Geometry utilities

Geometric predicates and primitive intersection tests. More...

Enumerations
enum class	IncludeBoundaryIntersection { No , Yes }
	Controls whether boundary contact counts as intersection in triangle_triangle_intersection(). More...

Functions
template<typename Scalar>
bool	triangle_triangle_intersection (span< const Scalar, 3 > t1_v0, span< const Scalar, 3 > t1_v1, span< const Scalar, 3 > t1_v2, span< const Scalar, 3 > t2_v0, span< const Scalar, 3 > t2_v1, span< const Scalar, 3 > t2_v2, IncludeBoundaryIntersection boundary=IncludeBoundaryIntersection::No)
	Check if two 3D triangles intersect using exact predicates for robustness.

Detailed Description

Geometric predicates and primitive intersection tests.

Enumeration Type Documentation

IncludeBoundaryIntersection

enum class IncludeBoundaryIntersection

strong

#include <lagrange/utils/triangle_triangle_intersection.h>

Controls whether boundary contact counts as intersection in triangle_triangle_intersection().

Enumerator
No	Only interior intersections count. Triangles touching at vertices or edges are not considered intersecting.
Yes	Any contact counts as intersection, including touching at vertices or edges.

Function Documentation

triangle_triangle_intersection()

template<typename Scalar>

bool triangle_triangle_intersection	(	span< const Scalar, 3 >	t1_v0,
		span< const Scalar, 3 >	t1_v1,
		span< const Scalar, 3 >	t1_v2,
		span< const Scalar, 3 >	t2_v0,
		span< const Scalar, 3 >	t2_v1,
		span< const Scalar, 3 >	t2_v2,
		IncludeBoundaryIntersection	boundary = IncludeBoundaryIntersection::No )

#include <lagrange/utils/triangle_triangle_intersection.h>

Check if two 3D triangles intersect using exact predicates for robustness.

This function uses Shewchuk's exact orient3D and orient2D predicates to robustly determine if two triangles intersect in 3D space. The algorithm tests each edge of one triangle against the other triangle using tetrahedra orientation tests, with special handling for coplanar cases using 2D projections.

Parameters

[in]	t1_v0	First vertex of triangle 1.
[in]	t1_v1	Second vertex of triangle 1.
[in]	t1_v2	Third vertex of triangle 1.
[in]	t2_v0	First vertex of triangle 2.
[in]	t2_v1	Second vertex of triangle 2.
[in]	t2_v2	Third vertex of triangle 2.
[in]	boundary	Whether touching at boundaries counts as intersection.

Template Parameters

Scalar

The scalar type (e.g., float, double).

Returns

True if the triangles intersect, false otherwise.

Note

Orientation and coplanarity decisions rely on Shewchuk's exact predicates for robustness. Some auxiliary computations (e.g., projection axis selection and collinear interval parameterization) use standard floating-point arithmetic.