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Feature-Based Surface Parameterization and Texture Mapping
Eugene Zhang, Konstantin
Mischaikow, and Greg Turk
AbstractSurface parameterization is necessary for many graphics tasks: texture-preserving simplification, remeshing, surface painting, and pre-computation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this paper, we propose an automatic parameterization method that segments a surface into patches that are then flattened with little stretch.
We observe that many objects consist of regions of relative simple shapes, each of which has a natural parameterization. Therefore, we propose a three-stage feature based patch creation method for manifold mesh surfaces. The first two stages, genus reduction and feature identification, are performed with the help of distance-based Morse functions. In the last stage, we create one or two patches for each feature region based on a covariance matrix of the feature's surface points.
To reduce the stretch during patch unfolding, we notice that the stretch is a 2x2 tensor which in ideal situations is the identity. Therefore, we define a new stretch metric that is based on isometry to measure and to guide the optimization process. Furthermore, we allow the boundary vertices of a patch to be optimized by adding scaffold triangles. We demonstrate our feature identification and patch unfolding methods for several textured models.
1. Feature-based surface segmentation results for various 3D models. Some models have handles (Buddha, Dragon and Feline).
2. 3D surfaces with textures (top row) and their corresponding texture maps (bottom row) that are generated based on our parameterization technique.