Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
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Computer-Aided Design
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Mathematical methods in computer aided geometric design
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Computer Aided Geometric Design
Approximating normals for marching cubes applied to locally supported isosurfaces
Proceedings of the conference on Visualization '02
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IEEE Transactions on Visualization and Computer Graphics
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IEEE Transactions on Visualization and Computer Graphics
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
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MICCAI '00 Proceedings of the Third International Conference on Medical Image Computing and Computer-Assisted Intervention
Computer Aided Geometric Design
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
Segmentation and Parametrization of Arbitrary Polygon Meshes
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Chord Length (Motivated) Parameterization of Marching Cubes IsoSurfaces
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
Parameterizing marching cubes isosurfaces with natural neighbor coordinates
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
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We describe a new technique for the parameterization of surfaces which applies to the isosurfaces produced by the marching cubes algorithm. The technique is motivated by methods of parameterization for curves including the centripetal and chord length methods. The technique for extending the concept of curve parameterization to an isosurface parameterization is based upon the 4*-network which is a collection of three mutually orthogonal planar polygons lying on and intersecting at the vertices of the marching cubes isosurface. Several examples from geometric modeling, and medical imaging analysis are included.