Topology-Consistent Design for 3D Freeform Meshes with Harmonic Interpolation

One of the most exciting aspects of shape modeling is the development of new algorithms and methods to create unusual, interesting and aesthetically pleasing shapes. In this paper, we present an interactive modeling system for generating freeform surfaces using a 2D user interface. In this paper, we firstly interpret the given 2D curve to be the projection of the 3D curve that has the minimum curvature. Then we propose a topology-consistent strategy to trace the simple faces on the interconnecting 3D curves. By using the face tracing algorithm, our system can identify the 3D surfaces automatically. After obtaining the boundary curves for the faces, we apply Delaunay triangulation on these faces. Finally, the shape of the triangule surface mesh that follows the 3D boundary curves is computed by using harmonic interpolation. Solving Laplace’s equations, we are able to construct simple and conceptual 3D models interactively. Although the incorporation of topological manipulation will introduce many new(and interesting) design problems that cannot be addressed in this paper, we show that automatically generated models are both beneficial and feasible.