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Parameterization of discrete surface is a fundamental and widely-used operation in graphics, required, for instance, for texture mapping or remeshing. As 3D data becomes more and more detailed, there is an increased need for fast and robust techniques to automatically compute least-distorted parameterizations of large meshes. In this paper, for a surface patch on a smooth, two-dimensional surface in R3 low-distortion Parameterizations are achieved by an optimal parameterization algorithm. Our proposed algorithm is described by initial parameterization, domain discretization and numerical optimization. The parameterization can be optimized with respect to the varying importance of conformality, length preservation and area preservation. The initial parameterization is provided for the subsequent optimization of the parameter domain. The domain discretization is introduced and a constrained Newton method is used to minimize a corresponding discrete energy. The numerical optimization method is provided for the optimal deformation to generate the final, optimal parameterization. Experiment results prove that our proposed algorithm is effective and robust. (6 pages)

The existence of artifacts in polygonal meshes makes it difficult for model operations, especially when comes to model rebuilding, rapid prototyping or other downstream applications. Model repair is the task of removing artifacts from a geometric model to produce an output model that is suitable for further processing by downstream applications that have certain quality requirements on their input. Existing model repair algorithms are capable of solving single artifact in a model. For different types of artifacts in a model, they may not result in satisfactory results. This paper proposes a surface oriented algorithm for model repair. This algorithm includes five contents: consistent normal orientation, hole filling on surface, manifolds mapping on surface, gap bridging between surface patches, mesh topology simplification. The proposed algorithm works well for different types of artifacts and can better preserve the detailed features of the original mesh. (5 pages)