Struct SymmetricEigen3 

pub struct SymmetricEigen3 {
    pub eigenvalues: Vec3,
    pub eigenvectors: Mat3,
}

The eigen decomposition of a symmetric 3x3 matrix (f32 precision).

Fields

eigenvalues: Vec3

The eigenvalues of the symmetric 3x3 matrix.

eigenvectors: Mat3

The three eigenvectors of the symmetric 3x3 matrix (as columns).

Implementations

impl SymmetricEigen3

pub fn new(mat: Mat3) -> Self

Computes the eigen decomposition of the given symmetric 3x3 matrix.

The eigenvalues are returned in ascending order eigen1 < eigen2 < eigen3. This can be reversed with the reverse method.

pub fn reverse(&self) -> Self

Reverses the order of the eigenvalues and their corresponding eigenvectors.

pub fn eigenvalues(mat: Mat3) -> Vec3

Computes the eigenvalues of a symmetric 3x3 matrix.

Reference: https://en.wikipedia.org/wiki/Eigenvalue_algorithm#3%C3%973_matrices

pub fn eigenvector1(mat: Mat3, eigenvalue1: f32) -> Vec3

Computes the unit-length eigenvector corresponding to the eigenvalue1 of mat that was computed from the root of a cubic polynomial with a multiplicity of 1.

If the other two eigenvalues are well separated, this method can be used for computing all three eigenvectors. However, to avoid numerical issues when eigenvalues are close to each other, it’s recommended to use the eigenvector2 method for the second eigenvector.

The third eigenvector can be computed as the cross product of the first two.

pub fn eigenvector2(mat: Mat3, eigenvector1: Vec3, eigenvalue2: f32) -> Vec3

Computes the unit-length eigenvector corresponding to the eigenvalue2 of mat that was computed from the root of a cubic polynomial with a potential multiplicity of 2.

The third eigenvector can be computed as the cross product of the first two.

pub fn eigenvector3(eigenvector1: Vec3, eigenvector2: Vec3) -> Vec3

Computes the third eigenvector as the cross product of the first two. If the given eigenvectors are valid, the returned vector should be unit length.

Trait Implementations

impl Clone for SymmetricEigen3

fn clone(&self) -> SymmetricEigen3

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SymmetricEigen3

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl From<DSymmetricEigen3> for SymmetricEigen3

fn from(e: DSymmetricEigen3) -> Self

Converts to this type from the input type.

impl From<SymmetricEigen3> for DSymmetricEigen3

fn from(e: SymmetricEigen3) -> Self

Converts to this type from the input type.

impl From<SymmetricEigen3> for SymmetricEigen3A

fn from(e: SymmetricEigen3) -> Self

Converts to this type from the input type.

impl From<SymmetricEigen3A> for SymmetricEigen3

fn from(e: SymmetricEigen3A) -> Self

Converts to this type from the input type.

impl PartialEq for SymmetricEigen3

fn eq(&self, other: &SymmetricEigen3) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for SymmetricEigen3

impl StructuralPartialEq for SymmetricEigen3