Singularities of Principal Direction Fields from 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Meshless parameterization and surface reconstruction
Computer Aided Geometric Design
Tight cocone: a water-tight surface reconstructor
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Anisotropic polygonal remeshing
ACM SIGGRAPH 2003 Papers
Direct Anisotropic Quad-Dominant Remeshing
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Parameterization of triangle meshes over quadrilateral domains
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Meshless Thin-Shell Simulation Based on Global Conformal Parameterization
IEEE Transactions on Visualization and Computer Graphics
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Periodic global parameterization
ACM Transactions on Graphics (TOG)
Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Designing quadrangulations with discrete harmonic forms
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
N-symmetry direction field design
ACM Transactions on Graphics (TOG)
Spectral quadrangulation with orientation and alignment control
ACM SIGGRAPH Asia 2008 papers
Extracting lines of curvature from noisy point clouds
Computer-Aided Design
ACM SIGGRAPH 2009 papers
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
A wave-based anisotropic quadrangulation method
ACM SIGGRAPH 2010 papers
Meshing point clouds using spherical parameterization
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Integer-grid maps for reliable quad meshing
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
QEx: robust quad mesh extraction
ACM Transactions on Graphics (TOG)
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Point cloud is a basic description of discrete shape information. Parameterization of unorganized points is important for shape analysis and shape reconstruction of natural objects. In this paper we present a new algorithm for global parameterization of an unorganized point cloud and its application to the meshing of the cloud. Our method is guided by principal directions so as to preserve the intrinsic geometric properties. After initial estimation of principal directions, we develop a kNN(k-nearest neighbor) graph-based method to get a smooth direction field. Then the point cloud is cut to be topologically equivalent to a disk. The global parameterization is computed and its gradients align well with the guided direction field. A mixed integer solver is used to guarantee a seamless parameterization across the cut lines. The resultant parameterization can be used to triangulate and quadrangulate the point cloud simultaneously in a fully automatic manner, where the shape of the data is of any genus.