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Feature-Based Surface Parameterization and Texture Mapping

TitleFeature-Based Surface Parameterization and Texture Mapping
Publication TypeJournal Article
Year of Publication2005
AuthorsZhang, E., K. Mischaikow, and G. Turk
JournalACM Transactions on Graphics
Pagination1 - 27
Date Published01/2005
Keywordssegmentation, surface parameterization, texture mapping, topology

Surface parameterization is necessary for many graphics tasks: texture-preserving simplification, remeshing, surface painting, and precomputation of solid textures. The stretch caused by a given parameterization determines the sampling rate on the surface. In this article, we present an automatic parameterization method for segmenting a surface into patches that are then flattened with little stretch.

Many objects consist of regions of relatively simple shapes, each of which has a natural parameterization. Based on this observation, we describe a three-stage feature-based patch creation method for manifold surfaces. The first two stages, genus reduction and feature identification, are performed with the help of distance-based surface 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 stretch during patch unfolding, we notice that stretch is a 2 × 2 tensor, which in ideal situations is the identity. Therefore, we use the <i>Green-Lagrange tensor</i> to measure and to guide the optimization process. Furthermore, we allow the boundary vertices of a patch to be optimized by adding <i>scaffold triangles</i>. We demonstrate our feature-based patch creation and patch unfolding methods for several textured models.

Finally, to evaluate the quality of a given parameterization, we describe an image-based error measure that takes into account stretch, seams, smoothness, packing efficiency, and surface visibility.

Short TitleACM Trans. Graph.TOG