#include <QuadricError.h>

Inheritance diagram for UE::Geometry::TAttrBasedQuadricError< RealType >:

Public Types
typedef RealType	ScalarType

typedef TVolPresQuadricError< RealType >	BaseClass

typedef TQuadricError< RealType >	BaseStruct

Public Types inherited from UE::Geometry::TVolPresQuadricError< RealType >
typedef TQuadricError< RealType >	BaseStruct

Public Types inherited from UE::Geometry::TQuadricError< RealType >
typedef RealType	ScalarType

Public Member Functions
	TAttrBasedQuadricError (const TVector< RealType > &P0, const TVector< RealType > &P1, const TVector< RealType > &P2, const TVector< RealType > &N0, const TVector< RealType > &N1, const TVector< RealType > &N2, const TVector< RealType > &NFace, const TVector< RealType > &CenterPoint, RealType AttrWeight)

	TAttrBasedQuadricError ()

	TAttrBasedQuadricError (const TAttrBasedQuadricError &Aother, const TAttrBasedQuadricError &Bother)

void	Add (RealType w, const TAttrBasedQuadricError &other)

bool	OptimalPoint (UE::Math::TVector< RealType > &OptPoint, RealType minThresh=1000.0 *TMathUtil< RealType >::Epsilon) const

RealType	Evaluate (const TVector< RealType > &point, const TVector< RealType > &InAttr) const

void	ComputeAttributes (const TVector< RealType > &point, TVector< RealType > &attr) const

RealType	Evaluate (const TVector< RealType > &point) const

Public Member Functions inherited from UE::Geometry::TVolPresQuadricError< RealType >
	TVolPresQuadricError ()

	TVolPresQuadricError (const TVector< RealType > &Normal, const TVector< RealType > &Point)

	TVolPresQuadricError (const TVolPresQuadricError &a, const TVolPresQuadricError &b)

	TVolPresQuadricError (const TVolPresQuadricError &a, const TVolPresQuadricError &b, const FPlaneData &DuplicatePlaneData)

void	Add (RealType w, const TVolPresQuadricError &b)

bool	OptimalPoint (UE::Math::TVector< RealType > &OutResult, RealType minThresh=1000.0 *TMathUtil< RealType >::Epsilon) const

Public Member Functions inherited from UE::Geometry::TQuadricError< RealType >
	TQuadricError ()

	TQuadricError (const TVector< RealType > &Normal, const TVector< RealType > &Point)

	TQuadricError (const TQuadricError &a, const TQuadricError &b)

void	Add (RealType w, const TQuadricError &b)

void	Add (const TQuadricError &b)

void	Subtract (const TQuadricError &b)

void	AddSeamQuadric (const TQuadricError &b)

void	SubtractSeamQuadric (const TQuadricError &b)

void	Scale (RealType w)

RealType	Evaluate (const UE::Math::TVector< RealType > &pt) const

TVector< RealType >	MultiplyA (const UE::Math::TVector< RealType > &pt) const

bool	SolveAxEqualsb (UE::Math::TVector< RealType > &OutResult, const RealType bvecx, const RealType bvecy, const RealType bvecz, const RealType minThresh=1000.0 *TMathUtil< RealType >::Epsilon) const

bool	OptimalPoint (UE::Math::TVector< RealType > &OutResult, RealType minThresh=1000.0 *TMathUtil< RealType >::Epsilon) const

Static Public Member Functions
static TAttrBasedQuadricError	Zero ()

Static Public Member Functions inherited from UE::Geometry::TVolPresQuadricError< RealType >
static TVolPresQuadricError	Zero ()

Static Public Member Functions inherited from UE::Geometry::TQuadricError< RealType >
static TQuadricError	Zero ()

static bool	InvertSymmetricMatrix (const RealType SM[6], RealType InvSM[6], RealType minThresh=1000.0 *TMathUtil< RealType >::Epsilon)

static TVector< RealType >	MultiplySymmetricMatrix (const RealType SM[6], const RealType vec[3])

static TVector< RealType >	MultiplySymmetricMatrix (const RealType SM[6], const UE::Math::TVector< RealType > &vec)

Public Attributes
RealType	a

RealType	attrweight = 1.

TVector< RealType >	grad [3]

RealType	d [3]

Public Attributes inherited from UE::Geometry::TVolPresQuadricError< RealType >
FPlaneData	PlaneData

Public Attributes inherited from UE::Geometry::TQuadricError< RealType >
RealType	Axx

RealType	Axy

RealType	Axz

RealType	Ayy

RealType	Ayz

RealType	Azz

RealType	bx

RealType	by

RealType	bz

RealType	c

Detailed Description

template<typename RealType>
class UE::Geometry::TAttrBasedQuadricError< RealType >

Quadric Error type for use in volume memory-less simplification with volume preservation constraints. using the normal as three additional attributes to contribute to the quadric error. See: http://hhoppe.com/newqem.pdf

Member Typedef Documentation

◆ BaseClass

template<typename RealType >

typedef TVolPresQuadricError<RealType> UE::Geometry::TAttrBasedQuadricError< RealType >::BaseClass

◆ BaseStruct

template<typename RealType >

typedef TQuadricError<RealType> UE::Geometry::TAttrBasedQuadricError< RealType >::BaseStruct

◆ ScalarType

template<typename RealType >

typedef RealType UE::Geometry::TAttrBasedQuadricError< RealType >::ScalarType

Constructor & Destructor Documentation

◆ TAttrBasedQuadricError() [1/3]

template<typename RealType >

UE::Geometry::TAttrBasedQuadricError< RealType >::TAttrBasedQuadricError	(	const TVector< RealType > &	P0,
		const TVector< RealType > &	P1,
		const TVector< RealType > &	P2,
		const TVector< RealType > &	N0,
		const TVector< RealType > &	N1,
		const TVector< RealType > &	N2,
		const TVector< RealType > &	NFace,
		const TVector< RealType > &	CenterPoint,
		RealType	AttrWeight
	)

inline

Given a scalar attribute 'a' defined at the vertices e.g. a0, a1, a2 (in this case the attribute is a single component of the vertex normal)

solve 4x4 system: (p0^t 1) (g[0]) = (a0) (p1^t 1) (g[1]) (a1) (p2^t 1) (g[2]) (a2) (n^t 0) ( d ) (0 )

for the interpolating gradient 'g' – note this is really p.dot(g) + d = a0 and n.dot(g) = 0

this system can be re-written as < e_20 | g > = (a2-a0) < e_10 | g > = (a1-a0) < n | g > = 0 and
< p0 | g > + d = a0. where e_20 is the edge vector p2 - p0 e_10 is the edge vector p1 - p0.

the first 3 equations can be solved for the vector 'g' either as a 3x3 matrix system or one could solve a 2x2 system since 'g' must be in the plane spanned by {e20, e10}
( give 'n' is orthogonal to the triangle face).

For this quadric, each component of the normal is treated as separate attribute.

◆ TAttrBasedQuadricError() [2/3]

template<typename RealType >

UE::Geometry::TAttrBasedQuadricError< RealType >::TAttrBasedQuadricError ( )

inline

◆ TAttrBasedQuadricError() [3/3]

template<typename RealType >

UE::Geometry::TAttrBasedQuadricError< RealType >::TAttrBasedQuadricError	(	const TAttrBasedQuadricError< RealType > &	Aother,
		const TAttrBasedQuadricError< RealType > &	Bother
	)

inline

Member Function Documentation

◆ Add()

template<typename RealType >

void UE::Geometry::TAttrBasedQuadricError< RealType >::Add	(	RealType	w,
		const TAttrBasedQuadricError< RealType > &	other
	)

inline

Area Weighted Add

◆ ComputeAttributes()

template<typename RealType >

void UE::Geometry::TAttrBasedQuadricError< RealType >::ComputeAttributes	(	const TVector< RealType > &	point,
		TVector< RealType > &	attr
	)		const

inline

◆ Evaluate() [1/2]

template<typename RealType >

RealType UE::Geometry::TAttrBasedQuadricError< RealType >::Evaluate ( const TVector< RealType > & point ) const

inline

◆ Evaluate() [2/2]

template<typename RealType >

RealType UE::Geometry::TAttrBasedQuadricError< RealType >::Evaluate	(	const TVector< RealType > &	point,
		const TVector< RealType > &	InAttr
	)		const

inline

◆ OptimalPoint()

template<typename RealType >

bool UE::Geometry::TAttrBasedQuadricError< RealType >::OptimalPoint	(	UE::Math::TVector< RealType > &	OptPoint,
		RealType	minThresh = `1000.0*TMathUtil<RealType>::Epsilon`
	)		const

inline

The optimal point minimizing the quadric error with respect to a volume conserving constraint

◆ Zero()

template<typename RealType >

static TAttrBasedQuadricError UE::Geometry::TAttrBasedQuadricError< RealType >::Zero ( )

inlinestatic

Member Data Documentation

◆ a

template<typename RealType >

RealType UE::Geometry::TAttrBasedQuadricError< RealType >::a

◆ attrweight

template<typename RealType >

RealType UE::Geometry::TAttrBasedQuadricError< RealType >::attrweight = 1.

◆ d

template<typename RealType >

RealType UE::Geometry::TAttrBasedQuadricError< RealType >::d[3]

◆ grad

template<typename RealType >

TVector<RealType> UE::Geometry::TAttrBasedQuadricError< RealType >::grad[3]

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

Engine/Source/Runtime/GeometryCore/Public/QuadricError.h

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Member Typedef Documentation

◆ BaseClass

◆ BaseStruct

◆ ScalarType

Constructor & Destructor Documentation

◆ TAttrBasedQuadricError() [1/3]

◆ TAttrBasedQuadricError() [2/3]

◆ TAttrBasedQuadricError() [3/3]

Member Function Documentation

◆ Add()

◆ ComputeAttributes()

◆ Evaluate() [1/2]

◆ Evaluate() [2/2]

◆ OptimalPoint()

◆ Zero()

Member Data Documentation

◆ a

◆ attrweight

◆ d

◆ grad