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S. Ohrhallinger and S. Mudur An Efficient Algorithm for Determining an Aesthetic Shape Connecting Unorganized 2D Points Computer Graphics Forum 32

Version of Record online: 5 JUL 2013 | DOI: 10.1111/cgf.12162

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We present an efficient algorithm for determining an aesthetically pleasing shape boundary connecting all the points in a given unorganised 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 Bmin is non-intersecting, interpolates all points and minimises 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 BCmin. BCmin and Bmin can be expressed similarly by parametrising a topological constraint. A close approximation of BCmin, termed BC0 can be computed fast using a greedy algorithm.

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