Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
IEEE Computer Graphics and Applications - Special issue on computer-aided geometric design
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
Modern Differential Geometry of Curves and Surfaces with Mathematica
Modern Differential Geometry of Curves and Surfaces with Mathematica
Optimizing 3D triangulations using discrete curvature analysis
Mathematical Methods for Curves and Surfaces
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Generalized barycentric coordinates on irregular polygons
Journal of Graphics Tools
The asymptotic decider: resolving the ambiguity in marching cubes
VIS '91 Proceedings of the 2nd conference on Visualization '91
IEEE Transactions on Visualization and Computer Graphics
Volumetric segmentation using Weibull E-SD fields
IEEE Transactions on Visualization and Computer Graphics
Lifting curve parameterization methods to isosurfaces
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Spherical parameterization of marching cubes IsoSurfaces based upon nearest neighbor coordinates
Journal of Computer Science and Technology
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 modification of the widely used marching cubes method that leads to the useful property that the resulting isosurfaces are locally single valued functions. This implies that conventional interpolation and approximation methods can be used to locally represent the surface. These representations can be used for computing approximations of local surface properties. We utilize this possibility in order to develop algorithms for locally approximating Gaussian and mean curvature, methods for constrained smoothing of isosurface, and techniques for the parameterization of isosurfaces.