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 
closet 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.

CACM April, 1963

Gluss, B.

CA630424 JB March 14, 1978  11:43 AM

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