Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Calculating Voxel-Polyhedron Intersections for Meshing Images



Stephen A. Langer, Andrew C.E. Reid


Finite element meshes constructed from 3D images are useful in materials science and medical applications when it is necessary to model the actual geometry of a sample, rather than an idealized approximation of it. Constructing the mesh involves computing the intersection of the mesh elements with the voxels (3D pixels) of the image. If done naively, this process is unstable, and small errors in the computed position of an intersection point can lead to large errors in the computed volume. We demonstrate the source of the instability and present a robust and efficient method of doing the computation, based on the r3d algorithm of Powell and Abel. The method was developed in the context of the OOF3D program at NIST, but the freely available code is completely independent of OOF3D.
Proceedings Title
Proceedings of the 29th International Meshing Roundtable
Conference Dates
June 22-25, 2021
Conference Location
Virtual , MD, US
Conference Title
29th International Meshing Roundtable (IMR)


finite element, meshing, image


Langer, S. and Reid, A. (2021), Calculating Voxel-Polyhedron Intersections for Meshing Images, Proceedings of the 29th International Meshing Roundtable, Virtual , MD, US, [online], (Accessed June 15, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 9, 2021, Updated May 4, 2023