Function cuboid_triangle_find_local_separating_edge_twoway

pub fn cuboid_triangle_find_local_separating_edge_twoway(
    cube1: &Cuboid,
    triangle2: &Triangle,
    pos12: &Isometry<f32>,
) -> (f32, Vector<f32>)

Finds the best separating axis by testing all edge-edge combinations between a cuboid and a triangle (3D only).

In 3D collision detection, when a box and triangle intersect, the contact may occur along an axis perpendicular to an edge from each shape. This function tests all 3×3 = 9 such axes (cross products of cuboid edges with triangle edges) to find the one with maximum separation.

Parameters

• cube1: The cuboid (in its local coordinate frame)
• triangle2: The triangle
• pos12: The position of the triangle relative to the cuboid

Returns

A tuple containing:

• Real: The maximum separation found across all edge-edge axes
  • Positive: Shapes are separated
  • Negative: Shapes are overlapping (penetration depth)
• Vector<Real>: The axis direction that gives this separation

The 9 Axes Tested

The function tests cross products between:

• 3 cuboid edge directions: X, Y, Z (aligned with cuboid axes)
• 3 triangle edge vectors: AB, BC, CA

This gives 3×3 = 9 potential separating axes. Each axis is normalized before testing, and degenerate axes (near-zero length, indicating parallel edges) are skipped.

Example

use parry3d::shape::{Cuboid, Triangle};
use parry3d::query::sat::cuboid_triangle_find_local_separating_edge_twoway;
use nalgebra::{Point3, Vector3, Isometry3};

let cube = Cuboid::new(Vector3::new(1.0, 1.0, 1.0));
let triangle = Triangle::new(
    Point3::origin(),
    Point3::new(1.0, 0.0, 0.0),
    Point3::new(0.0, 1.0, 0.0)
);

// Position triangle near the cube
let pos12 = Isometry3::translation(2.0, 0.0, 0.0);

let (separation, axis) = cuboid_triangle_find_local_separating_edge_twoway(
    &cube,
    &triangle,
    &pos12
);

println!("Edge-edge separation: {} along {}", separation, axis);

Usage in Complete SAT

For a complete cuboid-triangle SAT test, you must also test:

1. Cuboid face normals (X, Y, Z axes)
2. Triangle face normal (perpendicular to the triangle plane)
3. Edge-edge axes (this function)