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- W2040857066 abstract "Quadratic trigonometric spline curves with multiple shape parameters are presented in this paper. Analogous to the cubic B-spline curves, each trigonometric spline curve segment is generated by four consecutive control points. The trigonometric spline curves with a non–uniform knot vector are C <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sup> continuous. With a uniform knot vector, the trigonometric spline curves are C <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>3</sup> continuous when all shape parameter λ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>i</sub> =1. Taking different values of the shape parameters, one can globally or locally adjust the shapes of the curves, so that the trigonometric spline curves can be close to the cubic B-spline curves or closer to the given control polygon than the cubic B-spline curves. The trigonometric spline curves also can represent ellipse and generate a family of ellipse with the same control points. A quadratic trigonometric Bézier curves are also introduced as a special case of the given trigonometric spline curves." @default.
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- W2040857066 date "2007-10-01" @default.
- W2040857066 modified "2023-10-14" @default.
- W2040857066 title "Quadratic Trigonometric Spline Curves with Multiple Shape Parameters" @default.
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- W2040857066 doi "https://doi.org/10.1109/cadcg.2007.4407918" @default.
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