Struct cgmath::Basis3

pub struct Basis3<S> { /* fields omitted */ }

A three-dimensional rotation matrix.

The matrix is guaranteed to be orthogonal, so some operations, specifically inversion, can be implemented more efficiently than the implementations for math::Matrix3. To ensure orthogonality is maintained, the operations have been restricted to a subset of those implemented on Matrix3.

Methods

impl<S: BaseFloat> Basis3<S>

pub fn from_quaternion(quaternion: &Quaternion<S>) -> Basis3<S>

Create a new rotation matrix from a quaternion.

Trait Implementations

impl<S: BaseFloat> Rotation<Point3<S>> for Basis3<S>

fn look_at(dir: Vector3<S>, up: Vector3<S>) -> Basis3<S>

Create a rotation to a given direction with an 'up' vector.

fn between_vectors(a: Vector3<S>, b: Vector3<S>) -> Basis3<S>

Create a shortest rotation to transform vector 'a' into 'b'. Both given vectors are assumed to have unit length.

fn rotate_vector(&self, vec: Vector3<S>) -> Vector3<S>

Rotate a vector using this rotation.

fn invert(&self) -> Basis3<S>

Create a new rotation which "un-does" this rotation. That is, r * r.invert() is the identity.

fn rotate_point(&self, point: P) -> P

Rotate a point using this rotation, by converting it to its representation as a vector.

impl<S: BaseFloat> Rotation3<S> for Basis3<S>

fn from_axis_angle<A: Into<Rad<S>>>(axis: Vector3<S>, angle: A) -> Basis3<S>

Create a rotation using an angle around a given axis.

fn from_angle_x<A: Into<Rad<S>>>(theta: A) -> Basis3<S>

Create a rotation from an angle around the x axis (pitch).

fn from_angle_y<A: Into<Rad<S>>>(theta: A) -> Basis3<S>

Create a rotation from an angle around the y axis (yaw).

fn from_angle_z<A: Into<Rad<S>>>(theta: A) -> Basis3<S>

Create a rotation from an angle around the z axis (roll).

impl<S: Clone> Clone for Basis3<S>

fn clone(&self) -> Basis3<S>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<S> AsRef<Matrix3<S>> for Basis3<S>

fn as_ref(&self) -> &Matrix3<S>

Performs the conversion.

impl<S: PartialEq> PartialEq<Basis3<S>> for Basis3<S>

fn eq(&self, other: &Basis3<S>) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Basis3<S>) -> bool

This method tests for !=.

impl<S: BaseFloat> From<Quaternion<S>> for Basis3<S>

fn from(quat: Quaternion<S>) -> Basis3<S>

Performs the conversion.

impl<S: BaseFloat> From<Basis3<S>> for Matrix3<S>

fn from(b: Basis3<S>) -> Matrix3<S>

Performs the conversion.

impl<S: BaseFloat> From<Basis3<S>> for Quaternion<S>

fn from(b: Basis3<S>) -> Quaternion<S>

Performs the conversion.

impl<A: Angle> From<Euler<A>> for Basis3<A::Unitless> where
    A: Into<Rad<<A as Angle>::Unitless>>, 

fn from(src: Euler<A>) -> Basis3<A::Unitless>

Create a three-dimensional rotation matrix from a set of euler angles.

impl<S: Copy> Copy for Basis3<S>

impl<S: BaseFloat> Mul<Basis3<S>> for Basis3<S>

type Output = Basis3<S>

The resulting type after applying the * operator.

fn mul(self, other: Basis3<S>) -> Basis3<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<&'a Basis3<S>> for Basis3<S>

type Output = Basis3<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Basis3<S>) -> Basis3<S>

Performs the * operation.

impl<'a, S: BaseFloat> Mul<Basis3<S>> for &'a Basis3<S>

type Output = Basis3<S>

The resulting type after applying the * operator.

fn mul(self, other: Basis3<S>) -> Basis3<S>

Performs the * operation.

impl<'a, 'b, S: BaseFloat> Mul<&'a Basis3<S>> for &'b Basis3<S>

type Output = Basis3<S>

The resulting type after applying the * operator.

fn mul(self, other: &'a Basis3<S>) -> Basis3<S>

Performs the * operation.

impl<S: Debug> Debug for Basis3<S>

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

Formats the value using the given formatter.

impl<S: BaseFloat> Product<Basis3<S>> for Basis3<S>

fn product<I: Iterator<Item = Basis3<S>>>(iter: I) -> Basis3<S>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<'a, S: 'a + BaseFloat> Product<&'a Basis3<S>> for Basis3<S>

fn product<I: Iterator<Item = &'a Basis3<S>>>(iter: I) -> Basis3<S>

Method which takes an iterator and generates Self from the elements by multiplying the items.

impl<S: BaseFloat> AbsDiffEq<Basis3<S>> for Basis3<S>

type Epsilon = S::Epsilon

Used for specifying relative comparisons.

fn default_epsilon() -> S::Epsilon

The default tolerance to use when testing values that are close together.

fn abs_diff_eq(&self, other: &Self, epsilon: S::Epsilon) -> bool

A test for equality that uses the absolute difference to compute the approximate equality of two numbers.

fn abs_diff_ne(&self, other: &Rhs, epsilon: Self::Epsilon) -> bool

The inverse of ApproxEq::abs_diff_eq.

impl<S: BaseFloat> RelativeEq<Basis3<S>> for Basis3<S>

fn default_max_relative() -> S::Epsilon

The default relative tolerance for testing values that are far-apart.

fn relative_eq(
    &self,
    other: &Self,
    epsilon: S::Epsilon,
    max_relative: S::Epsilon
) -> bool

A test for equality that uses a relative comparison if the values are far apart.

fn relative_ne(
    &self,
    other: &Rhs,
    epsilon: Self::Epsilon,
    max_relative: Self::Epsilon
) -> bool

The inverse of ApproxEq::relative_eq.

impl<S: BaseFloat> UlpsEq<Basis3<S>> for Basis3<S>

fn default_max_ulps() -> u32

The default ULPs to tolerate when testing values that are far-apart.

fn ulps_eq(&self, other: &Self, epsilon: S::Epsilon, max_ulps: u32) -> bool

A test for equality that uses units in the last place (ULP) if the values are far apart.

fn ulps_ne(&self, other: &Rhs, epsilon: Self::Epsilon, max_ulps: u32) -> bool

The inverse of ApproxEq::ulps_eq.

impl<S: BaseFloat> One for Basis3<S>

fn one() -> Basis3<S>

Returns the multiplicative identity element of Self, 1.

fn set_one(&mut self)

Sets self to the multiplicative identity element of Self, 1.

fn is_one(&self) -> bool where
    Self: PartialEq<Self>, 

Returns true if self is equal to the multiplicative identity.