Curves and surfaces for computer aided geometric design: a practical guide
Curves and surfaces for computer aided geometric design: a practical guide
On the limited memory BFGS method for large scale optimization
Mathematical Programming: Series A and B
IEEE Transactions on Pattern Analysis and Machine Intelligence
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Surface modeling with oriented particle systems
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Dynamic deformation of solid primitives with constraints
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
Adaptive Polygonalization of Implicitly Defined Surfaces
IEEE Computer Graphics and Applications
Parameterized Families of Polynomials for Bounded Algebraic Curve and Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating the in/out function of a surface represented by points
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Curve reconstruction from noisy samples
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Curve reconstruction from noisy samples
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Medial set, boundary, and topology of random point sets
Proceedings of the 11th international conference on Theoretical foundations of computer vision
Robust reconstruction of 2D curves from scattered noisy point data
Computer-Aided Design
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Parametric deformable models have been extensively and very successfully used for reconstructing free-form curves and surfaces, and for tracking nonrigid deformations, but they require previous knowledge of the topological type of the data, and good initial curve or surface estimates. With deformable models, it is also computationally expensive to check for and to prevent self-intersections while tracking deformations. The Implicit Simplicial Models that we introduce in this paper are implicit curves and surfaces defined by piece-wise linear functions. This representation allows for local deformations, control of the topological type, and prevention of self-intersections during deformations. As a first application, we also describe in this paper an algorithm for two-dimensional curve reconstruction from unorganized sets of data points. The topology, the number of connected components, and the geometry of the data are all estimated using an adaptive space subdivision approach. The main four components of the algorithm are topology estimation, curve fitting, adaptive space subdivision, and mesh relaxation.