Marshall W. Bern

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We give a simple combinatorial algorithm that computes a piecewise linear approx imation of a smooth surface from a nite set of sample points The algorithm uses Voronoi vertices to remove triangles from the Delaunay triangulation We prove the algorithm correct by showing that for densely sampled surfaces where density depends on local feature size the(More)
We describe our experience with a new algorithm for the reconstruction of surfaces from unorganized sample points in IR . The algorithm is the first for this problem with provable guarantees. Given a “good sample” from a smooth surface, the output is guaranteed to be topologically correct and convergent to the original surface as the sampling density(More)
We study several versions of the problem of generating triangular meshes for finite element methods. We show how to triangulate a planar point set or polygonally bounded domain with triangles of bounded aspect ratio; how to triangulate a planar point set with triangles having no obtuse angles; how to triangulate a point set in arbitrary dimension with(More)
We survey the computational geometry relevant to nite element mesh generation. We especially focus on optimal triangulations of geometric domains in twoand three-dimensions. An optimal triangulation is a partition of the domain into triangles or tetrahedra, that is best according to some criterion that measures the size, shape, or number of triangles. We(More)
We construct a graph on a planar point set, which captures its shape in the following sense: if a smooth curve is sampled densely enough, the graph on the samples is a polygonalization of the curve, with no extraneous edges. The required sampling density varies with the Local Feature Size on the curve, so that areas of less detail can be sampled less(More)
Many mobile devices have touch-sensitive screens that people interact with using fingers or thumbs. However, such interaction is difficult because targets become occluded, and because fingers and thumbs have low input resolution. Recent research has addressed occlusion through visual techniques. However, the poor resolution of finger and thumb selection(More)
Marshall Bern * We study a basic problem in mathematical origami: determine if a given crease pattern can be folded to a flat origami. We show that assigning mountain and valley folds is NPhard. We also show that determining a suitable overlap order for flaps is NP-hard, even assuming a valid mountain and valley assignment.