Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
On the complexity of optimization problems for 3-dimensional convex polyhedra and decision trees
Computational Geometry: Theory and Applications
The algorithm design manual
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Proceedings of the sixth ACM symposium on Solid modeling and applications
Pointshop 3D: an interactive system for point-based surface editing
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
A Fast and Simple Stretch-Minimizing Mesh Parameterization
SMI '04 Proceedings of the Shape Modeling International 2004
Multilevel Solvers for Unstructured Surface Meshes
SIAM Journal on Scientific Computing
Fast algorithms for the all nearest neighbors problem
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Meshless Thin-Shell Simulation Based on Global Conformal Parameterization
IEEE Transactions on Visualization and Computer Graphics
Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Differentials-based segmentation and parameterization for point-sampled surfaces
Journal of Computer Science and Technology
Feature-based 3D morphing based on geometrically constrained sphere mapping optimization
Proceedings of the 2010 ACM Symposium on Applied Computing
Technical Section: Mesh reconstruction by meshless denoising and parameterization
Computers and Graphics
Technical Section: Meshless quadrangulation by global parameterization
Computers and Graphics
Feature-based 3D morphing based on geometrically constrained spherical parameterization
Computer Aided Geometric Design
Iso-parametric tool-path planning for point clouds
Computer-Aided Design
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We present a simple method for meshing a 3D point cloud to a manifold genus-0 mesh. Our approach is based on recent methods for spherical embedding of planar graphs, where we use instead a k-nearest neighborhood graph of the point cloud. Our approach proceeds in two steps: We first embed the neighborhood graph on a sphere using an iterative procedure, minimizing the tangential Laplacian. Then we triangulate the embedded points and apply the resulting mesh connectivity to the input points. Besides meshing, spherical embedding of point clouds may also be used for other applications such as texture mapping or morphing.