Degree elevation operator and geometric construction of C-B-spline curves
نویسندگان
چکیده
منابع مشابه
Degree Elevation of Interval B-Spline Curves
O. Ismail, Senior Member, IEEE Abstract— This paper presents an efficient method for degree elevation of interval B-spline curves. The four fixed Kharitonov's polynomials (four fixed B-spline curves) associated with the original interval B-spline curve are obtained. The method is based on the matrix identity. The B-spline basis functions are represented as linear combinations of the B-splines o...
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References: Prautzsch, H., 1984. Degree elevation of B-spline curves. CAGD 18 (12) Prautzsch, H., Piper, B., 1991. A fast algorithm to raise the degree of B-spline curves. CAGD 8 (4) Pigel, L., Tiller, W., 1994. Software-engineering approach to degree elevation of B-spline curves. CAD 26 (1) Liu, W., 1997. A simple, efficient degree raising algorithm for B-spline curves. CAGD 14 (7) Huang, Q.-X...
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We give a new, simple algorithm for simultaneous degree elevation and knot insertion for B-spline curves. The method is based on the simple approach of computing derivatives using the control points, resampling the knot vector, and then computing the new control points from the derivatives. We compare our approach with previous algorithms and illustrate it with examples. 2004 Elsevier B.V. Al...
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An algorithmic approach to degree reduction of interval B-spline curve is presented in this paper. The curves that are useful in geometric modeling should have a relatively smooth shape and should be intuitively connected with the path of the sequence of control points. One family of curves satisfying this requirement is represented by the B-spline curves. The four fixed Kharitonov's polynomial...
متن کاملDegree Reduction of B-Spline Curves
In this paper, we propose the generalized B divided difference, with which the (k− 1)th derivative of B-spline curves of order k can be obtained directly without the need to compute the first (k − 2) derivatives as before. Based on the generalized B divided difference, the necessary and sufficient condition for degree-reducible B-spline curves is presented. Algorithms for degree reduction of B-...
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ژورنال
عنوان ژورنال: Science China Information Sciences
سال: 2010
ISSN: 1674-733X,1869-1919
DOI: 10.1007/s11432-010-4053-2