Minimum Strictly Convex Quadrangulations of Convex Polygons
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1996
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Müller-Hannemann, Matthias
Weihe, Karsten
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We present a linear-time algorithm that decomposes a convex polygon conformally into a minimum number of strictly convex quadrilaterals. Moreover, we characterize the polygons that can be decomposed without additional vertices inside the polygon, and we present a linear-time algorithm for such decompositions, too. As an application, we consider the problem of constructing a minimum conformal refinement of a mesh in the three-dimensional space, which approximates the surface of a workpiece. The latter problem has resulted from a cooperation with an engineering company that sells CAD packages. We have proved that this problem is strongly NP-hard, and we present a linear-time algorithm with a constant approximation ratio of 4.
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MÜLLER-HANNEMANN, Matthias, Karsten WEIHE, 1996. Minimum Strictly Convex Quadrangulations of Convex PolygonsBibTex
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