The creation of smooth interpolating curves and surfaces is an important aspect of computer graphics. Trigonometric interpolation in the form of the Fourier transform has been a popular technique. For computer graphics, simpler curves and surfaces like the B´ezier curve and B-spline curve have been more popular due to the computational efficiency. Fitting B-spline or B´ezier curves or surfaces to unorganised data points has been more challenging since these curves are not naturally interpolating. Normally a system of equations needs to be solved to obtain the curves or surfaces with the added problem of identifying data points to form piecewise continuous surfaces. We solve the problem of periodic interpolating curves and surfaces using harmonic interpolation [73]. We extend harmonic interpolation to handle an even number of data points. We then show how harmonic interpolation can be applied using geometry images [29] to create smooth interpolating surfaces. We introduce algorithms to manipulate the amount of interpolated points, and the location of the interpolated points. Finally, we show how a smooth interpolating surface created by harmonic interpolation can be converted to a series of B´ezier surfaces. The combination of techniques allows us to quickly create a smooth interpolating surface from a set of unorganised points that have a known spherical structure. Keywords: Interpolation, harmonic interpolation, trigonometric interpolation, B´ezier curves surface fitting, tensor product surfaces. / Prof. W.F. Steeb
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uj/uj:14737 |
| Date | 07 December 2007 |
| Creators | Hardy, Alexandre |
| Source Sets | South African National ETD Portal |
| Detected Language | English |
| Type | Thesis |
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