Meshes are the most common representations for 3D surface models nowadays and there is a great demand for processing mesh models. Editing existing meshes is challenging because the editing is limited by the original mesh structure, namely, the irregularities of the vertex distribution and the connectivity. A desirable editing framework should satisfy the user’s editing intentions while maintaining the original shape features as much as possible. Therefore the description of the shape features is crucial and has a direct relation on the quality of the editing system....[ Read more ]

Meshes are the most common representations for 3D surface models nowadays and there is a great demand for processing mesh models. Editing existing meshes is challenging because the editing is limited by the original mesh structure, namely, the irregularities of the vertex distribution and the connectivity. A desirable editing framework should satisfy the user’s editing intentions while maintaining the original shape features as much as possible. Therefore the description of the shape features is crucial and has a direct relation on the quality of the editing system.

In this thesis we propose a new non-linear differential editing framework, based on the curvature flow Laplacian coordinates, for efficient editing of irregular meshes. This framework overcomes the main limitation of earlier linearized methods, specifically, it solves the common transformation problem of differential editing and avoids undesirable distortion under large-scale rotations and translations of the handles. In addition, our framework supports a new type of handles, point-handle, which enables automatic orientation estimation, thus further simplifying the user interface. To further improve the stability of our editing framework for editing meshes with poor sampling rate and triangle quality, we then propose to edit the meshes in the dual domain, based on the dual Laplacian coordinates.

Meshes created by modern scanning technology are typically huge. Editing such meshes using a nonlinear editing framework gives unacceptable slow performance. To solve this problem, we introduce the notion of handle-aware rigidity motivated by the observation that for each vertex the influence of deformations received from different handles is largely dependent on the locations of the handles on the mesh, and independent of the handles’ movement during deformation. We present a general reduced model, based on handle-aware isolines, enabling interactive editing of huge models with physically plausible deformation results.