Surface Reconstruction by Multiaxial Triangulation
IEEE Computer Graphics and Applications
A condition for isotopic approximation
Graphical Models - Solid modeling theory and applications
Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics)
Algorithmic Topology and Classification of 3-Manifolds (Algorithms and Computation in Mathematics)
Shape reconstruction from unorganized cross-sections
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Provably good 2D shape reconstruction from unorganized cross-sections
SGP '08 Proceedings of the Symposium on Geometry Processing
Reconstruction of multi-label domains from partial planar cross-sections
SGP '09 Proceedings of the Symposium on Geometry Processing
Online reconstruction of 3D objects from arbitrary cross-sections
ACM Transactions on Graphics (TOG)
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We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in ℜ3 from its crosssections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. in [LBD+08] preserves the homotopy type of the original object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that shape reconstruction from cross-sections comes with such theoretical guarantees.