Interactive Deformation of 3D Mesh Models

This paper proposes a framework for interactively deforming 3D mesh models. 3D mesh models are often used in finite element analysis, but existing surface-based deformation methods fail to deform volumetric elements consistently. In the method proposed here, vertices in a 3D mesh model are classified into boundary vertices and interior vertices. Boundary vertices are treated in the same way as a feature-preserving surface-based deformation; a mean curvature constraint is defined at each boundary vertex, and positional constraints and form-feature constraints are optionally specified at boundary vertices. At each interior vertex, a local volume is constructed as a set of polyhedra that share an interior vertex, and a constraint is assigned based on mean value coordinates. The combination of the mean value coordinates and the mean curvature normals work very well to deform both the boundary and interior of 3D mesh models naturally, without complicated weighting schemes or the rotation of constraints for 3D meshes. In this framework, all constraints are represented in linear forms and solved very efficiently using sparse linear system solvers. This research has shown that 3D mesh models can be deformed in an interactive manner and with a practical amount of preprocessing time.