On approximating polygonal curves in two and three dimensions
CVGIP: Graphical Models and Image Processing
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction from unorganized points
Computer Aided Geometric Design
Proceedings of the sixth ACM symposium on Solid modeling and applications
Faithful Least-Squares Fitting of Spheres, Cylinders, Cones and Tori for Reliable Segmentation
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Automatic CAD modeling of industrial pipes from range images
NRC '97 Proceedings of the International Conference on Recent Advances in 3-D Digital Imaging and Modeling
Approximating and intersecting surfaces from points
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Shrinking: Another Method for Surface Reconstruction
GMP '04 Proceedings of the Geometric Modeling and Processing 2004
New Results on Path Approximation
Algorithmica
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
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We present an automatic method for computing an accurate parametric model of a piecewise defined pipe surface, consisting of cylinder and torus segments, from an unorganized point set. Our main contributions are reconstruction of the spine curve of a pipe surface from surface samples, and approximation of the spine curve by G^1 continuous circular arcs and line segments. Our algorithm accurately outputs the parametric data required for bending machines to create the reconstructed tube.