Struct Reflection 

pub struct Reflection { /* private fields */ }

Reflection in the plane through origin with unit normal: p ↦ p − 2((p − o)·n) n. Lengths and angles are preserved and handedness is reversed, which is why it is a type of its own and not an crate::Isometry, whose every value is proper (ADR-0031).

use arris_math::{Point3, Reflection, Vec3};

let r = Reflection::new(Point3::new(0.0, 0.0, 1.0), Vec3::z()).unwrap();
assert_eq!(r.apply(Point3::new(1.0, 2.0, 3.0)), Point3::new(1.0, 2.0, -1.0));
// Reflecting twice returns the point.
let p = Point3::new(0.3, -0.4, 5.0);
assert!((r.apply(r.apply(p)) - p).norm() < 1e-15);
assert!(Reflection::new(Point3::origin(), Vec3::zeros()).is_err());

Implementations

impl Reflection

pub fn new(origin: Point3, normal: Vec3) -> Result<Self, ReflectionError>

The plane through origin with normal along normal (normalised). Errors: a non-finite input, or a zero normal.

pub fn plane_through( origin: Point3, normal: Vec3, ) -> Result<Self, ReflectionError>

The same as Reflection::new: the plane is named by a point on it and its normal.

pub fn origin(&self) -> Point3

A point on the plane.

pub fn normal(&self) -> UnitVec3

The plane’s unit normal.

pub fn apply(&self, p: Point3) -> Point3

The mirror image of p.

pub fn apply_vec(&self, v: Vec3) -> Vec3

The image of a displacement: the plane’s offset does not act on it.

pub fn apply_unit(&self, u: UnitVec3) -> UnitVec3

The image of a direction, re-normalised so it is unit to rounding.

pub fn apply_frame(&self, frame: &Frame) -> Frame

The image of a frame as a quadric is placed after a mirror: O′ = R O, X′ = R X, Y′ = −R Y, Z′ = R Z. Right-handed by construction (X′ × Y′ = R Z); the surface it places is the mirror image reparametrised by u ↦ 2π − u (ADR-0031 §2).

use arris_math::{Frame, Reflection, Vec3, Point3};

let r = Reflection::new(Point3::origin(), Vec3::x()).unwrap();
let f = r.apply_frame(&Frame::world());
assert!((f.x().into_inner() - (-Vec3::x())).norm() < 1e-15);
assert!((f.y().into_inner() - (-Vec3::y())).norm() < 1e-15);
assert!((f.z().into_inner() - Vec3::z()).norm() < 1e-15);

pub fn apply_frame_reversed(&self, frame: &Frame) -> Frame

The image of a frame keeping the parametrisation of what it places: O′ = R O, X′ = R X, Y′ = R Y, Z′ = X′ × Y′ = −R Z. A plane’s and a conic curve’s frame after a mirror (ADR-0031 §2): the same parameters, the normal turned the other way.

Trait Implementations

impl Clone for Reflection

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Reflection

impl Debug for Reflection

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

Formats the value using the given formatter.

impl PartialEq for Reflection

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for Reflection