Machine interpretation of line drawings
Machine interpretation of line drawings
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
A Shape From Shading Analysis for a Single Perspective Image of a Polyhedron
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
How many 2D silhouettes does it take to reconstruct a 3D object?
Computer Vision and Image Understanding
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear Programming and Network Flows
Linear Programming and Network Flows
Reconstruction and visualization of polyhedra using projections
Reconstruction and visualization of polyhedra using projections
IBM Journal of Research and Development
IBM Journal of Research and Development
An improved algorithm for reconstructing a simple polygon from the visibility angles
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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We study the problem of constructing convex polygons and convex polyhedra given the number of visible edges and visible faces from some orthogonal projections. In 2D, we find necessary and sufficient conditions for the existence of a feasible polygon of size N and give an algorithm to construct one, if it exists. When N is not known, we give an algorithm to find the maximum and minimum size of a feasible polygon. In 3D, when the directions span a single plane we show that a feasible polyhedron can be constructed from a feasible polygon. We also give an algorithm to construct a feasible polyhedron when the directions are covered by two planes. Finally, we show that the problem becomes NP-complete for three or more planes.