A non-Hamiltonian, nondegenerate Delaunay Triangulation
Information Processing Letters
r-regular shape reconstruction from unorganized points
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Polynomial time approximation schemes for Euclidean traveling salesman and other geometric problems
Journal of the ACM (JACM)
Curve reconstruction: connecting dots with good reason
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
TSP-based curve reconstruction in polynomial time
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction from unorganized points
Computer Aided Geometric Design
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Curve Reconstruction in Arbitrary Dimension and the Traveling Salesman Problem
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
An approximation scheme for planar graph TSP
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Curve and Surface Reconstruction in R2 and R3
HPC-ASIA '97 Proceedings of the High-Performance Computing on the Information Superhighway, HPC-Asia '97
A distance-based parameter free algorithm for curve reconstruction
Computer-Aided Design
VICUR: A human-vision-based algorithm for curve reconstruction
Robotics and Computer-Integrated Manufacturing
On the shape of a set of points in the plane
IEEE Transactions on Information Theory
On the number of cycles in planar graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
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Given an unorganized two-dimensional point cloud, we address the problem of efficiently constructing a single aesthetically pleasing closed interpolating shape, without requiring dense or uniform spacing. Using Gestalt's laws of proximity, closure and good continuity as guidance for visual aesthetics, we require that our constructed shape be a minimal perimeter, non-self intersecting manifold. We find that this yields visually pleasing results. Our algorithm is distinct from earlier shape reconstruction approaches, in that it exploits the overlap between the desired shape and a related minimal graph, the Euclidean Minimum Spanning Tree (EMST). Our algorithm segments the EMST to retain as much of it as required and then locally partitions and solves the problem efficiently. Comparison with some of the best currently known solutions shows that our algorithm yields better results.