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Tet Plane Intersect

Python wrapper around a C library for calculating intersections between tetrahedra and planes. This code is based on John Burkardt's Matlab code which calculates the intersection points between a single tetrahedron and a plane. This functionality is extended to enable calculation of intersections for multiple tetrahedra with a given plane in batch.

Installation

To install simply run the below commands

git clone [email protected]:chrisk314/tet-plane-intersection.git
cd tet-plane-intersect
pip install .

Calculating intersections

The function tet_plane_inter_tris_batch can be used to calculate the intersections between a collection of tetrahedra and a plane in batch. The intersection of a tetrahedron with a plane has 0, 1, 2, 3, or 4 points. This function converts any 4-point intersections into two 3-point intersections, i.e., two triangles. This provides the convenience of working with the intersections in the form of triangles only.

The below example code calls tet_plane_inter_tris_batch to obtain the triangles produced by the intersection between the tetrahedra geometry specified in the tetrahedra numpy array and the plane specified by the point pp and normal normal.

import numpy as np
from tet_plane_intersect import tet_plane_inter_tris_batch

pp = np.array([0.5, 0., 0.])      # A point on the plane.
normal = np.array([1.,0.,0.])     # Vector normal to the plane.
tetrahedra = np.array([           # Tetrahedra to test for intersection.
    [[0.0696218 ,  0.51675287,  0.27622866],
     [0.77795185,  0.35896   ,  0.76889514],
     [0.93955095,  0.46952051,  0.50414596],
     [0.88091001,  0.0994195 ,  0.58077994]],
    [[0.22094245,  0.2076138 ,  0.97860943],
     [0.07205741,  0.20692974,  0.03908092],
     [0.42881122,  0.14083737,  0.73928276],
     [0.81604653,  0.96100499,  0.73425617]],
    [[0.36762177,  0.19788064,  0.32692846],
     [0.74746389,  0.26432934,  0.82284067],
     [0.59302365,  0.03474258,  0.48759837],
     [0.90889265,  0.50532202,  0.09855027]]
])

pint, area, center, tri_num, tri_ptr =\
        tet_plane_inter_tris_batch(pp, normal, tetrahedra)

The call returns an ndarray of intersection points (triangle vertex coords), an ndarray of triangle areas, an ndarray of triangle center coordinates, the number of intersection triangles for each of the input tetrahedra, and the offsets of the data for each tetrahedron in the output arrays.