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Interactive least squares surface fitting

University of British Columbia

This thesis is concerned with the design and implementation of a surface fitting package in an interactive graphics environment. Surface fitting techniques are used to generate a smooth looking, easy to evaluate, bivariate function given a set of data points on some domain in the plane, and are thus useful for a variety of applications. We consider the implementation of a surface fitting technique using weighted least squares with tensor products of B-splines on regular data grids (i.e. the position of the data points can be represented as the cross product of two vectors). While somewhat more restrictive than other surface fitting methods, this technique, when applicable, is extremely efficient. Knot placement and weight placement are discussed as methods of adapting the spline surface to rapidly varying regions on the domain. A disadvantage of the original method used to solve for the coefficients of the spline surface is that the domain of the function to be approximated must be rectangular. An algorithm to extend the surface fitting method to non-rectangular domains, thus removing this restriction, is presented. An interactive surface fitting package is provided, which allows a user to fit a spline surface to a set of data points on a regular grid. This provides a powerful tool which may be used to effectively modify the spline surface and indicate the accuracy of the approximation.

Text

2010-03-22

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http://hdl.handle.net/2429/22271

Computer Science

University of British Columbia

Graduate