Reverse Engineering Using a Subdivision Surface Scheme

Subdivision surfaces are finding their way into many Computer Aided Design and Animation packages. Popular choices include Loop, Catmull-Clark, Doo-Sabin etc. Subdivision surfaces have many design advantages over traditional use of NURBs. NURB surfaces always are problematic when multiple patches meet. Reverse engineering (RE) is associated with the idea of scanning physical objects and representing the resulting dense cloud of points with mathematical surfaces. In RE the goal is to convert the dense point of scanned points into a patchwork of NURB surfaces with most effort going into automating the process. With the emergence of subdivision surfaces as popular modeling tools, it only follows that a similar process be devised for this class of surfaces. Our paper looks at developing one such method for Loop surfaces. Given a dense triangular mesh, we would like to obtain a control mesh for a Loop subdivision surface which approximates the given mesh. This process benefits subdivision surfaces in animation and manipulation as mentioned in [DeR98] that need speed over accuracy with an ability to manipulate the control mesh and to regenerate the smooth surface quickly. Like subdivision wavelets in a multi-resolution analysis [Lou97], our method can perform level-ofdetails (LOD) with arbitrary topological meshes useful in applications requiring a fast transfer, less storage, and a fast rendering and interaction. The paper shows the process as well as some early results which are promising. The resulting coarse control mesh is approximately 6.25% of the original mesh therefore this method can also be used as a lossy compression scheme.