Least squares fitting of planes to surfaces using dynamic programming

Dynamic programming has recently been used by Stone, by Bellman and by Gluss to determine the closest fit of broken line segments to a curve in an interval under the constraint that the number of segments is fixed. In the present paper successive models are developed to extend the method to the fitting of broken plane segments to surfaces z = g(x, y) defined over certain types of subareas of the (x, y)-space. The first model considers a rectangular area, with the constraint that the plane segments are defined over a grid in the (x, y)-space. It is then shown how this model may be incorporated into an algorithm that provides successive approximations to optimal fits for any type of closed area. Finally, applications are briefly described.

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