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Improved documentation of inertia and slightly changed the interface (added a constructor)

This commit is contained in:
Paolo Cignoni 2012-10-16 07:36:35 +00:00
parent bebfa3eb8b
commit ac9b6b16f2
1 changed files with 45 additions and 23 deletions
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68
vcg/complex/algorithms/inertia.h
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@ -23,22 +23,6 @@
#ifndef _VCG_INERTIA_
#define _VCG_INERTIA_
/*
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
*/
#include <eigenlib/Eigen/Core>
#include <eigenlib/Eigen/Eigenvalues>
@ -48,10 +32,27 @@ namespace vcg
{
namespace tri
{
template <class InertiaMeshType>
/*! \brief Methods 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:
<b>Brian Mirtich,</b>
``Fast and Accurate Computation of Polyhedral Mass Properties,''
journal of graphics tools, volume 1, number 2, 1996
*/
template <class MeshType>
class Inertia
{
typedef InertiaMeshType MeshType;
typedef typename MeshType::VertexType VertexType;
typedef typename MeshType::VertexPointer VertexPointer;
typedef typename MeshType::VertexIterator VertexIterator;
@ -82,6 +83,12 @@ private :
double T0, T1[3], T2[3], TP[3];
public:
/*! \brief Basic constructor
When you create a Inertia object, you have to specify the mesh that it refers to.
The properties are computed at that moment. Subsequent modification of the mesh does not affect these values.
*/
Inertia(MeshType &m) {Compute(m);}
/* compute various integrations over projection of face */
void compProjectionIntegrals(FaceType &f)
@ -176,6 +183,11 @@ void CompFaceIntegrals(FaceType &f)
}
/*! main function to be called.
It requires a watertight mesh with per face normals.
*/
void Compute(MeshType &m)
{
tri::UpdateNormal<MeshType>::PerFaceNormalized(m);
@ -216,11 +228,19 @@ void Compute(MeshType &m)
TP[X] /= 2; TP[Y] /= 2; TP[Z] /= 2;
}
/*! \brief Return the Volume (or mass) of the mesh.
Meaningful only if the mesh is watertight.
*/
ScalarType Mass()
{
return static_cast<ScalarType>(T0);
}
/*! \brief Return the Center of Mass (or barycenter) of the mesh.
Meaningful only if the mesh is watertight.
*/
Point3<ScalarType> CenterOfMass()
{
Point3<ScalarType> r;
@ -275,18 +295,20 @@ void InertiaTensor(Eigen::Matrix3d &J )
}
/** Compute eigenvalues and eigenvectors of inertia tensor.
The eigenvectors make a rotation matrix that aligns the mesh along the axes of min/max inertia
*/
/*! \brief Return the Inertia tensor the mesh.
The result is factored as eigenvalues and eigenvectors (as ROWS).
*/
void InertiaTensorEigen(Matrix33<ScalarType> &EV, Point3<ScalarType> &ev )
{
Eigen::Matrix3d it;
InertiaTensor(it);
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eig(it);
Eigen::Vector3d c_val = eig.eigenvalues();
Eigen::Matrix3d c_vec = eig.eigenvectors();
Eigen::Matrix3d c_vec = eig.eigenvectors(); // eigenvector are stored as columns.
EV.FromEigenMatrix(c_vec);
EV.transposeInPlace();
ev.FromEigenVector(c_val);
}