Intersection of triangles in space based on cutting off segment

TL;DR

The paper introduces a novel 3D triangle intersection detection method that simplifies the problem by reducing it to a plane cut-off problem using combined computer graphics algorithms, improving efficiency.

Contribution

A new triangle-triangle intersection method in 3D space that integrates Cohen-Sutherland and FC-algorithms for more efficient computation.

Findings

Reduces 3D intersection problem to a plane cut-off problem

Develops a coding scheme for points relative to triangle planes

Applicable to tetrahedron intersection and image processing

Abstract

The article proposes a new method for finding the triangle-triangle intersection in 3D space, based on the use of computer graphics algorithms -- cutting off segments on the plane when moving and rotating the beginning of the coordinate axes of space. This method is obtained by synthesis of two methods of cutting off segments on the plane -- Cohen-Sutherland algorithm and FC-algorithm. In the proposed method, the problem of triangle-triangle intersection in 3D space is reduced to a simpler and less resource-intensive cut-off problem on the plane. The main feature of the method is the developed scheme of coding the points of the cut-off in relation to the triangle segment plane. This scheme allows you to get rid of a large number of costly calculations. In the article the cases of intersection of triangles at parallelism, intersection and coincidence of planes of triangles are considered. The proposed method can be used in solving the problem of tetrahedron intersection, using the finite element method, as well as in image processing.