کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
440165 | 690979 | 2013 | 10 صفحه PDF | دانلود رایگان |
In this paper, linear methods to find the multi-degree reduction of Bézier curves with G1G1-, G2G2-, and G3G3-continuity at the end points of the curves are derived. This is a significant improvement over existing geometric continuity degree reduction methods. The general equations for G2G2- and G3G3-multi-degree reduction schemes are non-linear; we were able to simplify these non-linear equations to linear ones by requiring C1C1-continuity. Our linear solution is given in an explicit, non-iterative form, and thus has lower computational costs than existing methods which were either non-linear or iterative. Further, there are no other existing G3G3-methods for multi-degree reduction. We give some examples and figures to demonstrate the efficiency, simplicity, and stability of our methods.
► We derive linear methods for multi-degree reduction of Bézier curves.
► Our linear solutions are given in an explicit, non-iterative form.
► Our methods have G1G1-, G2G2-, or G3G3-continuity at end points.
► For the G2G2 and G3G3 methods, we also require C1C1-continuity at end points.
Journal: Computer-Aided Design - Volume 45, Issue 2, February 2013, Pages 405–414