Struct DRot2 

#[repr(C)]
pub struct DRot2 {
    pub re: f64,
    pub im: f64,
}

A 2D rotation represented as a unit complex number (f64 precision).

The rotation is stored as re + im * i where re = cos(angle) and im = sin(angle).

Fields

re: f64

Real part (cosine of the angle).

im: f64

Imaginary part (sine of the angle).

Implementations

impl DRot2

pub const IDENTITY: Self

The identity rotation (no rotation).

pub const fn from_cos_sin_unchecked(re: f64, im: f64) -> Self

Creates a new unit complex from cosine and sine values.

The caller must ensure that re*re + im*im = 1.

pub fn from_matrix_unchecked(mat: DMat2) -> Self

Creates a rotation from a rotation matrix (without normalization).

pub fn identity() -> Self

Creates the identity rotation.

pub fn new(angle: f64) -> Self

Creates a rotation from an angle in radians.

pub fn from_angle(angle: f64) -> Self

Creates a rotation from an angle in radians.

pub fn angle(&self) -> f64

Returns the rotation angle in radians.

pub fn cos(&self) -> f64

Returns the cosine of the rotation angle (the real part).

pub fn sin(&self) -> f64

Returns the sine of the rotation angle (the imaginary part).

pub fn inverse(self) -> Self

Returns the inverse rotation.

pub fn length(&self) -> f64

Computes the length (magnitude) of self.

For a valid unit rotation, this should always be 1.0.

pub fn length_squared(&self) -> f64

Computes the squared length of self.

This is faster than length() as it avoids a square root. For a valid unit rotation, this should always be 1.0.

pub fn length_recip(&self) -> f64

Computes 1.0 / length().

pub fn normalize(&self) -> Self

Returns self normalized to length 1.0.

For valid unit rotations this should be a no-op.

pub fn is_finite(&self) -> bool

Returns true if, and only if, all elements are finite.

pub fn is_nan(&self) -> bool

Returns true if any element is NaN.

pub fn is_normalized(&self) -> bool

Returns whether self is of length 1.0 or not.

Uses a precision threshold of approximately 1e-4.

pub fn transform_vector(&self, v: DVec2) -> DVec2

Rotates a 2D vector by this rotation.

pub fn inverse_transform_vector(&self, v: DVec2) -> DVec2

Transforms a 2D vector by the inverse of this rotation.

pub fn to_mat(&self) -> DMat2

Returns the rotation matrix equivalent to this rotation.

pub fn from_mat(mat: DMat2) -> Self

Creates a rotation from a 2x2 rotation matrix.

The matrix should be a valid rotation matrix (orthogonal with determinant 1).

pub fn from_mat_unchecked(mat: DMat2) -> Self

Creates a rotation from a 2x2 matrix without normalization.

Alias for from_matrix_unchecked.

pub fn from_rotation_arc(from: DVec2, to: DVec2) -> Self

Gets the minimal rotation for transforming from to to.

Both vectors must be normalized. The rotation is in the plane spanned by the two vectors.

pub fn slerp(&self, other: &Self, t: f64) -> Self

Spherical linear interpolation between two rotations.

pub fn powf(&self, n: f64) -> Self

Raises this rotation to a power.

For example, powf(2.0) will return a rotation with double the angle.

pub fn rotate_towards(&self, rhs: &Self, max_angle: f64) -> Self

Rotates self towards rhs up to max_angle (in radians).

When max_angle is 0.0, the result will be equal to self. When max_angle is equal to self.angle_between(rhs), the result will be equal to rhs. If max_angle is negative, rotates towards the exact opposite of rhs. Will not go past the target.

pub fn angle_between(&self, rhs: &Self) -> f64

Returns the angle (in radians) between self and rhs.

pub fn dot(&self, rhs: Self) -> f64

Computes the dot product of self and rhs.

The dot product is equal to the cosine of the angle between two rotations.

pub fn lerp(&self, rhs: Self, s: f64) -> Self

Performs a linear interpolation between self and rhs based on the value s.

When s is 0.0, the result will be equal to self. When s is 1.0, the result will be equal to rhs. For rotations, slerp is usually preferred over lerp.

pub fn normalize_mut(&mut self)

Normalizes self in place.

Does nothing if self is already normalized or zero length.

Trait Implementations

impl AbsDiffEq for DRot2

Available on crate feature approx only.

type Epsilon = f64

Used for specifying relative comparisons.

fn default_epsilon() -> Self::Epsilon

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

fn abs_diff_eq(&self, other: &Self, epsilon: Self::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 AbsDiffEq::abs_diff_eq.

impl Clone for DRot2

fn clone(&self) -> DRot2

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for DRot2

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

Formats the value using the given formatter.

impl Default for DRot2

fn default() -> Self

Returns the “default value” for a type.

impl From<DRot2> for DPose2

fn from(rotation: DRot2) -> Self

Converts to this type from the input type.

impl From<DRot2> for Rot2

fn from(r: DRot2) -> Self

Converts to this type from the input type.

impl From<Rot2> for DRot2

fn from(r: Rot2) -> Self

Converts to this type from the input type.

impl Mul<DPose2> for DRot2

type Output = DPose2

The resulting type after applying the * operator.

fn mul(self, rhs: DPose2) -> Self::Output

Performs the * operation.

impl Mul<DRot2> for &DRot2

type Output = DRot2

The resulting type after applying the * operator.

fn mul(self, rhs: DRot2) -> Self::Output

Performs the * operation.

impl Mul<DRot2> for DPose2

type Output = DPose2

The resulting type after applying the * operator.

fn mul(self, rhs: DRot2) -> Self::Output

Performs the * operation.

impl Mul<DVec2> for DRot2

type Output = DVec2

The resulting type after applying the * operator.

fn mul(self, rhs: DVec2) -> Self::Output

Performs the * operation.

impl Mul for DRot2

type Output = DRot2

The resulting type after applying the * operator.

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

Performs the * operation.

impl MulAssign<DRot2> for DPose2

fn mul_assign(&mut self, rhs: DRot2)

Performs the *= operation.

impl MulAssign for DRot2

fn mul_assign(&mut self, rhs: Self)

Performs the *= operation.

impl PartialEq for DRot2

fn eq(&self, other: &DRot2) -> 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 RelativeEq for DRot2

Available on crate feature approx only.

fn default_max_relative() -> Self::Epsilon

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

fn relative_eq( &self, other: &Self, epsilon: Self::Epsilon, max_relative: Self::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 RelativeEq::relative_eq.

impl UlpsEq for DRot2

Available on crate feature approx only.

fn default_max_ulps() -> u32

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

fn ulps_eq(&self, other: &Self, epsilon: Self::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 UlpsEq::ulps_eq.

impl Copy for DRot2

impl StructuralPartialEq for DRot2