Parametrization and smooth approximation of surface triangulations
Computer Aided Geometric Design
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
Non-distorting Flattening for Virtual Colonoscopy
MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Shrouds: optimal separating surfaces for enumerated volumes
VISSYM '03 Proceedings of the symposium on Data visualisation 2003
Computer Aided Geometric Design
Lifting curve parameterization methods to isosurfaces
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
MC*: Star Functions for Marching Cubes
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
Conformal virtual colon flattening
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Parameterizing marching cubes isosurfaces with natural neighbor coordinates
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Model transduction for triangle meshes
Journal of Computer Science and Technology
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We present some new methods for parameterizing the triangle mesh surface (TMS) which result from the Marching Cubes (MC) algorithm. The methods apply to surfaces of genus zero and the parameter domain is a unit sphere. We take advantage of some special properties of the TMS resulting from the MC algorithm to obtain simple, computational efficient representations of the nearest neighbor coordinates and utilize these coordinates in the characterization of the parameterization by means of systems of equations which are solved iteratively. Examples and comparisons are presented.