B-スプライン曲線の一考察

概要

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This paper proposes a method to describe and visualize B-spline curves for clear understandingof non-uniform rational B-spline curves used for designing software such as CAD. Particularattention is given to handling of the recursion formula to determine the basis functions,handling of the domain and the basis functions when increasing control points, and the effectsof the knot vectors towards the B-spline curves. The paper also demonstrates howconsideration of the B-spline curves helps solving certain problems associated with the Beziercurves used for drawing software such as Illustrator®. Finally, the paper shows how themathematics used in the process of describing the B-spline curves is related to the mathematicstaught at Salesian Polytechnic.
2012-10-31