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Interpolation from a cloud of points

Baker, Timothy J.

Proceedings, 12th International Meshing Roundtable, Sandia National Laboratories, pp.55-63, Sept 2003


12th International Meshing Roundtable
September 14-17, 2003
Santa Fe, New Mexico, U.S.A.

Dept of MAE, Princeton University, Princeton, NJ 08544, U.S.A.

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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