International Journal of Computational Geometry & Applications · 1996 · 30 citations · 0 references
ComputingComputer ScienceMathematicsComputational GeometryGeometric ModelingGeometry3D ReconstructionGeometric ApproximationGeometry ProcessingShape RepresentationSurface ReconstructionThree-dimensional ReconstructionConvex PolyhedraPolyhedron TheoryShape Reconstruction
The problem of reconstructing a three-dimensional object from parallel slices has application in computer vision and medicine. Here we explore a specific existence question: given two polygons in parallel planes, is it always possible to find a polyhedron that has those polygons as faces, and whose vertices are precisely the vertices of the two polygons? We answer this question in the negative by providing an example of two polygons that cannot be connected to form a simple polyhedron. One polygon is a triangle, the other a somewhat complicated shape with spiraling pockets.