A survey of curve and surface methods in CAGD
Computer Aided Geometric Design
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Automatic reconstruction of B-spline surfaces of arbitrary topological type
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
A Level-Set Approach to 3D Reconstruction from Range Data
International Journal of Computer Vision
Computer Vision and Image Understanding
Computing and Rendering Point Set Surfaces
IEEE Transactions on Visualization and Computer Graphics
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Optimization methods for scattered data approximation with subdivision surfaces
Graphical Models - Solid modeling theory and applications
A composite approach to meshing scattered data
Graphical Models - Special issue on SPM 05
Interpolation by geometric algorithm
Computer-Aided Design
On Smooth Bicubic Surfaces from Quad Meshes
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
Point-tangent/point-normal B-spline curve interpolation by geometric algorithms
Computer-Aided Design
Higher-order level-set method and its application in biomolecular surfaces construction
Journal of Computer Science and Technology
The convergence of the geometric interpolation algorithm
Computer-Aided Design
Generating B-spline curves with points, normals and curvature constraints: a constructive approach
The Visual Computer: International Journal of Computer Graphics
Technical Section: An extended iterative format for the progressive-iteration approximation
Computers and Graphics
B-spline surface fitting by iterative geometric interpolation/approximation algorithms
Computer-Aided Design
Uniform B-Spline Curve Interpolation with Prescribed Tangent and Curvature Vectors
IEEE Transactions on Visualization and Computer Graphics
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In this paper, we present a procedure for automatically reconstructing an arbitrary topological surface from an unorganized point data set; this surface will have three representations, namely quadrilateral meshes, Catmull-Clark subdivision surfaces, and B-spline surfaces. Our novel reconstruction method adapts a level set method to capture the topology of the point clouds in a robust manner and then employs an iterative geometric fitting algorithm to generate high-quality Catmull-Clark subdivision surfaces. A quadrilateral mesh is generated by projecting the control net of the resulting Catmull-Clark surface onto its limit surface. Finally, the control net of the Catmull-Clark surface is converted to that of a B-spline surface. The reconstructed models of topologically complex models show the effectiveness of the proposed algorithm.