A sphere in 3-D space. More...

#include <TSphere.h>

Public Member Functions
	TSphere ()=default

	TSphere (T radius)

bool	isIntersecting (const TLineSegment< T > &segment, real *out_hitT) const
	Checks whether the `segment` is interseting with this sphere.

bool	isInside (const TVector3< T > &point) const
	Same as `isIntersecting()`, except the cost is slightly higher to reduce numerical error.

T	getRadius () const

T	getArea () const

TAABB3D< T >	getAABB () const

bool	mayOverlapVolume (const TAABB3D< T > &volume) const
	Conservatively checks whether this sphere overlaps a volume. By conservative, it means true can be returned even though the sphere does not overlap the volume; but if it actually does, true must be returned. The test considers the sphere as hollow and the volume is solid.

T	uniformSurfaceSamplePdfA () const

TVector2< T >	surfaceToLatLong01 (const TVector3< T > &surface) const

TVector2< T >	latLong01ToPhiTheta (const TVector2< T > &latLong01) const

TVector3< T >	latLong01ToSurface (const TVector2< T > &latLong01) const

TVector2< T >	surfaceToPhiTheta (const TVector3< T > &surface) const
	Map Cartesian to spherical coordinates on the surface of the sphere.

TVector3< T >	phiThetaToSurface (const TVector2< T > &phiTheta) const
	Map spherical to Cartesian coordinates on the surface of the sphere.

template<typename SurfaceToUv >
std::pair< TVector3< T >, TVector3< T > >	surfaceDerivativesWrtUv (const TVector3< T > &surface, SurfaceToUv surfaceToUv, T hInRadians=to_radians< T >(1)) const
	Calculate dPdU and dPdV with finite difference.

Map 2-D sample to a position on the surface.
TVector3< T >	sampleToSurfaceArchimedes (const std::array< T, 2 > &sample) const

TVector3< T >	sampleToSurfaceArchimedes (const std::array< T, 2 > &sample, T *out_pdfA) const

TVector3< T >	sampleToSurfaceAbsCosThetaWeighted (const std::array< T, 2 > &sample) const

TVector3< T >	sampleToSurfaceAbsCosThetaWeighted (const std::array< T, 2 > &sample, T *out_pdfA) const

Static Public Member Functions
static TSphere	makeUnit ()

Detailed Description

template<typename T>
class ph::math::TSphere< T >

A sphere in 3-D space.

The center of the sphere is at the origin.

Constructor & Destructor Documentation

◆ TSphere() [1/2]

template<typename T >

ph::math::TSphere< T >::TSphere ( )

default

◆ TSphere() [2/2]

template<typename T >

ph::math::TSphere< T >::TSphere ( T radius )

inlineexplicit

Parameters

radius Radius of the sphere.

Member Function Documentation

◆ getAABB()

template<typename T >

TAABB3D< T > ph::math::TSphere< T >::getAABB ( ) const

inline

◆ getArea()

template<typename T >

T ph::math::TSphere< T >::getArea ( ) const

inline

◆ getRadius()

template<typename T >

T ph::math::TSphere< T >::getRadius ( ) const

inline

◆ isInside()

template<typename T >

bool ph::math::TSphere< T >::isInside ( const TVector3< T > & point ) const

inline

Same as isIntersecting(), except the cost is slightly higher to reduce numerical error.

◆ isIntersecting()

template<typename T >

bool ph::math::TSphere< T >::isIntersecting	(	const TLineSegment< T > &	segment,
		real *	out_hitT ) const

inline

Checks whether the segment is interseting with this sphere.

Parameters

	segment	The line section to intersect with.
[out]	out_hitT	The parametric distance of the hit point for `segment`.

◆ latLong01ToPhiTheta()

template<typename T >

TVector2< T > ph::math::TSphere< T >::latLong01ToPhiTheta ( const TVector2< T > & latLong01 ) const

inline

◆ latLong01ToSurface()

template<typename T >

TVector3< T > ph::math::TSphere< T >::latLong01ToSurface ( const TVector2< T > & latLong01 ) const

inline

◆ makeUnit()

template<typename T >

TSphere< T > ph::math::TSphere< T >::makeUnit ( )

inlinestatic

◆ mayOverlapVolume()

template<typename T >

bool ph::math::TSphere< T >::mayOverlapVolume ( const TAABB3D< T > & volume ) const

inline

Conservatively checks whether this sphere overlaps a volume. By conservative, it means true can be returned even though the sphere does not overlap the volume; but if it actually does, true must be returned. The test considers the sphere as hollow and the volume is solid.

◆ phiThetaToSurface()

template<typename T >

TVector3< T > ph::math::TSphere< T >::phiThetaToSurface ( const TVector2< T > & phiTheta ) const

inline

Map spherical to Cartesian coordinates on the surface of the sphere.

◆ sampleToSurfaceAbsCosThetaWeighted() [1/2]

template<typename T >

TVector3< T > ph::math::TSphere< T >::sampleToSurfaceAbsCosThetaWeighted ( const std::array< T, 2 > & sample ) const

inline

The mapped positions are weighted according to the cosine of the zenith angle.

Parameters

sample Uniform 2-D sample in [0, 1].

Returns: The sampled surface position.

◆ sampleToSurfaceAbsCosThetaWeighted() [2/2]

template<typename T >

TVector3< T > ph::math::TSphere< T >::sampleToSurfaceAbsCosThetaWeighted	(	const std::array< T, 2 > &	sample,
		T *	out_pdfA ) const

inline

An overload with PDF.

Parameters

[out] out_pdfA Area domain PDF of sampling this surface position.

◆ sampleToSurfaceArchimedes() [1/2]

template<typename T >

TVector3< T > ph::math::TSphere< T >::sampleToSurfaceArchimedes ( const std::array< T, 2 > & sample ) const

inline

A common mapping method that is based on Archimedes' derivation that the horizontal slices of a sphere have equal area. The mapped positions are distributed uniformly if the sample is uniform. For a unit sphere, this method effectively generates normalized directions.

Parameters

sample Uniform 2-D sample in [0, 1].

Returns: The sampled surface position.

◆ sampleToSurfaceArchimedes() [2/2]

template<typename T >

TVector3< T > ph::math::TSphere< T >::sampleToSurfaceArchimedes	(	const std::array< T, 2 > &	sample,
		T *	out_pdfA ) const

inline

An overload with PDF.

Parameters

[out] out_pdfA Area domain PDF of sampling this surface position.

◆ surfaceDerivativesWrtUv()

template<typename T >

template<typename SurfaceToUv >

std::pair< TVector3< T >, TVector3< T > > ph::math::TSphere< T >::surfaceDerivativesWrtUv	(	const TVector3< T > &	surface,
		SurfaceToUv	surfaceToUv,
		T	hInRadians = to_radians<T>(1) ) const

inline

Calculate dPdU and dPdV with finite difference.

This is a partial derivatives calculator for arbitrary UV maps; however, as it is only a finite difference approximation, artifacts can occur around the discontinuities of the underlying UV mapping.

Parameters

surface	Coordinates of the point of interest on the surface.
surfaceToUv	A mapper that maps surface coordinates to UV.
hInRadians	Half inverval in radians used in the finite difference. Should within (0, pi/4].

Returns: A pair containing dPdU and dPdV.

◆ surfaceToLatLong01()

template<typename T >

TVector2< T > ph::math::TSphere< T >::surfaceToLatLong01 ( const TVector3< T > & surface ) const

inline

◆ surfaceToPhiTheta()

template<typename T >

TVector2< T > ph::math::TSphere< T >::surfaceToPhiTheta ( const TVector3< T > & surface ) const

inline

Map Cartesian to spherical coordinates on the surface of the sphere.

◆ uniformSurfaceSamplePdfA()

template<typename T >

T ph::math::TSphere< T >::uniformSurfaceSamplePdfA ( ) const

inline

The documentation for this class was generated from the following files:

Source/Math/Geometry/TSphere.h
Source/Math/Geometry/TSphere.ipp

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ TSphere() [1/2]

◆ TSphere() [2/2]

Member Function Documentation

◆ getAABB()

◆ getArea()

◆ getRadius()

◆ isInside()

◆ isIntersecting()

◆ latLong01ToPhiTheta()

◆ latLong01ToSurface()

◆ makeUnit()

◆ mayOverlapVolume()

◆ phiThetaToSurface()

◆ sampleToSurfaceAbsCosThetaWeighted() [1/2]

◆ sampleToSurfaceAbsCosThetaWeighted() [2/2]

◆ sampleToSurfaceArchimedes() [1/2]

◆ sampleToSurfaceArchimedes() [2/2]

◆ surfaceDerivativesWrtUv()

◆ surfaceToLatLong01()

◆ surfaceToPhiTheta()

◆ uniformSurfaceSamplePdfA()