
Interpolation from a cloud of points
Baker, Timothy J.
Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.5563, Sept 2003

IMR PROCEEDINGS

12th International Meshing Roundtable
September 1417, 2003
Santa Fe, New Mexico, U.S.A.
Dept of MAE, Princeton University, Princeton, NJ 08544, U.S.A.
baker@tornado.princeton.edu
Abstract
Let V={P1,P2,...,Pn} be a set of points in either 2D or 3D space and let {q1, q2, ...,qn} be scalar values associated with the points. This paper presents a method for interpolating values of the scalar variable q at any position X in the convex hull ofV. The interpolant consists of the sum of the linear interpolant for a simplex T that contains X and a least squares estimate of the higher order terms. The least squares fit is made through the cloud of m points in V that are closest to X and are not alreadyvertices of T. Conditions that determine the invertibility of the least sqaures systemare examined and related to geometric constraints on the position of points in the cloud.
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