Projection Operation for Multidimensional Geometric Modeling with Real Functions

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Abstract

We discuss different techniques to projecting geometric objects defined by real functions of several variables. The result of this operation is an object of the lower dimension with its own defining function. We discuss several approaches: analytical methods, approximate projections and global maximum searches. The accuracy is compared for two algorithms: the union of maximal cross-sections and the global search with the quadratic interpolation. The following applications are illustrated: 3D solid projection onto a 2D plane; 4D to 3D projection for sweeping by a moving solid; 3D reconstruction from the medial axis.