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Erschienen in:
2019 | OriginalPaper | Buchkapitel
4. ODF Using a Cubic Bézier
verfasst von : Alvin Penner
Erschienen in: Fitting Splines to a Parametric Function
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Abstract
Construction and manipulation of a cubic Bézier using control points is described. A family of hypoTrochoid curves, to which we will fit the Bézier spline, is defined. The hypoTrochoid curves can range from being highly asymmetric to symmetric, based on their relative curvatures at the endpoints. The ODF calculation is initialized by fitting the curvature exactly at the endpoints. Two classes of ODF solutions are found, one of which is qualitatively similar to the result obtained by fitting the endpoint curvature, while the other class is fundamentally different. Continuity of the rms error as the shape changes can only be obtained by jumping from one class to another. The eigenvalues of the response matrix are used to define more clearly the nature of the solution when these jumps occur.