A novel algorithm for a continuous and fast 3D projection of points on triangulated surfaces for CAM/CAD/CAE applications

Abstract

In the present work, a novel algorithm for the continuous projection of point triangles belonging to a triangle mesh is presented. The algorithm uses the normals defined at the vertices of the triangle to perform the projection. The direction of projection is not chosen a priori but depends on the point to be projected: the proposed algorithm, named Fast Continuous Projection method (FCP) lets the projection direction vary continuously on the mesh. Moreover, the direction is coherent with the original surface that is approximated with the triangle mesh. An optimized version of the algorithm is also presented: this uses pre-evaluated matrices to reduce the calculation time. This algorithm can be effectively used when a large set of points has to be projected on a coarse mesh as, for example, to generate the scanning vectors for laser engraving/milling.

Keywords

• Projection method
• Triangle mesh
• Vertex normals
• Parameterization
• Bilinear projection
• Continuous projection