Struct ultraviolet::rotor::Rotor3

#[repr(C)]
pub struct Rotor3 {
    pub s: f32,
    pub bv: Bivec3,
}

A Rotor in 3d space.

Please see the module level documentation for more information on rotors!

Fields

s: f32

bv: Bivec3

Implementations

impl Rotor3

pub const fn new(scalar: f32, bivector: Bivec3) -> Self

pub fn identity() -> Self

pub fn from_rotation_between(from: Vec3, to: Vec3) -> Self

Construct a Rotor that rotates one vector to another.

pub fn from_angle_plane(angle: f32, plane: Bivec3) -> Self

Construct a rotor given a bivector which defines a plane and rotation orientation, and a rotation angle.

plane must be normalized!

This is the equivalent of an axis-angle rotation.

pub fn into_angle_plane(self) -> (f32, Bivec3)

Return the angle and the normalized plane of the rotation represented by self. The value of the returned angle is between 0 and PI.

pub fn scale_by(&mut self, scale: f32)

Multiply the angle of the rotation represented by self by scale.

pub fn scaled_by(self, scale: f32) -> Self

Return a rotor representing the same rotatation as self but with an angle multiplied by scale

pub fn from_rotation_xy(angle: f32) -> Self

Create new Rotor from a rotation in the xy plane (also known as “around the z axis”).

pub fn from_rotation_xz(angle: f32) -> Self

Create new Rotor from a rotation in the xz plane (also known as “around the y axis”).

pub fn from_rotation_yz(angle: f32) -> Self

Create new Rotor from a rotation in the yz plane (also known as “around the x axis”).

pub fn from_euler_angles(roll: f32, pitch: f32, yaw: f32) -> Self

Angles are applied in the order roll -> pitch -> yaw

• Roll is rotation inside the xy plane (“around the z axis”)
• Pitch is rotation inside the yz plane (“around the x axis”)
• Yaw is rotation inside the xz plane (“around the y axis”)

pub fn mag_sq(&self) -> f32

pub fn mag(&self) -> f32

pub fn normalize(&mut self)

pub fn normalized(&self) -> Self

pub fn reverse(&mut self)

pub fn reversed(&self) -> Self

pub fn dot(&self, rhs: Self) -> f32

pub fn rotate_by(&mut self, rhs: Self)

Rotates this rotor by another rotor in-place. Note that if you are looking to compose rotations which will then be applied to another object/vector (you probably are), you should NOT use this operation. Rather, just use regular left-multiplication as in matrix composition, i.e.

second_rotor * first_rotor

pub fn rotated_by(self, rhs: Self) -> Self

Rotates this rotor by another rotor and returns the result. Note that if you are looking to compose rotations, you should NOT use this operation and rather just use regular left-multiplication like as in matrix composition, i.e.

second_rotor * first_rotor

pub fn rotate_vec(self, vec: &mut Vec3)

Rotates a vector by this rotor.

self must be normalized!

pub fn rotate_vecs(self, vecs: &mut [Vec3])

Rotates multiple vectors by this rotor.

This will be faster than calling rotate_vec individually on many vecs as intermediate values can be precomputed once and applied to each vector.

self must be normalized!

pub fn into_matrix(self) -> Mat3

pub fn into_quaternion_array(self) -> [f32; 4]

Convert this rotor into an array that represents a quaternion. This is in the form [vector, scalar].

pub fn from_quaternion_array(array: [f32; 4]) -> Self

Convert an array that represents a quaternion in the form [vector, scalar] into a rotor.

pub fn layout() -> Layout

Trait Implementations

impl Add<Rotor3> for Rotor3

type Output = Rotor3

The resulting type after applying the + operator.

fn add(self, rhs: Self) -> Self

Performs the + operation.

impl AddAssign<Rotor3> for Rotor3

fn add_assign(&mut self, rhs: Self)

Performs the += operation.

impl Clone for Rotor3

fn clone(&self) -> Rotor3

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Rotor3

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

Formats the value using the given formatter.

impl Default for Rotor3

fn default() -> Self

Returns the “default value” for a type.

impl<'de> Deserialize<'de> for Rotor3

fn deserialize<D>(deserializer: D) -> Result<Self, D::Error>where D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl Div<f32> for Rotor3

type Output = Rotor3

The resulting type after applying the / operator.

fn div(self, rhs: f32) -> Self

Performs the / operation.

impl DivAssign<f32> for Rotor3

fn div_assign(&mut self, rhs: f32)

Performs the /= operation.

impl From<Rotor3> for Mat3

fn from(rotor: Rotor3) -> Mat3

Converts to this type from the input type.

impl Lerp<f32> for Rotor3

fn lerp(&self, end: Self, t: f32) -> Self

Linearly interpolate between self and end by t between 0.0 and 1.0. i.e. (1.0 - t) * self + (t) * end.

For interpolating Rotors with linear interpolation, you almost certainly want to normalize the returned Rotor. For example,

let interpolated_rotor = rotor1.lerp(rotor2, 0.5).normalized();

For most cases (especially where performance is the primary concern, like in animation interpolation for games, this ‘normalized lerp’ or ‘nlerp’ is probably what you want to use. However, there are situations in which you really want the interpolation between two Rotors to be of constant angular velocity. In this case, check out Slerp.

impl Mul<Isometry3> for Rotor3

type Output = Isometry3

The resulting type after applying the * operator.

fn mul(self, iso: Isometry3) -> Isometry3

Performs the * operation.

impl Mul<Rotor3> for Isometry3

type Output = Isometry3

The resulting type after applying the * operator.

fn mul(self, rotor: Rotor3) -> Isometry3

Performs the * operation.

impl Mul<Rotor3> for Rotor3

The composition of self with q, i.e. self * q gives the rotation as though you first perform q and then self.

fn mul(self, q: Self) -> Self

The composition of self with q, i.e. self * q gives the rotation as though you first perform q and then self.

type Output = Rotor3

The resulting type after applying the * operator.

impl Mul<Rotor3> for Similarity3

type Output = Similarity3

The resulting type after applying the * operator.

fn mul(self, rotor: Rotor3) -> Similarity3

Performs the * operation.

impl Mul<Rotor3> for f32

type Output = Rotor3

The resulting type after applying the * operator.

fn mul(self, rotor: Rotor3) -> Rotor3

Performs the * operation.

impl Mul<Similarity3> for Rotor3

type Output = Similarity3

The resulting type after applying the * operator.

fn mul(self, iso: Similarity3) -> Similarity3

Performs the * operation.

impl Mul<Vec3> for Rotor3

type Output = Vec3

The resulting type after applying the * operator.

fn mul(self, rhs: Vec3) -> Vec3

Performs the * operation.

impl Mul<f32> for Rotor3

type Output = Rotor3

The resulting type after applying the * operator.

fn mul(self, rhs: f32) -> Self

Performs the * operation.

impl MulAssign<f32> for Rotor3

fn mul_assign(&mut self, rhs: f32)

Performs the *= operation.

impl PartialEq<Rotor3> for Rotor3

fn eq(&self, other: &Rotor3) -> bool

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

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

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

impl Serialize for Rotor3

fn serialize<T>(&self, serializer: T) -> Result<T::Ok, T::Error>where T: Serializer,

Serialize this value into the given Serde serializer.

impl Slerp<f32> for Rotor3

fn slerp(&self, end: Self, t: f32) -> Self

Spherical-linear interpolation between self and end based on t from 0.0 to 1.0.

self and end should both be normalized or something bad will happen!

Basically, interpolation that maintains a constant angular velocity from one orientation on a unit hypersphere to another. This is sorta the “high quality” interpolation for Rotors, and it can also be used to interpolate other things, one example being interpolation of 3d normal vectors.

Note that you should often normalize the result returned by this operation, when working with Rotors, etc!

impl Sub<Rotor3> for Rotor3

type Output = Rotor3

The resulting type after applying the - operator.

fn sub(self, rhs: Self) -> Self

Performs the - operation.

impl SubAssign<Rotor3> for Rotor3

fn sub_assign(&mut self, rhs: Self)

Performs the -= operation.

impl Zeroable for Rotor3

fn zeroed() -> Self

Calls zeroed.

impl Copy for Rotor3

impl Pod for Rotor3

impl StructuralPartialEq for Rotor3