Sketching freeform meshes using graph rotation functions

Abstract

We present a new approach for sketching free form meshes with topology consistency. Firstly, we interpret the given 2D curve to be the projection of the 3D curve with the minimum curvature. Then we adopt a topology-consistent strategy based on the graph rotation system, to trace the simple faces on the interconnecting 3D curves. With 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 triangle mesh that follows the 3D boundary curves is computed by using harmonic interpolation. Meanwhile our system provides real-time algorithms for both control curve generation and the subsequent surface optimization. With the incorporation of topological manipulation into geometrical modeling, we show that automatically generated models are both beneficial and feasible.