vcl::MeshInertia< MeshType > Class Template Reference

The MeshInertia class provides several for computing Polyhedral Mass properties (like inertia tensor, volume, etc). More...

#include <vclib/space/complex/mesh_inertia.h>

Public Member Functions
	MeshInertia (const MeshType &m)
ScalarType	volume () const
	Returns the volume (or mass) of the mesh. Meaningful only if the mesh is watertight.
Point3< ScalarType >	centerOfMass () const
template<typename Matrix33 >
Matrix33	inertiaTensor () const
template<typename Matrix33 >
void	inertiaTensorEigen (Matrix33 &eigenValues, Point3< ScalarType > &eigenVector) const
	Computes the inertia tensor mesh.

Private Types
enum	{ X = 0 , Y = 1 , Z = 2 }
using	VertexType = MeshType::VertexType
using	FaceType = MeshType::FaceType
using	ScalarType = VertexType::CoordType::ScalarType

Private Member Functions
void	faceIntegrals (const FaceType &f, const Point3< ScalarType > &n)
void	projectionIntegrals (const FaceType &f)
	Computes various integrations over projection of the given face.

Static Private Member Functions
static ScalarType	sqr (const ScalarType &x)
static ScalarType	cube (const ScalarType &x)

Private Attributes
int	mA
int	mB
int	mC
double	mP1
double	mPa
double	mPb
double	mPaa
double	mPab
double	mPbb
double	mPaaa
double	mPaab
double	mPabb
double	mPbbb
double	mFa
double	mFb
double	mFc
double	mFaa
double	mFbb
double	mFcc
double	mFaaa
double	mFbbb
double	mFccc
double	mFaab
double	mFbbc
double	mFcca
double	mT0 = 0
double	mT1 [3] = {0, 0, 0}
double	mT2 [3] = {0, 0, 0}
double	mTP [3] = {0, 0, 0}

Detailed Description

template<FaceMeshConcept MeshType>
class vcl::MeshInertia< MeshType >

The MeshInertia class provides several for computing Polyhedral Mass properties (like inertia tensor, volume, etc).

The algorithm is based on a three step reduction of the volume integrals to successively simpler integrals. The algorithm is designed to minimize the numerical errors that can result from poorly conditioned alignment of polyhedral faces. It is also designed for efficiency. All required volume integrals of a polyhedron are computed together during a single walk over the boundary of the polyhedron; exploiting common subexpressions reduces floating point operations.

For more information, check out:

Brian Mirtich, `‘Fast and Accurate Computation of Polyhedral Mass Properties,’' journal of graphics tools, volume 1, number 2, 1996

Member Function Documentation

inertiaTensorEigen()

template<FaceMeshConcept MeshType>

template<typename Matrix33 >

void vcl::MeshInertia< MeshType >::inertiaTensorEigen ( Matrix33 &  eigenValues, Point3< ScalarType > &  eigenVector  ) const

inline

Computes the inertia tensor mesh.

The result is factored as eigenvalues and eigenvectors (as ROWS).

Parameters

[out]	eigenValues
[out]	eigenVector

projectionIntegrals()

template<FaceMeshConcept MeshType>

void vcl::MeshInertia< MeshType >::projectionIntegrals ( const FaceType &  f )

inlineprivate

Computes various integrations over projection of the given face.

Parameters

f

volume()

template<FaceMeshConcept MeshType>

ScalarType vcl::MeshInertia< MeshType >::volume ( ) const

inline

Returns the volume (or mass) of the mesh. Meaningful only if the mesh is watertight.

Returns

---

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

• vclib/core/include/vclib/space/complex/mesh_inertia.h