Abstract
As opposed to the 3D cubic grid, the body-centered cubic (BCC) grid has some favorable topological properties: each set of voxels in the grid is a 3-manifold, with 2-manifold boundary. Thus, the Euler characteristic of an object O in this grid can be computed as half of the Euler characteristic of its boundary partial O. We propose three new algorithms to compute the Euler characteristic in the BCC grid with this surface-based approach: one based on (critical point) Morse theory and two based on the discrete Gauss–Bonnet theorem. We provide a comparison between the three new algorithms and the classic approach based on counting the number of cells, either of the 3D object or of its 2D boundary surface.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
