Struct SymmetricEigen3

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

The eigen decomposition of a symmetric 3x3 matrix.

Fields

eigenvalues: Vec3

The eigenvalues of the symmetric 3x3 matrix.

These should be in ascending order eigen1 <= eigen2 <= eigen3.

eigenvectors: Mat3

The three eigenvectors of the symmetric 3x3 matrix. Each eigenvector should be unit length and orthogonal to the other eigenvectors.

The eigenvectors are ordered to correspond to the eigenvalues. For example, eigenvectors.x_axis corresponds to eigenvalues.x.

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, bool)

Computes the eigenvalues of a symmetric 3x3 matrix, also returning whether the input matrix is diagonal.

If the matrix is already diagonal, the eigenvalues are returned as is without reordering. Otherwise, the eigenvalues are computed and returned in ascending order such that eigen1 <= eigen2 <= eigen3.

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 copy 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 FromReflect for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn from_reflect(reflect: &dyn PartialReflect) -> Option<Self>

Constructs a concrete instance of Self from a reflected value.

fn take_from_reflect( reflect: Box<dyn PartialReflect>, ) -> Result<Self, Box<dyn PartialReflect>>

Attempts to downcast the given value to Self using, constructing the value using from_reflect if that fails.

impl GetTypeRegistration for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn get_type_registration() -> TypeRegistration

Returns the default TypeRegistration for this type.

fn register_type_dependencies(registry: &mut TypeRegistry)

Registers other types needed by this 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 PartialReflect for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn get_represented_type_info(&self) -> Option<&'static TypeInfo>

Returns the TypeInfo of the type represented by this value.

fn clone_value(&self) -> Box<dyn PartialReflect>

Clones the value as a Reflect trait object.

fn try_apply(&mut self, value: &dyn PartialReflect) -> Result<(), ApplyError>

Tries to apply a reflected value to this value.

fn reflect_kind(&self) -> ReflectKind

Returns a zero-sized enumeration of “kinds” of type.

fn reflect_ref(&self) -> ReflectRef<'_>

Returns an immutable enumeration of “kinds” of type.

fn reflect_mut(&mut self) -> ReflectMut<'_>

Returns a mutable enumeration of “kinds” of type.

fn reflect_owned(self: Box<Self>) -> ReflectOwned

Returns an owned enumeration of “kinds” of type.

fn try_into_reflect( self: Box<Self>, ) -> Result<Box<dyn Reflect>, Box<dyn PartialReflect>>

Attempts to cast this type to a boxed, fully-reflected value.

fn try_as_reflect(&self) -> Option<&dyn Reflect>

Attempts to cast this type to a fully-reflected value.

fn try_as_reflect_mut(&mut self) -> Option<&mut dyn Reflect>

Attempts to cast this type to a mutable, fully-reflected value.

fn into_partial_reflect(self: Box<Self>) -> Box<dyn PartialReflect>

Casts this type to a boxed, reflected value.

fn as_partial_reflect(&self) -> &dyn PartialReflect

Casts this type to a reflected value.

fn as_partial_reflect_mut(&mut self) -> &mut dyn PartialReflect

Casts this type to a mutable, reflected value.

fn reflect_partial_eq(&self, value: &dyn PartialReflect) -> Option<bool>

Returns a “partial equality” comparison result.

fn apply(&mut self, value: &(dyn PartialReflect + 'static))

Applies a reflected value to this value.

fn reflect_hash(&self) -> Option<u64>

Returns a hash of the value (which includes the type).

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

Debug formatter for the value.

fn serializable(&self) -> Option<Serializable<'_>>

Returns a serializable version of the value.

fn is_dynamic(&self) -> bool

Indicates whether or not this type is a dynamic type.

impl Reflect for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn into_any(self: Box<Self>) -> Box<dyn Any>

Returns the value as a Box<dyn Any>.

fn as_any(&self) -> &dyn Any

Returns the value as a &dyn Any.

fn as_any_mut(&mut self) -> &mut dyn Any

Returns the value as a &mut dyn Any.

fn into_reflect(self: Box<Self>) -> Box<dyn Reflect>

Casts this type to a boxed, fully-reflected value.

fn as_reflect(&self) -> &dyn Reflect

Casts this type to a fully-reflected value.

fn as_reflect_mut(&mut self) -> &mut dyn Reflect

Casts this type to a mutable, fully-reflected value.

fn set(&mut self, value: Box<dyn Reflect>) -> Result<(), Box<dyn Reflect>>

Performs a type-checked assignment of a reflected value to this value.

impl Struct for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn field(&self, name: &str) -> Option<&dyn PartialReflect>

Returns a reference to the value of the field named name as a &dyn PartialReflect.

fn field_mut(&mut self, name: &str) -> Option<&mut dyn PartialReflect>

Returns a mutable reference to the value of the field named name as a &mut dyn PartialReflect.

fn field_at(&self, index: usize) -> Option<&dyn PartialReflect>

Returns a reference to the value of the field with index index as a &dyn PartialReflect.

fn field_at_mut(&mut self, index: usize) -> Option<&mut dyn PartialReflect>

Returns a mutable reference to the value of the field with index index as a &mut dyn PartialReflect.

fn name_at(&self, index: usize) -> Option<&str>

Returns the name of the field with index index.

fn field_len(&self) -> usize

Returns the number of fields in the struct.

fn iter_fields(&self) -> FieldIter<'_>

Returns an iterator over the values of the reflectable fields for this struct.

fn clone_dynamic(&self) -> DynamicStruct

Clones the struct into a DynamicStruct.

fn get_represented_struct_info(&self) -> Option<&'static StructInfo>

Will return None if TypeInfo is not available.

impl TypePath for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync,

fn type_path() -> &'static str

Returns the fully qualified path of the underlying type.

fn short_type_path() -> &'static str

Returns a short, pretty-print enabled path to the type.

fn type_ident() -> Option<&'static str>

Returns the name of the type, or None if it is anonymous.

fn crate_name() -> Option<&'static str>

Returns the name of the crate the type is in, or None if it is anonymous.

fn module_path() -> Option<&'static str>

Returns the path to the module the type is in, or None if it is anonymous.

impl Typed for SymmetricEigen3

where SymmetricEigen3: Any + Send + Sync, Vec3: FromReflect + TypePath + MaybeTyped + RegisterForReflection, Mat3: FromReflect + TypePath + MaybeTyped + RegisterForReflection,

fn type_info() -> &'static TypeInfo

Returns the compile-time info for the underlying type.

impl Copy for SymmetricEigen3

impl StructuralPartialEq for SymmetricEigen3