Spherical parameterization is one of geometry processing techniques which maps a mesh to a sphere, and is expected to the use in the various applications of computer graphics, CAD/CAM and so on. In this paper, we propose a robust and fast computation method for high quality conformal spherical parameterization. Our approach is based on using multi-resolution representation of a mesh. We utilize such a hierarchical mesh structure to the computation of parameterization. We demonstrate through several experiments that our approach is faster than the previous approaches and enables robust and stable computation of spherical parameterization.
We also propose a method for creating parametric curves as one of methods for generating controllable curves on triangular meshes. A curve on a mesh is frequently used as a boundary curve of a specific region of a mesh in mesh modeling and applications such as texture mapping, remeshing or morphing. Although the curve defined in this paper is a piecewise linear approximation of a strict parametric curve, it is guaranteed that such a curve is just on a mesh. The basic idea is creating a curve on a spherical parameterization instead of direct definition on a mesh. The computation of this curve is done by using only the control points on a spherical parameterization which does not depend on the number of vertices in a mesh. This enables interactive creation/modification of curves even for dense meshes.
Papers
- Takashi Kanai: “Parametric Curves on Meshes”, Proc. 3rd International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia (GRAPHITE 2005) (Dunedin, New Zealand, 30 November – 2 December 2005), pp.413-416, ACM Press, NY, 2005. [pdf (Adboe PDF) (2.8MB)]
- Takashi Kanai: “Hierarchical Computation of Conformal Spherical Embeddings”, The 6th International Conference on Mathematical Methods for Curves and Surfaces (Tromso, Norway, 1-6 July 2004), 2004. [Presentation Slide (Adobe PDF) (1.1MB)]