// Description: Uniform distortion
#ifndef PASTELMATH_UNIFORM_DISTORTION_H
#define PASTELMATH_UNIFORM_DISTORTION_H
#include "pastel/sys/vector.h"
namespace Pastel
{
//! Uniformly samples a point from an annulus
/*!
Preconditions:
'uv' is in [0, 1]^N.
minRadius >= 0
maxRadius >= 0
minRadius < maxRadius
The annulus is considered as the set:
{x | minRadius <= norm(x) <= minRadius}
If 'uv' are random variables uniformly distributed
on the square, then the returned points are random
variables uniformly distributed on the annulus.
*/
template <typename Real, int N> requires (N == 1)
Vector<Real, N> uniformlySampleAnnulus(
const Vector<Real, N>& uv,
const NoDeduction<Real>& minRadius,
const NoDeduction<Real>& maxRadius);
template <typename Real, int N> requires (N == 2)
Vector<Real, N> uniformlySampleAnnulus(
const Vector<Real, N>& uv,
const NoDeduction<Real>& minRadius,
const NoDeduction<Real>& maxRadius);
template <typename Real, int N> requires (N == 3)
Vector<Real, N> uniformlySampleAnnulus(
const Vector<Real, N>& uv,
const NoDeduction<Real>& minRadius,
const NoDeduction<Real>& maxRadius);
//! Uniformly samples a point from a simplex.
/*!
Preconditions:
'uv' is in [0, 1]^N.
The simplex is considered as the set
{x | sum(x) <= 1, allGreaterEqual(x, 0)}
If 'uv' are random variables uniformly distributed
on the cube, then the returned points are random
variables uniformly distributed on the simplex.
*/
template <typename Real, int N> requires (N == 1)
Vector<Real, N> uniformlySampleSimplex(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N == 2)
Vector<Real, N> uniformlySampleSimplex(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N >= 3 || N == Dynamic)
Vector<Real, N> uniformlySampleSimplex(
const Vector<Real, N>& uv);
//! Uniformly samples a point from a ball.
/*!
Preconditions:
'uv' is in [0, 1]^N.
Returns:
A point from the set {x in R^N | norm(x) <= 1}.
If 'uv' is a uniformly distributed random variable on the cube,
so is the returned value on the ball.
*/
template <typename Real, int N> requires (N == 1)
Vector<Real, N> uniformlySampleBall(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N == 2)
Vector<Real, N> uniformlySampleBall(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N == 3)
Vector<Real, N> uniformlySampleBall(
const Vector<Real, N>& uv);
// TODO: provide functions for 4d and up?
//! Uniformly samples a point from a sphere.
/*!
Preconditions:
'uv' is in [0, 1]^N
Returns:
A point from the set {x in R^(N + 1) | norm(x) = 1}.
If 'uv' is a uniformly distributed random variable on the cube,
so is the returned value on the sphere.
*/
template <typename Real, int N> requires (N == 1)
Vector<Real, AddN<N>> uniformlySampleSphere(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N == 2)
Vector<Real, AddN<N>> uniformlySampleSphere(
const Vector<Real, N>& uv);
// TODO: provide functions for 4d and up?
//! Uniformly samples a point from a hemisphere.
/*!
Preconditions:
'uv' is in [0, 1]^N.
Returns:
A point from the set {x in R^(N + 1) | norm(x) <= 1, x[N] >= 0}.
If 'uv' is a uniformly distributed random variable on the cube,
so is the returned value on the hemisphere.
*/
template <typename Real, int N> requires (N == 1)
Vector<Real, AddN<N>>
uniformlySampleHemisphere(
const Vector<Real, N>& uv);
template <typename Real, int N> requires (N == 2)
Vector<Real, AddN<N>>
uniformlySampleHemisphere(
const Vector<Real, N>& uv);
// TODO: provide functions for 4d and up?
//! Samples a cosine-weighted point from a hemisphere.
/*!
Preconditions:
'uv' is in [0, 1]^N.
The hemisphere is considered as the set
{x in R^(N+1) | norm(x) = 1, x[N] >= 0}
If 'uv' are random variables uniformly distributed
on the square, then the returned points are random
variables cosine-distributed on the hemisphere.
*/
template <typename Real, int N>
Vector<Real, AddN<N>> cosineSampleHemisphere(
const Vector<Real, N>& uv);
}
#include "pastel/math/sampling/uniform_distortion.hpp"
#endif