Struct Triangle2 

pub struct Triangle2<S> { /* private fields */ }

A 2-simplex or triangle in 2D space

Creation methods should fail with a debug assertion if the points are colinear.

Implementations

impl<S: OrderedField> Triangle<S>

pub fn new(a: Point2<S>, b: Point2<S>, c: Point2<S>) -> Option<Self>

where S: AbsDiffEq<Epsilon = S>,

Returns None if the points are colinear:

assert!(Triangle::new (
  [-1.0, -1.0].into(),
  [ 0.0,  0.0].into(),
  [ 1.0,  1.0].into()
).is_none());

pub fn noisy(a: Point2<S>, b: Point2<S>, c: Point2<S>) -> Self

where S: AbsDiffEq<Epsilon = S>,

Panics if the points are colinear:

let s = Triangle::noisy (
  [-1.0, -1.0].into(),
  [ 0.0,  0.0].into(),
  [ 1.0,  1.0].into());

pub fn unchecked(a: Point2<S>, b: Point2<S>, c: Point2<S>) -> Self

where S: AbsDiffEq<Epsilon = S>,

Debug panic if the points are colinear:

let s = Triangle::unchecked (
  [-1.0, -1.0].into(),
  [ 0.0,  0.0].into(),
  [ 1.0,  1.0].into());

pub fn from_array([a, b, c]: [Point2<S>; 3]) -> Option<Self>

where S: AbsDiffEq<Epsilon = S>,

pub const fn point_a(self) -> Point2<S>

pub const fn point_b(self) -> Point2<S>

pub const fn point_c(self) -> Point2<S>

pub const fn points(self) -> [Point2<S>; 3]

pub fn point(self, s: Normalized<S>, t: Normalized<S>) -> Option<Point2<S>>

Return a parameterized point on the triangle.

Returns None if s + t > 1.0.

pub const fn edge_ab(self) -> Segment2<S>

pub const fn edge_bc(self) -> Segment2<S>

pub const fn edge_ca(self) -> Segment2<S>

pub const fn edges(self) -> [Segment2<S>; 3]

Returns edges [AB, BC, CA]

pub const fn rewind(self) -> Self

Change triangle winding by swapping points B and C.

Equivalent to triangle.acb().

pub const fn acb(self) -> Self

Change triangle winding by swapping points B and C

pub fn perpendicular_ab(self) -> NonZero2<S>

Returns perpendicular vector to edge AB.

let s = Triangle::unchecked (
  [0.0, 0.0].into(),
  [0.0, 2.0].into(),
  [2.0, 1.0].into());
assert_eq!(*s.perpendicular_ab(), [-2.0, 0.0].into());
let s = Triangle::unchecked (
  [ 0.0, 0.0].into(),
  [ 0.0, 2.0].into(),
  [-2.0, 1.0].into());
assert_eq!(*s.perpendicular_ab(), [2.0, 0.0].into());

pub fn perpendicular_bc(self) -> NonZero2<S>

Returns perpendicular vector to edge BC.

let s = Triangle::unchecked (
  [2.0, 1.0].into(),
  [0.0, 0.0].into(),
  [0.0, 2.0].into());
assert_eq!(*s.perpendicular_bc(), [-2.0, 0.0].into());
let s = Triangle::unchecked (
  [-2.0, 1.0].into(),
  [ 0.0, 0.0].into(),
  [ 0.0, 2.0].into());
assert_eq!(*s.perpendicular_bc(), [2.0, 0.0].into());

pub fn perpendicular_ca(self) -> NonZero2<S>

Returns perpendicular vector to edge CA.

let s = Triangle::unchecked (
  [0.0, 2.0].into(),
  [2.0, 1.0].into(),
  [0.0, 0.0].into());
assert_eq!(*s.perpendicular_ca(), [-2.0, 0.0].into());
let s = Triangle::unchecked (
  [ 0.0, 2.0].into(),
  [-2.0, 1.0].into(),
  [ 0.0, 0.0].into());
assert_eq!(*s.perpendicular_ca(), [2.0, 0.0].into());

pub fn area(self) -> Positive<S>

where S: Real,

pub fn centroid(self) -> Point2<S>

Barycentric coordinate $1/3 : 1/3 : 1/3$ corresponds to the center of mass (barycenter) of a uniform triangular lamina

pub fn incenter(self) -> Point2<S>

where S: Real + Real,

Trilinear coordinate $1 : 1 : 1$ corresponds to center of inscribed circle

pub fn barycentric(self, coords: Vector3<S>) -> Point2<S>

pub fn trilinear(self, coords: Vector3<S>) -> Point2<S>

where S: Real + Real,

pub fn affine_plane(self) -> Plane2<S>

pub fn nearest_point(self, point: Point2<S>) -> TrianglePoint<S>

Trait Implementations

impl<S: Clone> Clone for Triangle<S>

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<S: Copy> Copy for Triangle<S>

impl<S: Debug> Debug for Triangle<S>

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

Formats the value using the given formatter.

impl<S: Field + Sqrt> Default for Triangle<S>

fn default() -> Self

A default triangle is arbitrarily chosen to be the equilateral triangle with point at 1.0 on the Y axis:

use std::f64::consts::FRAC_1_SQRT_2;
let s = Triangle::default();
let t = Triangle::noisy (
  [           0.0,            1.0].into(),
  [-FRAC_1_SQRT_2, -FRAC_1_SQRT_2].into(),
  [ FRAC_1_SQRT_2, -FRAC_1_SQRT_2].into()
);
approx::assert_relative_eq!(s.point_a(), t.point_a());
approx::assert_relative_eq!(s.point_b(), t.point_b());
approx::assert_relative_eq!(s.point_c(), t.point_c());

impl<S: Eq> Eq for Triangle<S>

impl<S: Real> From<Triangle<S>> for Hull2<S>

fn from(triangle: Triangle<S>) -> Self

Converts to this type from the input type.

impl<S: OrderedField> From<Triangle<S>> for Plane2<S>

fn from(triangle: Triangle2<S>) -> Self

Converts to this type from the input type.

impl<S> Index<usize> for Triangle<S>

where S: Copy,

type Output = Point2<S>

The returned type after indexing.

fn index(&self, index: usize) -> &Point2<S>

Performs the indexing (container[index]) operation.

impl<S: PartialEq> PartialEq for Triangle<S>

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

Equality operator ==.

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

Inequality operator !=.

impl<S> Primitive<S, Point2<S>> for Triangle<S>

where S: OrderedField + AbsDiffEq,

fn translate(&mut self, displacement: Vector2<S>)

fn scale(&mut self, scale: Positive<S>)

fn support(&self, direction: NonZero2<S>) -> (Point2<S>, S)

Returns the point with largeest dot product in search direction

impl<S: PartialEq> StructuralPartialEq for Triangle<S>

impl<S> TryFrom<[Point2<S>; 3]> for Triangle<S>

where S: OrderedField + AbsDiffEq<Epsilon = S>,

type Error = [Point2<S>; 3]

The type returned in the event of a conversion error.

fn try_from([a, b, c]: [Point2<S>; 3]) -> Result<Self, Self::Error>

Performs the conversion.