Free-form shape design using triangulated surfaces
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Computer Aided Geometric Design
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Think globally, fit locally: unsupervised learning of low dimensional manifolds
The Journal of Machine Learning Research
Applied Multidimensional Scaling
Applied Multidimensional Scaling
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A general algorithm framework for 3D mesh parametrization is proposed in this paper. Under this framework, a parametrization algorithm is divided into three steps. In the first step, the linearly reconstructing weights of each vertex with respect to its neighbours are computed. These weights are then used to computed a initial parametrization mesh, and in the third step, this initial mesh is rotated and scaled to obtain a parametrization mesh with high isometric precision. Four parametrization algorithms are proposed based on this framework. Examples show the effectiveness and applicability of the parametrization algorithms proposed in the paper.