampling.h>

Global random number generator that produces floats between [0,1)

Vec3f random_in_unit_sphere()
#include <darts/sampling.h>

Sample a random point uniformly within a unit sphere (uses the global randf() RNG and rejection sampling)

Vec2f random_in_unit_disk()
#include <darts/sampling.h>

Sample a random point uniformly within a unit disk (uses the global randf() RNG and rejection sampling)

Vec2f sample_disk(const Vec2f& rv)
#include <darts/sampling.h>

Uniformly sample a vector on a 2D disk with radius 1, centered around the origin.

float sample_disk_pdf(const Vec2f& p)
#include <darts/sampling.h>

Probability density of sample_disk()

Vec3f sample_sphere(const Vec2f& rv)
#include <darts/sampling.h>

Uniformly sample a vector on the unit sphere with respect to solid angles.

float sample_sphere_pdf()
#include <darts/sampling.h>

Probability density of sample_sphere()

Vec3f sample_hemisphere(const Vec2f& rv)
#include <darts/sampling.h>

Uniformly sample a vector on the unit hemisphere around the pole (0,0,1) with respect to solid angles.

float sample_hemisphere_pdf(const Vec3f& v)
#include <darts/sampling.h>

Probability density of sample_hemisphere()

Vec3f sample_hemisphere_cosine(const Vec2f& rv)
#include <darts/sampling.h>

Uniformly sample a vector on the unit hemisphere around the pole (0,0,1) with respect to projected solid angles.

float sample_hemisphere_cosine_pdf(const Vec3f& v)
#include <darts/sampling.h>

Probability density of sample_hemisphere_cosine()

Vec3f sample_hemisphere_cosine_power(float exponent, const Vec2f& rv)
#include <darts/sampling.h>

Sample a vector on the unit hemisphere with a cosine-power density about the pole (0,0,1)

float sample_hemisphere_cosine_power_pdf(float exponent, float cosine)
#include <darts/sampling.h>

Probability density of sample_hemisphere_cosine_power()

Vec3f sample_sphere_cap(const Vec2f& rv, float cos_theta_max)
#include <darts/sampling.h>

Uniformly sample a vector on a spherical cap around (0, 0, 1)

A spherical cap is the subset of a unit sphere whose directions make an angle of less than 'theta' with the north pole. This function expects the cosine of 'theta' as a parameter.

float sample_sphere_cap_pdf(float cos_theta, float cos_theta_max)
#include <darts/sampling.h>

Probability density of sample_sphere_cap()

Vec3f sample_triangle(const Vec3f& v0, const Vec3f& v1, const Vec3f& v2, const Vec2f& rv)
#include <darts/sampling.h>

Sample a point uniformly on a triangle with vertices v0, v1, v2.

Parameters
v0 The vertices of the triangle to sample
v1 The vertices of the triangle to sample
v2 The vertices of the triangle to sample
rv Two random variables uniformly distributed in [0,1)

float sample_triangle_pdf(const Vec3f& v0, const Vec3f& v1, const Vec3f& v2)
#include <darts/sampling.h>

Sampling density of sample_triangle()