Powell-Sabin splines are C-continuous piecewise quadratic polynomials defined on arbitrary triangulations. They admit a compact representation in a normalized B-spline basis with a geometric interpretation involving control triangles. This paper discusses several piecewise linear approximations for the graphical display of PowellSabin splines. We analyse their approximation error to the spline ...

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

We consider the piecewise linear approximation of saddle functions of the form f(x, y) = ax − by under the L∞ error norm. We show that interpolating approximations are not optimal. One can get slightly smaller errors by allowing the vertices of the approximation to move away from the graph of the function.

A method is presented for segmenting gray-value images into objects (or their parts) and for recognizing the detected objects. Starting from edge maps, the method extracts axial descriptions of symmetrical shapes. Initially, a piecewise linear approximation of the binary edge map is obtained. From any two of the resulting linear segments, a Linear Segment Pair (LSP) is formed and several of its...

Piecewise Linear Functions” Juan Pablo Vielma Business Analytics and Mathematical Sciences Department, IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, and Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA 15261, [email protected] Shabbir Ahmed, George Nemhauser H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technolo...

We investigate an implicit method to compute a piecewise linear representation of a surface from a set of sample points. As implicit surface functions we use the weighted sum of piecewise linear kernel functions. For such a function we can partition Rd in such a way that these functions are linear on the subsets of the partition. For each subset in the partition we can then compute the zero lev...