Class FastQuaternionSVD

Fast Approximate SVD of 3x3 matrix that returns quaternions. Implemented based on https://github.com/benjones/quatSVD/blob/master/quatSVD.hpp which was re-implemented from http://pages.cs.wisc.edu/~sifakis/project_pages/svd.html

By default, only does a small number of diagonalization iterations (4), which limits the accuracy of the solution. Results are still orthonormal but error when reconstructing matrix will be larger. This is fine for many applications. Can increase accuracy by increasing NumJacobiIterations parameter

Note: does not produce same quaternions as running SingularValueDecomposition on matrix and converting resulting U/V to quaternions. The numbers will be similar but the signs will be different

Useful properties:

  • quaternions are rotations, there are no mirrors like in normal SVD

TODO:

  • SymmetricMatrix3d currently a class, could make a struct (see comments)
Inheritance
Object
FastQuaternionSVD
Inherited Members
Namespace: g3
Assembly: cs.temp.dll.dll
Syntax
public class FastQuaternionSVD

Constructors

FastQuaternionSVD()

Declaration
public FastQuaternionSVD()

FastQuaternionSVD(Matrix3d, Double, Int32)

Declaration
public FastQuaternionSVD(Matrix3d matrix, double epsilon = 2.2204460492503131E-16, int jacobiIters = 4)
Parameters
Type Name Description
Matrix3d matrix
Double epsilon
Int32 jacobiIters

Fields

S

Declaration
public Vector3d S
Field Value
Type Description
Vector3d

U

Declaration
public Quaterniond U
Field Value
Type Description
Quaterniond

V

Declaration
public Quaterniond V
Field Value
Type Description
Quaterniond

Methods

ReconstructMatrix()

Compute U * S * V^T, useful for error-checking

Declaration
public Matrix3d ReconstructMatrix()
Returns
Type Description
Matrix3d

Solve(Matrix3d, Double, Int32)

Declaration
public void Solve(Matrix3d matrix, double epsilon = 2.2204460492503131E-16, int jacobiIters = -1)
Parameters
Type Name Description
Matrix3d matrix
Double epsilon
Int32 jacobiIters