Resumen de A point basis for multivariable piecewise linear interpolation and design centering
Results are given which establish a computational foundation for simplicial approximation and design centering of a convex body. A simplicial polyhedron is used to approximate the convex body and the “design center”, i.e. the point inside the body furthest in some norm from its exterior, is approximated by the point in the polyhedron furthest from its exterior. A point representation of the polyhedron is used, so that there is no necessity for computing or storing the faces of the approximation. Since in N space there can be factorially more faces than points, we are able to achieve significant efficiencies in both operation count and storage requirements, compared to previously reported methods. We give results for the 2 norm and the max norm, and demonstrate that our new method is operable in the nonconvex case, and can handle a mixed basis of faces and points as well.
