Connect-the-dots: a new heuristic
Computer Vision, Graphics, and Image Processing
Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
Handbook of combinatorics (vol. 1)
The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
r-regular shape reconstruction from unorganized points
Computational Geometry: Theory and Applications - special issue on applied computational geometry
A simple provable algorithm for curve reconstruction
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
Curve reconstruction: connecting dots with good reason
Computational Geometry: Theory and Applications
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Reconstructing a collection of curves with corners and endpoints
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Traveling Salesman-Based Curve Reconstruction in Polynomial Time
SIAM Journal on Computing
A greedy Delaunay-based surface reconstruction algorithm
The Visual Computer: International Journal of Computer Graphics
Curve and Surface Reconstruction: Algorithms with Mathematical Analysis (Cambridge Monographs on Applied and Computational Mathematics)
Smooth surface reconstruction via natural neighbour interpolation of distance functions
Computational Geometry: Theory and Applications
Constructing 3D motions from curvature and torsion profiles
Computer-Aided Design
SMI 2013: Minimizing edge length to connect sparsely sampled unstructured point sets
Computers and Graphics
EXPERIMENTAL APPROACH TO CURVE RECONSTRUCTION BASED ON HUMAN VISUAL PERCEPTION
Journal of Integrated Design & Process Science
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This paper introduces an optimization-based approach for the curve reconstruction problem, where piecewise linear approximations are computed from sets of points sampled from target curves. In this approach, the problem is formulated as an optimization problem. To be more concrete, at first the Delaunay triangulation for the sample points is computed, and a weight is assigned with each Delaunay edge. Then the problem becomes minimization or maximization of the total weights of the edges that constitute the reconstruction. This paper proposes one exact method and two approximate methods, and shows that the obtained results are improved both theoretically and empirically. In addition, the optimization-based approach is further extended to three dimensions, where surfaces are to be reconstructed, and the quality of the reconstructions is examined.