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/*****************************************************************************
* *
* PrimeSense PSCommon Library *
* Copyright (C) 2012 PrimeSense Ltd. *
* *
* This file is part of PSCommon. *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); *
* you may not use this file except in compliance with the License. *
* You may obtain a copy of the License at *
* *
* http://www.apache.org/licenses/LICENSE-2.0 *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* *
*****************************************************************************/
#include "XnSymmetricMatrix3x3.h"
#include "XnMatrix3x3.h"
//#define USE_STABLE_EIGENVALUES
//#define ALWAYS_USE_SCALING_FOR_EIGENVALUES
namespace xnl
{
static XnFloat GetScaleFactorForEigenValues(const SymmetricMatrix3x3& mat)
{
static const XnFloat target = 1e3f;
XnFloat maxAbs = mat.MaxAbs();
return maxAbs>0 ? target/maxAbs : 1.0f;
}
Vector3D SymmetricMatrix3x3::GetEigenValuesNoScaling() const
{
#ifdef USE_STABLE_EIGENVALUES
Vector3D eigenvalues;
Matrix3X3 eigenvectors;
EigenDecomposition(*this, eigenvectors, eigenvalues);
return eigenvalues;
#else
XnFloat m = (XnFloat)Math::ONE_THIRD*Trace();
XnFloat a00 = m_x00-m, a11 = m_x11-m, a22 = m_x22-m;
XnFloat a01_sqr = Math::Sqr(m_x01);
XnFloat a02_sqr = Math::Sqr(m_x02);
XnFloat a12_sqr = Math::Sqr(m_x12);
XnFloat p = (XnFloat)Math::ONE_SIXTH * (a00*a00+a11*a11+a22*a22 + 2*(a01_sqr+a02_sqr+a12_sqr));
XnFloat q = (XnFloat).5*(a00*(a11*a22-a12_sqr)-a11*a02_sqr-a22*a01_sqr) + m_x01*m_x02*m_x12;
XnFloat sqrt_p = Math::Sqrt(p), disc = p*p*p-q*q;
XnFloat phi = (XnFloat)Math::ONE_THIRD*atan2(Math::Sqrt(Math::Max((XnFloat)0,disc)),q);
XnFloat c=cos(phi) , s=sin(phi);
XnFloat sqrt_p_cos = sqrt_p*c, root_three_sqrt_p_sin = (XnFloat)Math::ROOT_THREE*sqrt_p*s;
Vector3D lambda(m+2*sqrt_p_cos, m-sqrt_p_cos-root_three_sqrt_p_sin, m-sqrt_p_cos+root_three_sqrt_p_sin);
Math::ExchangeSort(lambda.z, lambda.y, lambda.x);
return lambda;
#endif
}
Vector3D SymmetricMatrix3x3::GetEigenValuesWithScaling() const
{
XnFloat factor = GetScaleFactorForEigenValues(*this);
SymmetricMatrix3x3 normalizedMatrix = *this;
normalizedMatrix *= factor;
return (1/factor)*normalizedMatrix.GetEigenValuesNoScaling();
}
Vector3D SymmetricMatrix3x3::GetEigenValues() const
{
#ifdef ALWAYS_USE_SCALING_FOR_EIGENVALUES
return GetEigenValuesWithScaling();
#else
return GetEigenValuesNoScaling();
#endif
}
void SymmetricMatrix3x3::GetEigenVectors(const Vector3D &lambda,Matrix3x3 &eigenvectors,XnFloat tolerance) const
{
XnFloat tiny = tolerance * Math::MaxAbs(lambda.x,lambda.z);
if(lambda.x-lambda.y<=tiny)
{
if(lambda.y-lambda.z<=tiny)
eigenvectors = Matrix3x3::Identity();
else {
Vector3D v2;
GetEigenVector(lambda.z,v2);
Vector3D v1=v2.UnitOrthogonalVector();
Vector3D v0;
CrossProduct(v1,v2,v0);
eigenvectors.Set(v0,v1,v2);
}
}
else if(lambda.y-lambda.z<=tiny) {
Vector3D v0;
GetEigenVector(lambda.x,v0);
Vector3D v1=v0.UnitOrthogonalVector();
Vector3D v2;
CrossProduct(v0,v1,v2);
eigenvectors.Set(v0,v1,v2);
}
else {
Vector3D v0;
GetEigenVector(lambda.x,v0);
Vector3D v2;
GetEigenVector(lambda.z,v2);
Vector3D v1;
CrossProduct(v2,v0,v1);
eigenvectors.Set(v0,v1,v2);
}
}
void SymmetricMatrix3x3::GetEigenVector(XnFloat lambda,Vector3D &v) const
{
SymmetricMatrix3x3 COMat((m_x11-lambda)*(m_x22-lambda) - m_x12*m_x12, m_x12*m_x02 - m_x01*(m_x22-lambda), m_x01*m_x12 - (m_x11-lambda)*m_x02,
(m_x00-lambda)*(m_x22-lambda) - m_x02*m_x02, m_x01*m_x02 - (m_x00-lambda)*m_x12,
(m_x00-lambda)*(m_x11-lambda) - m_x01*m_x01);
XnFloat scales[3] = {Math::Sqr(COMat.m_x00) + Math::Sqr(COMat.m_x01) + Math::Sqr(COMat.m_x02),
Math::Sqr(COMat.m_x01) + Math::Sqr(COMat.m_x11) + Math::Sqr(COMat.m_x12),
Math::Sqr(COMat.m_x02) + Math::Sqr(COMat.m_x12) + Math::Sqr(COMat.m_x22)};
//XnInt32 i = ArgMax(scales[0], scales[1], scales[2]);
if (scales[0] > scales[1])
{
if (scales[0] > scales[2])
{
//assert(i==0);
const XnFloat s=Math::OneOverSqrtHelper<XnFloat>::OneOverSqrt(scales[0]);
v.Set(COMat.m_x00*s,COMat.m_x01*s,COMat.m_x02*s);
return;
}
else
{
//assert(i==2);
const XnFloat s=Math::OneOverSqrtHelper<XnFloat>::OneOverSqrt(scales[2]);
v.Set(COMat.m_x02*s,COMat.m_x12*s,COMat.m_x22*s);
return;
}
}
else if (scales[1] > scales[2])
{
//assert(i==1);
const XnFloat s=Math::OneOverSqrtHelper<XnFloat>::OneOverSqrt(scales[1]);
v.Set(COMat.m_x01*s,COMat.m_x11*s,COMat.m_x12*s);
return;
}
else
{
//assert(i==2);
const XnFloat s=Math::OneOverSqrtHelper<XnFloat>::OneOverSqrt(scales[2]);
v.Set(COMat.m_x02*s,COMat.m_x12*s,COMat.m_x22*s);
return;
}
}
// No scaling
void SymmetricMatrix3x3::SolveEigenProblemNoScaling(Vector3D &eigenvalues,Matrix3x3 &eigenvectors,XnFloat tolerance) const
{
#ifdef USE_STABLE_EIGENVALUES
EigenDecomposition(*this, eigenvectors, eigenvalues);
#else
eigenvalues = GetEigenValuesNoScaling(); // This function takes care of the scaling for us
GetEigenVectors(eigenvalues,eigenvectors,tolerance);
#endif
}
// With scaling
void SymmetricMatrix3x3::SolveEigenProblemWithScaling(Vector3D &eigenvalues,Matrix3x3 &eigenvectors,XnFloat tolerance) const
{
#ifdef USE_STABLE_EIGENVALUES
XnFloat factor = GetScaleFactorForEigenValues(*this);
SymmetricMatrix3x3 normalizedMatrix(factor*x00,factor*x01,factor*x02,factor*x11,factor*x12,factor*x22);
EigenDecomposition(normalizedMatrix, eigenvectors, eigenvalues);
eigenvalues *= (1/factor);
#else
eigenvalues = GetEigenValuesWithScaling();
GetEigenVectors(eigenvalues,eigenvectors,tolerance);
#endif
}
// Uses scaling if ALWAYS_USE_SCALING_FOR_EIGENVALUES is defined
void SymmetricMatrix3x3::SolveEigenProblem(Vector3D& eigenvalues,Matrix3x3& eigenvectors,XnFloat tolerance) const
{
#ifdef ALWAYS_USE_SCALING_FOR_EIGENVALUES
SolveEigenProblemWithScaling(eigenvalues, eigenvectors, tolerance);
#else
SolveEigenProblemNoScaling(eigenvalues, eigenvectors, tolerance);
#endif
}
// Uses scaling if ALWAYS_USE_SCALING_FOR_EIGENVALUES is defined
void SymmetricMatrix3x3::SolveSingleEigenProblem(XnInt32 i,Vector3D& eigenvalues,Vector3D& eigenvector,XnFloat /*tolerance*/) const
{
#ifdef USE_STABLE_EIGENVALUES
Matrix3x3 eigenvectors;
SolveEigenProblem(eigenvalues, eigenvectors, tolerance); // This function takes care of the scaling for us
eigenvector = eigenvectors.GetColumn(i);
#else
eigenvalues = GetEigenValues(); // This function takes care of the scaling for us
GetEigenVector(eigenvalues[i], eigenvector);
#endif
}
XnFloat SymmetricMatrix3x3::MaxAbs() const {
return Math::Max(Math::MaxAbs(m_x00,m_x01,m_x02),Math::MaxAbs(m_x11,m_x12),(XnFloat)Math::Abs(m_x22));
}
} // XnLib
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