Efficient feature extraction for 2D/3D objects in mesh representation

Meshes are dominantly used to represent 3D models as they fit well with graphics rendering hardware. Features such as volume, moments, and Fourier transform coefficients need to be calculated from the mesh representation efficiently. We propose an algorithm to calculate these features without transforming the mesh into other representations such as the volumetric representation. To calculate a feature for a mesh, we show that we can first compute it for each elementary shape such as a triangle or a tetrahedron, and then add up all the values for the mesh. The algorithm is simple and efficient, with many potential applications.