What question did this study set out to answer?

The aim is to develop direct methods for fitting smooth curves and surfaces to point data.

August 1, 1987Open Access

Direct least-squares fitting of algebraic surfaces

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The aim is to develop direct methods for fitting smooth curves and surfaces to point data.
Developed four fitting methods: exact fit, simple fit, spherical fit, and blend fit.
All methods are dimension-independent and apply to 2D curves and 3D surfaces.
Methods require specific computational operations for fitting surfaces of various orders.
Spherical fit provides robustness that previous direct circle and sphere fitters have not achieved.
All methods, except simple fit, achieve a robustness level previously attainable only for fitting planes.
Incremental additions and deletions of points are computationally efficient, with low costs per operation.

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Developed direct methods for fitting shapes to points, indicating robust surface fitting techniques.

Vaughan Pratt (1987) studied this question.

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