ph::math::TBasicTriangle< T > Class Template Reference

Basic 3-D triangle functionalities. More...

#include <TBasicTriangle.h>

Inheritance diagram for ph::math::TBasicTriangle< T >:

Public Member Functions
	TBasicTriangle (TVector3< T > vA, TVector3< T > vB, TVector3< T > vC)
	TBasicTriangle (std::array< TVector3< T >, 3 > vertices)
T	getArea () const
TVector3< T >	getFaceNormal () const
TVector3< T >	getCentroid () const
TAABB3D< T >	getAABB () const
T	getAspectRatio () const
	Calculate aspect ratio of this triangle. For a triangle, its aspect ratio is defined to be the ratio of the circumradius to twice the inradius. The higher the aspect ratio, the narrower the shape of the triangle. A triangle with extreme aspect ratio will look like a needle. The smallest aspect ratio possible is 1 (an equilateral triangle), while the largest possible aspect ratio is infinity (degenerate).
TVector3< T >	safeGetFaceNormal (const TVector3< T > &failSafe={0, 1, 0}) const
	Calculate face normal with a fail-safe value. The vertices may form a degenerate triangle (zero cross product and thus producing NaNs after being normalized, or vertices with Inf/NaN), in such case the fail-safe vector will be returned.
std::pair< TVector3< T >, TVector3< T > >	getEdgeVectors () const
TVector3< T >	surfaceToBarycentric (const TVector3< T > &position) const
TVector3< T >	barycentricToSurface (const TVector3< T > &barycentricCoords) const
TVector3< T >	sampleToBarycentricOsada (const std::array< T, 2 > &sample) const
	Map the 2D sample to a position on the surface of the triangle. A common mapping on triangles which is based on slicing the triangular area into stripes. The mapped positions (after being converted from barycentric coordinates) are distributed uniformly if the sample is uniform. Reference: Osada et al., Section 4.2, "Shape Distributions", TOG02.
TVector3< T >	sampleToBarycentricOsada (const std::array< T, 2 > &sample, T *out_pdfA) const
T	uniformSurfaceSamplePdfA () const
bool	isDegenerate () const
TVector3< T >	getVa () const
TVector3< T >	getVb () const
TVector3< T >	getVc () const

Static Public Member Functions
static TVector3< T >	interpolate (const std::array< TVector3< T >, 3 > &attributes, const TVector3< T > &barycentricCoords)
static TVector3< T >	interpolate (const TVector3< T > &attributeA, const TVector3< T > &attributeB, const TVector3< T > &attributeC, const TVector3< T > &barycentricCoords)
static bool	calcSurfaceParamDerivatives (const std::array< TVector3< T >, 3 > &attributes, const std::array< TVector2< T >, 3 > &parameterizations, TVector3< T > *out_dXdU, TVector3< T > *out_dXdV)

Protected Member Functions
	PH_DEFINE_INLINE_RULE_OF_5_MEMBERS (TBasicTriangle)

Detailed Description

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

Basic 3-D triangle functionalities.

The class is not intended to be used polymorphically.

Constructor & Destructor Documentation

TBasicTriangle() [1/2]

template<typename T >

ph::math::TBasicTriangle< T >::TBasicTriangle ( TVector3< T > vA, TVector3< T > vB, TVector3< T > vC )

inline

TBasicTriangle() [2/2]

template<typename T >

ph::math::TBasicTriangle< T >::TBasicTriangle ( std::array< TVector3< T >, 3 > vertices )

inlineexplicit

Member Function Documentation

barycentricToSurface()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::barycentricToSurface ( const TVector3< T > & barycentricCoords ) const

inline

calcSurfaceParamDerivatives()

template<typename T >

bool ph::math::TBasicTriangle< T >::calcSurfaceParamDerivatives ( const std::array< TVector3< T >, 3 > & attributes, const std::array< TVector2< T >, 3 > & parameterizations, TVector3< T > * out_dXdU, TVector3< T > * out_dXdV )

inlinestatic

getAABB()

template<typename T >

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

inline

getArea()

template<typename T >

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

inline

getAspectRatio()

template<typename T >

T ph::math::TBasicTriangle< T >::getAspectRatio ( ) const

inline

Calculate aspect ratio of this triangle. For a triangle, its aspect ratio is defined to be the ratio of the circumradius to twice the inradius. The higher the aspect ratio, the narrower the shape of the triangle. A triangle with extreme aspect ratio will look like a needle. The smallest aspect ratio possible is 1 (an equilateral triangle), while the largest possible aspect ratio is infinity (degenerate).

Note

For integer types, returns 0 for degenerate triangles.

getCentroid()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::getCentroid ( ) const

inline

getEdgeVectors()

template<typename T >

std::pair< TVector3< T >, TVector3< T > > ph::math::TBasicTriangle< T >::getEdgeVectors ( ) const

inline

getFaceNormal()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::getFaceNormal ( ) const

inline

getVa()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::getVa ( ) const

inline

getVb()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::getVb ( ) const

inline

getVc()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::getVc ( ) const

inline

interpolate() [1/2]

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::interpolate ( const std::array< TVector3< T >, 3 > & attributes, const TVector3< T > & barycentricCoords )

inlinestatic

interpolate() [2/2]

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::interpolate ( const TVector3< T > & attributeA, const TVector3< T > & attributeB, const TVector3< T > & attributeC, const TVector3< T > & barycentricCoords )

inlinestatic

isDegenerate()

template<typename T >

bool ph::math::TBasicTriangle< T >::isDegenerate ( ) const

inline

Returns

Whether the triangle is a point, line, or contains non-finite vertices.

PH_DEFINE_INLINE_RULE_OF_5_MEMBERS()

template<typename T >

ph::math::TBasicTriangle< T >::PH_DEFINE_INLINE_RULE_OF_5_MEMBERS ( TBasicTriangle< T > )

protected

safeGetFaceNormal()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::safeGetFaceNormal ( const TVector3< T > & failSafe = {0, 1, 0} ) const

inline

Calculate face normal with a fail-safe value. The vertices may form a degenerate triangle (zero cross product and thus producing NaNs after being normalized, or vertices with Inf/NaN), in such case the fail-safe vector will be returned.

Parameters

failSafe

The value to use when the face normal cannot be obtained.

Returns

The face normal. Potentially being failSafe.

sampleToBarycentricOsada() [1/2]

template<typename T >

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

inline

Map the 2D sample to a position on the surface of the triangle. A common mapping on triangles which is based on slicing the triangular area into stripes. The mapped positions (after being converted from barycentric coordinates) are distributed uniformly if the sample is uniform. Reference: Osada et al., Section 4.2, "Shape Distributions", TOG02.

Returns

Sampled barycentric coordinates.

sampleToBarycentricOsada() [2/2]

template<typename T >

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

inline

An overload with PDF. Expected the input sample to be uniform.

surfaceToBarycentric()

template<typename T >

TVector3< T > ph::math::TBasicTriangle< T >::surfaceToBarycentric ( const TVector3< T > & position ) const

inline

uniformSurfaceSamplePdfA()

template<typename T >

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

inline

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

• Source/Math/Geometry/TBasicTriangle.h
• Source/Math/Geometry/TBasicTriangle.ipp