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Reconstruction of Three Dimensional Convex Bodies from the Curvatures of Their Shadows

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DOI: 10.4236/ajcm.2015.52007    2,129 Downloads   2,513 Views  
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In this article, we study necessary and sufficient conditions for a function, defined on the space of flags to be the projection curvature radius function for a convex body. This type of inverse problems has been studied by Christoffel, Minkwoski for the case of mean and Gauss curvatures. We suggest an algorithm of reconstruction of a convex body from its projection curvature radius function by finding a representation for the support function of the body. We lead the problem to a system of differential equations of second order on the sphere and solve it applying a consistency method suggested by the author of the article.

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The authors declare no conflicts of interest.

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Aramyan, R. (2015) Reconstruction of Three Dimensional Convex Bodies from the Curvatures of Their Shadows. American Journal of Computational Mathematics, 5, 86-95. doi: 10.4236/ajcm.2015.52007.


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