The intersection of a triangular triangle in 3d space

Question

I am working with some 3D geometry. I need to find the intersection of a triangle with another triangle.

What algorithm can i use?

Answer 1

This document describes one implementation:

http://knight.temple.edu/~lakaemper/courses/cis350_2004/etc/moeller_triangle.pdf

Note that there are different methods depending on whether you want to know the point / segment where the intersection occurred, or simply indicate whether the intersection occurred. This article will provide you with a line segment representing the intersection.

Answer 2

, -, ( ) , 2006 ( PDF):

, , . " ." 17.5 (2006): 527-535.

( , ): " " , .

( PDF), ( PDF), CGAL (, "Triangle_3_Triangle_3_do_intersect.h" ).

: , (p0, p1, p2) (q0, q1, q2),

p0 = (-21, -72, 63)
p1 = (-78, 99, 40)
p2 = (-19, -78, -83)
q0 = (96, 77, -51)
q1 = (-95, -1, -16)
q2 = (9, 5, -21)

. :

( ):

#include <iostream>

inline void setPoint(double p[3], const double x, const double y, const double z)
{
    p[0] = x; p[1] = y; p[2] = z;
}

inline void computeEdges(double v0[3], double v1[3], const double p0[3], const double p1[3], const double p2[3])
{
    v0[0] = p1[0]-p0[0];
    v0[1] = p1[1]-p0[1];
    v0[2] = p1[2]-p0[2];
    v1[0] = p2[0]-p0[0];
    v1[1] = p2[1]-p0[1];
    v1[2] = p2[2]-p0[2];
}

void main()
{
    unsigned int numErrors(0), count(0);
    double p0[3], p1[3], p2[3], q0[3], q1[3], q2[3];
    double v0[3], v1[3], w0[3], w1[3];
    bool res, answer;
    int ret;

    std::cout << "Testing the correctness of tr_tri_intersect3D" << std::endl;

    {
        // Non excluding triangles in generic positions, big determinants, intersecting
        ++count;
        setPoint(p0, -21, -72, 63);
        setPoint(p1, -78, 99, 40);
        setPoint(p2, -19, -78, -83);
        setPoint(q0, 96, 77, -51);
        setPoint(q1, -95, -1, -16);
        setPoint(q2, 9, 5, -21);
        answer = true;

        computeEdges(v0, v1, p0, p1, p2);
        computeEdges(w0, w1, q0, q1, q2);
        int ret = tr_tri_intersect3D(p0, v0, v1, q0, w0, w1);
        bool res = ( ret != 0 );

        if( res != answer )
        {
            std::cout << "# wrong answer on test " << count << "!\n";
            ++numErrors;
        }
    }

}

: , 1 12 +/- .

, : , , , , , - !

Answer 3

Googling showlead this. , !

Answer 4

Devillers . " " - (, google , ...)

, ( ) , , 4 ( , ). , , , ...

, , , , , ( ). , - 4 , , () , 4, , .

, , , , , . , .