Quasi-angle-preserving mesh deformation using the least-squares approach

Abstract

We propose an angle-based mesh representation, which is invariant under translation, rotation, and uniform scaling, to encode the geometric details of a triangular mesh. Angle-based mesh representation consists of angle quantities defined on the mesh, from which the mesh can be reconstructed uniquely up to translation, rotation, and uniform scaling. The reconstruction process requires solving three sparse linear systems: the first system encodes the length of edges between vertices on the mesh, the second system encodes the relationship of local frames between two adjacent vertices on the mesh, and the third system defines the position of the vertices via the edge length and the local frames. From this angle-based mesh representation, we propose a quasi-angle-preserving mesh deformation system with the least-squares approach via handle translation, rotation, and uniform scaling. Several detail-preserving mesh editing examples are presented to demonstrate the effectiveness of the proposed method.