Struct Transform 

pub struct Transform { /* private fields */ }

A similarity transform: orthonormal rotation or reflection, uniform scale, translation.

Applied as p -> linear * (scale * p) + translation.

Implementations

impl Transform

pub const IDENTITY: Self

The identity.

pub fn from_parts( linear: Matrix3, scale: f64, translation: Vector, eps: f64, ) -> OgeomResult<Self>

A transform from the parts it is stored as.

linear is the orthonormal part alone and scale the uniform factor beside it, which is how a Transform holds them. The kind is re-derived rather than taken on trust, since it is a function of the other three.

For reading a document back. Going the long way round (multiplying the scale into the matrix and asking GeneralTransform::to_similarity to factor it out again) recovers a transform that is close, not the one that was written, and a round trip that drifts a little each time is not a round trip.

Errors

OgeomError::Construction if linear is not orthonormal within eps, or scale is not finite and non-zero; a placement that squashes space is not a placement.

pub fn translation(v: Vector) -> Self

A translation.

pub fn rotation(axis: Axis, angle: f64) -> Self

A rotation of angle radians about axis.

pub fn from_quaternion(q: Quaternion) -> Self

A rotation given as a quaternion, about an axis through the origin.

pub fn scaling(centre: Point, factor: f64, tol: Tolerances) -> OgeomResult<Self>

A uniform scaling about centre.

Errors

OgeomError::Construction if factor is zero or non-finite. A zero scale collapses every shape to a point and is not invertible, so it is refused rather than allowed to produce degenerate geometry.

pub fn point_mirror(centre: Point) -> Self

Reflection through a point.

pub fn plane_mirror(origin: Point, normal: Direction) -> Self

Reflection in the plane through origin with the given normal.

pub fn axis_mirror(axis: Axis) -> Self

Reflection in a line: a half turn about it.

pub fn to_frame(frame: &Frame) -> Self

The transform taking world coordinates into frame’s local coordinates.

pub fn from_frame(frame: &Frame) -> Self

The transform taking frame’s local coordinates into world coordinates.

pub fn between_frames(from: &Frame, to: &Frame) -> Self

The transform taking from’s local coordinates into to’s.

pub const fn kind(&self) -> TransformKind

This transform’s classification.

pub const fn linear(&self) -> Matrix3

The orthonormal part.

pub const fn scale_factor(&self) -> f64

The uniform scale factor. Negative for a point mirror.

pub const fn translation_vector(&self) -> Vector

The translation.

pub fn preserves_handedness(&self) -> bool

Whether this transform preserves handedness.

A shape transformed by a transform that does not must have its orientation flipped to stay consistent; otherwise a mirrored solid ends up inside out.

pub fn apply(&self, p: Point) -> Point

Apply to a point.

pub fn apply_vector(&self, v: Vector) -> Vector

Apply to a free vector. Translation does not affect it.

pub fn apply_direction( &self, d: Direction, tol: Tolerances, ) -> OgeomResult<Direction>

Apply to a direction, renormalizing.

A similarity maps unit vectors to vectors of length |scale|, so the result is rescaled. Under a negative scale the direction reverses, which is the correct behaviour and not a sign error.

Errors

OgeomError::Construction if the result cannot be normalized, which a valid similarity never produces.

pub fn apply_frame(&self, f: &Frame, tol: Tolerances) -> OgeomResult<Frame>

Apply to a frame, transforming origin and all three axes.

Errors

OgeomError::Construction if the transformed axes cannot be renormalized.

pub fn inverse(&self) -> OgeomResult<Self>

The inverse.

Errors

OgeomError::Numeric if the linear part is singular, which a valid similarity never is.

pub fn is_equal(&self, other: &Self, tol: Tolerances) -> bool

Whether two transforms agree in effect.

pub fn to_general(&self) -> GeneralTransform

This transform as a general affine one.

Trait Implementations

impl Clone for Transform

fn clone(&self) -> Transform

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Transform

impl Debug for Transform

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

Formats the value using the given formatter.

impl Default for Transform

fn default() -> Self

Returns the “default value” for a type.

impl From<Transform> for GeneralTransform

fn from(t: Transform) -> Self

Converts to this type from the input type.

impl Mul for Transform

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

Composition. (a * b) applies b first, then a.

type Output = Transform

The resulting type after applying the * operator.

impl PartialEq for Transform

fn eq(&self, other: &Transform) -> 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 StructuralPartialEq for Transform