Struct Triangle

Source

#[repr(C)]pub struct Triangle {
    pub a: Point3,
    pub b: Point3,
    pub c: Point3,
}

Expand description

A triangle defined by three vertices in 3D space.

A triangle is the simplest polygon in 3D space, consisting of three vertices connected by three edges. It’s a fundamental building block in computer graphics, computational geometry, and physics simulations.

The triangle is defined by three vertices A, B, and C. The orientation and properties are computed based on the relative positions of these vertices.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::Point3;

// Create a triangle
let triangle = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0),
);

§Mathematical Properties

Area = 0.5 * |(B-A) × (C-A)|
Normal = normalize((B-A) × (C-A))
Center = (A + B + C) / 3

Fields§

§a: Point3

First vertex of the triangle

§b: Point3

Second vertex of the triangle

§c: Point3

Third vertex of the triangle

Implementations§

Source §

impl Triangle

Source

pub fn new( a: impl Into<[Real; 3]>, b: impl Into<[Real; 3]>, c: impl Into<[Real; 3]>, ) -> Self

Creates a new triangle from three vertices.

§Arguments

a - First vertex
b - Second vertex
c - Third vertex

§Returns

A new Triangle instance.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::Point3;

let triangle = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0),
);

Source

pub fn center(&self) -> Point3

Computes the geometric center (centroid) of the triangle.

The centroid is calculated as the average of all three vertices: C = (A + B + C) / 3

§Returns

The centroid coordinates as a Point3.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::Point3;

let triangle = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(2.0, 0.0, 0.0),
    Point3::new(0.0, 2.0, 0.0),
);

let center = triangle.center();
assert_eq!(center, Point3::new(2.0/3.0, 2.0/3.0, 0.0));

Source

pub fn normal(&self) -> UnitVec3

Computes the normal vector of the triangle.

The normal is calculated using the cross product of two edges: N = normalize((B-A) × (C-A))

The direction follows the right-hand rule based on the vertex order (A, B, C).

§Returns

The unit normal vector as a UnitVec3.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::{Point3, UnitVec3};

let triangle = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0),
);

let normal = triangle.normal();
// Triangle lies in the XY plane, normal points in +Z direction
assert!(normal.z > 0.9); // Close to 1.0 for unit vector

Source

pub fn area(&self) -> Real

Computes the area of the triangle.

The area is calculated using half the magnitude of the cross product: Area = 0.5 * |(B-A) × (C-A)|

§Returns

The area as a Real value.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::Point3;

let triangle = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(2.0, 0.0, 0.0),
    Point3::new(0.0, 2.0, 0.0),
);

let area = triangle.area();
assert_eq!(area, 2.0); // Right triangle with legs of length 2

Source

pub fn is_degenerate(&self) -> bool

Checks if the triangle is degenerate (has zero area).

A triangle is degenerate if all three vertices are collinear, which means the cross product of two edges has zero (or near-zero) magnitude.

§Returns

true if the triangle is degenerate, false otherwise.

§Examples

use phys_geom::shape::Triangle;
use phys_geom::math::Point3;

// Non-degenerate triangle
let triangle1 = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0),
);
assert!(!triangle1.is_degenerate());

// Degenerate triangle (all points on a line)
let triangle2 = Triangle::new(
    Point3::new(0.0, 0.0, 0.0),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(2.0, 0.0, 0.0),
);
assert!(triangle2.is_degenerate());