Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Placing the largest similar copy of a convex polygon among polygonal obstacles
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Shape reconstruction from unorganized cross-sections
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Geometric tomography with topological guarantees
Proceedings of the twenty-sixth annual symposium on Computational geometry
Homotopic object reconstruction using natural neighbor barycentric coordinates
Transactions on Computational Science XIV
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This paper deals with the reconstruction of 2-dimensional geometric shapes from unorganized 1-dimensional cross-sections. We study the problem in its full generality following the approach of Boissonnat and Memari [BM07] for the analogous 3D problem. We propose a new variant of this method and provide sampling conditions to guarantee that the output of the algorithm has the same topology as the original object and is close to it (for the Hausdorff distance).