Struct Triangle

#[repr(C)]
pub struct Triangle {
    pub a: Point<f32>,
    pub b: Point<f32>,
    pub c: Point<f32>,
}

A triangle shape defined by three vertices.

A triangle is one of the most fundamental shapes in computational geometry. It’s the simplest 2D polygon and the building block for triangle meshes.

Structure

• a, b, c: The three vertices of the triangle
• Edges: AB (from a to b), BC (from b to c), CA (from c to a)
• Orientation: Counter-clockwise (CCW) is the standard convention

Properties

• Convex: Always convex
• 2D/3D: Can be used in both dimensions
• In 2D: A filled triangular region with area
• In 3D: A flat surface embedded in 3D space (zero volume)

Orientation Convention

Triangles are typically defined with counter-clockwise vertex order:

• Looking at the triangle from the “front”, vertices go a → b → c in CCW order
• The normal vector (3D) points toward the observer
• Right-hand rule: Curl fingers from a→b→c, thumb points along normal

Use Cases

• Mesh building block: Fundamental unit of triangle meshes
• Simple collision shapes: Fast collision detection
• Terrain representation: Ground planes and surfaces
• Testing and debugging: Simple shape for verification

Example

use parry3d::shape::Triangle;
use nalgebra::Point3;

// Create a right triangle in the XY plane
let triangle = Triangle::new(
    Point3::origin(),  // a: origin
    Point3::new(3.0, 0.0, 0.0),  // b: along +X
    Point3::new(0.0, 4.0, 0.0)   // c: along +Y
);

// Area of 3-4-5 right triangle is 6.0
assert_eq!(triangle.area(), 6.0);

// Check if a point is inside
let inside = Point3::new(1.0, 1.0, 0.0);
assert!(triangle.contains_point(&inside));

Fields

a: Point<f32>

The first vertex of the triangle.

b: Point<f32>

The second vertex of the triangle.

c: Point<f32>

The third vertex of the triangle.

Implementations

impl Triangle

pub fn aabb(&self, pos: &Isometry<f32>) -> Aabb

Computes the world-space Aabb of this triangle, transformed by pos.

pub fn local_aabb(&self) -> Aabb

Computes the local-space Aabb of this triangle.

impl Triangle

pub fn bounding_sphere(&self, pos: &Isometry<f32>) -> BoundingSphere

Computes the world-space bounding sphere of this triangle, transformed by pos.

pub fn local_bounding_sphere(&self) -> BoundingSphere

Computes the local-space bounding sphere of this triangle.

impl Triangle

pub fn new(a: Point<f32>, b: Point<f32>, c: Point<f32>) -> Triangle

Creates a triangle from three vertices.

Arguments

• a - The first vertex
• b - The second vertex
• c - The third vertex

Convention

For proper normal calculation and consistent collision detection, vertices should be ordered counter-clockwise when viewed from the “front” side.

Example

use parry3d::shape::Triangle;
use nalgebra::Point3;

// Create a triangle in the XY plane
let tri = Triangle::new(
    Point3::origin(),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0)
);

assert_eq!(tri.area(), 0.5);

pub fn from_array(arr: &[Point<f32>; 3]) -> &Triangle

Creates the reference to a triangle from the reference to an array of three points.

pub fn vertices(&self) -> &[Point<f32>; 3]

Reference to an array containing the three vertices of this triangle.

pub fn edges(&self) -> [Segment; 3]

The three edges of this triangle: [AB, BC, CA].

pub fn scaled(self, scale: &Vector<f32>) -> Self

Computes a scaled version of this triangle.

pub fn transformed(&self, m: &Isometry<f32>) -> Self

Returns a new triangle with vertices transformed by m.

pub fn edges_scaled_directions(&self) -> [Vector<f32>; 3]

The three edges scaled directions of this triangle: [B - A, C - B, A - C].

pub fn local_support_edge_segment(&self, dir: Vector<f32>) -> Segment

Return the edge segment of this cuboid with a normal cone containing a direction that that maximizes the dot product with local_dir.

pub fn support_face(&self, dir: Vector<f32>) -> PolygonalFeature

Return the face of this triangle with a normal that maximizes the dot product with dir.

pub fn extents_on_dir(&self, dir: &Unit<Vector<f32>>) -> (f32, f32)

Computes the extents of this triangle on the given direction.

This computes the min and max values of the dot products between each vertex of this triangle and dir.

pub fn area(&self) -> f32

The area of this triangle.

pub fn unit_angular_inertia(&self) -> f32

Computes the unit angular inertia of this triangle.

pub fn center(&self) -> Point<f32>

The geometric center of this triangle.

pub fn perimeter(&self) -> f32

The perimeter of this triangle.

pub fn circumcircle(&self) -> (Point<f32>, f32)

The circumcircle of this triangle.

pub fn contains_point(&self, p: &Point<f32>) -> bool

Tests if a point is inside of this triangle.

pub fn orientation(&self, epsilon: f32) -> TriangleOrientation

The orientation of the triangle, based on its signed area.

Returns TriangleOrientation::Degenerate if the triangle’s area is smaller than epsilon.

pub fn orientation2d( a: &Point2<f32>, b: &Point2<f32>, c: &Point2<f32>, epsilon: f32, ) -> TriangleOrientation

The orientation of the 2D triangle, based on its signed area.

Returns TriangleOrientation::Degenerate if the triangle’s area is smaller than epsilon.

pub fn angle_closest_to_90(&self) -> usize

Find the index of a vertex in this triangle, such that the two edges incident in that vertex form the angle closest to 90 degrees in the triangle.

pub fn reverse(&mut self)

Reverse the orientation of this triangle by swapping b and c.

Trait Implementations

impl Clone for Triangle

fn clone(&self) -> Triangle

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Triangle

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

Formats the value using the given formatter.

impl Default for Triangle

fn default() -> Triangle

Returns the “default value” for a type.

impl From<[OPoint<f32, Const<2>>; 3]> for Triangle

fn from(arr: [Point<f32>; 3]) -> Self

Converts to this type from the input type.

impl PartialEq for Triangle

fn eq(&self, other: &Triangle) -> 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 PointQuery for Triangle

fn project_local_point(&self, pt: &Point<f32>, solid: bool) -> PointProjection

Projects a point on self.

fn project_local_point_and_get_feature( &self, pt: &Point<f32>, ) -> (PointProjection, FeatureId)

Projects a point on the boundary of self and returns the id of the feature the point was projected on.

fn project_local_point_with_max_dist( &self, pt: &Point<f32>, solid: bool, max_dist: f32, ) -> Option<PointProjection>

Projects a point onto the shape, with a maximum distance limit.

fn project_point_with_max_dist( &self, m: &Isometry<f32>, pt: &Point<f32>, solid: bool, max_dist: f32, ) -> Option<PointProjection>

Projects a point on self transformed by m, unless the projection lies further than the given max distance.

fn distance_to_local_point(&self, pt: &Point<f32>, solid: bool) -> f32

Computes the minimal distance between a point and self.

fn contains_local_point(&self, pt: &Point<f32>) -> bool

Tests if the given point is inside of self.

fn project_point( &self, m: &Isometry<f32>, pt: &Point<f32>, solid: bool, ) -> PointProjection

Projects a point on self transformed by m.

fn distance_to_point( &self, m: &Isometry<f32>, pt: &Point<f32>, solid: bool, ) -> f32

Computes the minimal distance between a point and self transformed by m.

fn project_point_and_get_feature( &self, m: &Isometry<f32>, pt: &Point<f32>, ) -> (PointProjection, FeatureId)

Projects a point on the boundary of self transformed by m and returns the id of the feature the point was projected on.

fn contains_point(&self, m: &Isometry<f32>, pt: &Point<f32>) -> bool

Tests if the given point is inside of self transformed by m.

impl PointQueryWithLocation for Triangle

type Location = TrianglePointLocation

Additional shape-specific projection information

fn project_local_point_and_get_location( &self, pt: &Point<f32>, solid: bool, ) -> (PointProjection, Self::Location)

Projects a point on self.

fn project_point_and_get_location( &self, m: &Isometry<f32>, pt: &Point<f32>, solid: bool, ) -> (PointProjection, Self::Location)

Projects a point on self transformed by m.

fn project_local_point_and_get_location_with_max_dist( &self, pt: &Point<f32>, solid: bool, max_dist: f32, ) -> Option<(PointProjection, Self::Location)>

Projects a point on self, with a maximum projection distance.

fn project_point_and_get_location_with_max_dist( &self, m: &Isometry<f32>, pt: &Point<f32>, solid: bool, max_dist: f32, ) -> Option<(PointProjection, Self::Location)>

Projects a point on self transformed by m, with a maximum projection distance.

impl PolygonalFeatureMap for Triangle

fn local_support_feature( &self, dir: &Unit<Vector<f32>>, out_feature: &mut PolygonalFeature, )

Compute the support polygonal face of self towards the dir.

fn is_convex_polyhedron(&self) -> bool

Is this shape a ConvexPolyhedron?

impl RayCast for Triangle

fn cast_local_ray_and_get_normal( &self, ray: &Ray, max_time_of_impact: f32, solid: bool, ) -> Option<RayIntersection>

Computes the time of impact, and normal between this transformed shape and a ray.

fn cast_local_ray( &self, ray: &Ray, max_time_of_impact: f32, solid: bool, ) -> Option<f32>

Computes the time of impact between this transform shape and a ray.

fn intersects_local_ray(&self, ray: &Ray, max_time_of_impact: f32) -> bool

Tests whether a ray intersects this transformed shape.

fn cast_ray( &self, m: &Isometry<f32>, ray: &Ray, max_time_of_impact: f32, solid: bool, ) -> Option<f32>

Computes the time of impact between this transform shape and a ray.

fn cast_ray_and_get_normal( &self, m: &Isometry<f32>, ray: &Ray, max_time_of_impact: f32, solid: bool, ) -> Option<RayIntersection>

Computes the time of impact, and normal between this transformed shape and a ray.

fn intersects_ray( &self, m: &Isometry<f32>, ray: &Ray, max_time_of_impact: f32, ) -> bool

Tests whether a ray intersects this transformed shape.

impl Shape for Triangle

fn clone_dyn(&self) -> Box<dyn Shape>

Clones this shape into a boxed trait-object.

fn scale_dyn( &self, scale: &Vector<f32>, _num_subdivisions: u32, ) -> Option<Box<dyn Shape>>

Scales this shape by scale into a boxed trait-object.

fn compute_local_aabb(&self) -> Aabb

Computes the Aabb of this shape.

fn compute_local_bounding_sphere(&self) -> BoundingSphere

Computes the bounding-sphere of this shape.

fn compute_aabb(&self, position: &Isometry<f32>) -> Aabb

Computes the Aabb of this shape with the given position.

fn mass_properties(&self, _density: f32) -> MassProperties

Compute the mass-properties of this shape given its uniform density.

fn is_convex(&self) -> bool

Is this shape known to be convex?

fn shape_type(&self) -> ShapeType

Gets the type tag of this shape.

fn as_typed_shape(&self) -> TypedShape<'_>

Gets the underlying shape as an enum.

fn ccd_thickness(&self) -> f32

fn ccd_angular_thickness(&self) -> f32

fn as_support_map(&self) -> Option<&dyn SupportMap>

Converts this shape into its support mapping, if it has one.

fn as_polygonal_feature_map(&self) -> Option<(&dyn PolygonalFeatureMap, f32)>

Converts this shape to a polygonal feature-map, if it is one.

fn feature_normal_at_point( &self, _feature: FeatureId, _point: &Point<f32>, ) -> Option<Unit<Vector<f32>>>

The shape’s normal at the given point located on a specific feature.

fn clone_box(&self) -> Box<dyn Shape>

👎Deprecated: renamed to clone_dyn

Clones this shape into a boxed trait-object.

fn compute_bounding_sphere(&self, position: &Isometry<f32>) -> BoundingSphere

Computes the bounding-sphere of this shape with the given position.

fn as_composite_shape(&self) -> Option<&dyn CompositeShape>

fn compute_swept_aabb( &self, start_pos: &Isometry<f32>, end_pos: &Isometry<f32>, ) -> Aabb

Computes the swept Aabb of this shape, i.e., the space it would occupy by moving from the given start position to the given end position.

impl SupportMap for Triangle

fn local_support_point(&self, dir: &Vector<f32>) -> Point<f32>

Evaluates the support function of this shape in local space.

fn local_support_point_toward(&self, dir: &Unit<Vector<f32>>) -> Point<f32>

Same as local_support_point except that dir is guaranteed to be normalized (unit length).

fn support_point( &self, transform: &Isometry<f32>, dir: &Vector<f32>, ) -> Point<f32>

Evaluates the support function of this shape transformed by transform.

fn support_point_toward( &self, transform: &Isometry<f32>, dir: &Unit<Vector<f32>>, ) -> Point<f32>

Same as support_point except that dir is guaranteed to be normalized (unit length).

impl Copy for Triangle

impl StructuralPartialEq for Triangle