Feature-aligned Surface Parameterization Using Secondary Laplace Operator and Loop Subdivision

Surface parameterization is of great importance for many applications such as quadrangulation, texture mapping and surface fitting. An important issue for surface parameterization is how to align parametric lines with feature directions. To address this issue, in this paper we first utilize Loop subdivision basis functions and isogeometric analysis (IGA) to calculate eigenfunctions of the secondary Laplace operator (SLO) on triangle meshes. Eigenfunctions are then used for centroidal Voronoi tessellation (CVT) based surface segmentation, and boundaries of the segmented regions are extracted as feature lines which contain concave creases and convex ridges. Along each feature line, adjacent triangles are defined as guidance triangles to parameterize the surface using a constrained cross field method, where feature lines are preserved and aligned to parametric lines. Several examples are presented in the end to verify the robustness of our algorithm.