Communications of the Korean Mathematical Society (대한수학회논문집)
- Volume 10 Issue 2
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- Pages.483-490
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- 1995
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON THE CONSTRUCTION AND THE EXISTENCE OF PARAMETRIC CUBIC$g^2$ B-SPLINE
Abstract
A parametric cubic spline interpolating at fixed number of nodes is constructed by formulating a parametric cubic $g^2$ B-splines $S_3(t)$ with not equally spaced parametric knots. Since the fact that each component is in $C^2$ class is not enough to provide the geometric smoothness of parametric curves, the existence of $S_3(t)$ oriented toward the modified second-order geometric continuity is focalized in our work.
Keywords
- parametric cubic splines;
- free-form curve;
- self-interactive curve;
- geometric smoothness;
- geometric continuity;
- cumulative chord length;
- parametric cubic $g^2$ B-spline