Piecewise Approximations of Real Algebraic Surfaces
نویسندگان
چکیده
We use a combination of both symbolic and numerical techniques to construct several degree bounded G 0 and G 1 continuous, piecewise approximations of real algebraic surfaces. These approximations are based upon an adaptive triangulation (a G 0 planar approximation) of the real components of the algebraic surface, and includes both singular points and singular curves on the surface. The approximations could be either low degree piecewise implicit algebraic patches (A-patches) or low degree piecewise rational Bernstein-Bezier patches, or NURBS. At certain singular points and singular curves on the surface we use the classical Newton power series factorizations to determine the distinct self intersecting surface branches. Details of the implementation of these algorithms and approximation error bounds are also provided.
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