Interpolating an unorganized 2D point cloud with a single closed shape

Ohrhallinger, Stefan; Mudur, Sudhir P.

doi:10.1016/j.cad.2011.09.009

Cited by 6 publications

(15 citation statements)

References 26 publications

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“…We also prove that like other Delaunay-based methods based on a local-sampling condition, the complexity of our method is O(n log n), which is a major advantage over [OM11]. However, given the relaxed topological constraint of greater than two incident edges per vertex, we are able to use a greedy algorithm to compute an approximation to BC min , which we call as BC 0 .…”

Section: Global Search Approachmentioning

confidence: 84%

“…Since that algorithm tries to recover the exact B min using a sequence of edge-swap operations, it exhibits linearithmic time only if there is a single such sequence. Further, the greater concern is that algorithm [OM11] can deteriorate quickly into combinatorial complexity. Yet, when this constraint is not met, it fails for many cases which this method reconstructs well (see, for example, Figure 10d).…”

Section: Comparisonmentioning

confidence: 99%

“…(a) Crocodile point set from[OM11]. (c) Exhaustive non-linearithmic search[OM11] yields B min . (c) Exhaustive non-linearithmic search[OM11] yields B min .…”

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confidence: 99%

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An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

Ohrhallinger

Mudur

2013

Computer Graphics Forum

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We present anefficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganized set of 2D points, with no other information than point coordinates. By posing shape construction as a minimisation problem which follows the Gestalt laws, our desired shape B min is non-intersecting, interpolates all points and minimizes a criterion related to these laws. The basis for our algorithm is an initial graph, an extension of the Euclidean minimum spanning tree but with no leaf nodes, called as the minimum boundary complex BC min . BC min and B min can be expressed similarly by parametrizing a topological constraint. A close approximation of BC min , termed BC 0 can be computed fast using a greedy algorithm. BC 0 is then transformed into a closed interpolating boundary B out in two steps to satisfy B min 's topological and minimization requirements. Computing B min exactly is an NP (Non-Polynomial)-hard problem, whereas B out is computed in linearithmic time. We present many examples showing considerable improvement over previous techniques, especially for shapes with sharp corners. Source code is available online.

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Section: Global Search Approachmentioning

confidence: 84%

Section: Comparisonmentioning

confidence: 99%

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An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points

Ohrhallinger

Mudur

2013

Computer Graphics Forum

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“…An example in R 2 is edge length, and minimizing the total length of the boundary shape has shown to yield good results [29]. We therefore try to extend this to R 3 .…”

Section: Choosing a Suitable Criterionmentioning

confidence: 99%

Minimizing edge length to connect sparsely sampled unstructured point sets

Ohrhallinger

Mudur

Wimmer

2013

Computers & Graphics

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Most methods for interpolating unstructured point clouds handle densely sampled point sets quite well but get into trouble when the point set contains regions with much sparser sampling, a situation often encountered in practice. In this paper, we present a new method that provides a better interpolation of sparsely sampled features.We pose the surface construction problem as finding the triangle mesh which minimizes the sum of all triangles' longest edge. Since searching for matching umbrellas among sparsely sampled points to yield a closed manifold shape is a difficult problem, we introduce suitable heuristics. Our algorithm first connects the points by triangles chosen in order of their longest edge and with the requirement that all edges must have at least 2 incident triangles. This yields a closed non-manifold shape which we call the Boundary Complex. Then we transform it into a manifold triangulation using topological operations. We show that in practice, runtime is linear to that of the Delaunay triangulation of the points. Source code is available online.

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“…In this paper, an algorithm of unstructured grid generation of clouds [12,16] of points on a surface is provided. The paper contains a theoretical background, the formal definition of the semi-Delaunay property, and the triangulation algorithm of points scattered on the surface.…”

Section: Summary and Closurementioning

confidence: 99%