TETRAHEDRON_SLICE_DISPLAY
Display Tetrahedron/Plane Intersection

TETRAHEDRON_SLICE_DISPLAY is a MATLAB program which displays the intersection of a tetrahedron with a plane.

The intersection of a plane and a tetrahedron is a convex planar polygon which is bounded by 0 to 4 points. The possibilities are:

• 0) empty (no intersection);
• 1) a single point;
• 2) a single line segment;
• 3) a triangle;
• 4) a quadrilateral.

Given the data, the program displays a wireframe image of the tetrahedron, the points of intersection, and the convex polygon.

The user defines the tetrahedron by giving a 3x4 vertex array T containing the XYZ coordinates of the vertices.

The user defines the plane using the normal form. That is, the user gives a single point P which lies on the plane, and a vector NORMAL which defines the direction normal to the plane.

Usage:

tetrahedron_slice_display ( p, normal, t )

• p is a point on the plane;
• normal is the normal vector to the plane;
• t contains the coordinates of the vertices.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

GEOMETRY, a MATLAB library which performs geometric calculations in 2, 3 and N dimensional space.

TETRAHEDRON_PROPERTIES, a MATLAB program which computes properties of a tetrahedron whose vertex coordinates are read from a file.

TETRAHEDRON_SLICE_ANIMATE, a MATLAB program which is given a tetrahedron and a vector, and displays an evenly spaced sequence of planes that intersect the tetrahedron and are normal to the vector.

TETRAHEDRONS, a dataset directory which contains examples of tetrahedrons;

Source Code:

• parallelogram_area_3d.m, computes the area of a parallelogram in 3D;
• plane_normal_tetrahedron_intersect.m, finds intersections of a normal plane and a tetrahedron;
• quad_area_3d.m, returns the area of a quadrilateral in 3D;
• r8_sign_opposite_strict.m, is TRUE if two R8's have strictly opposite signs.
• tetrahedron_slice_display.m, displays an image of the intersection of a tetrahedron and a plane.

Examples and Tests:

• tetrahedron_slice_display_test.m a sample calling program.
• slice.png the image of the computed intersection.

You can go up one level to the MATLAB source codes.