一种基于区间Bézier曲线的Offset逼近曲线
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摘要
Offset曲线结构比较复杂,给其在工业应用中的有效处理带来比较大的困难。具有带状区域的区间Bézier曲线,其边界结构相对简单。为此,提出了一种基于区间Bézier曲线的等距逼近曲线算法,将区间Bézier曲线控制顶点的布置由矩形改为正多边形,并逐渐逼近圆,使整个包络区域边界更加逼近Offset曲线。通过实例验证了算法的可行性。
Because of the complex structure of the offset curve, it is very difficult to deal with it effectively in industrial applications. The boundary structure of the interval Bézier curve with strip region is relatively simple. On this basis, an offset approximation curve algorithm based on interval Bézier curve is proposed, and the arrangement of the control points of the interval Bezier curve is changed from rectangle to regular polygon, and the circle is approximated gradually, so that the entire envelope area boundary is more close to the offset curve. The feasibility of the algorithm is verified by numerical examples.
Because of the complex structure of the offset curve, it is very difficult to deal with it effectively in industrial applications. The boundary structure of the interval Bézier curve with strip region is relatively simple. On this basis, an offset approximation curve algorithm based on interval Bézier curve is proposed, and the arrangement of the control points of the interval Bezier curve is changed from rectangle to regular polygon, and the circle is approximated gradually, so that the entire envelope area boundary is more close to the offset curve. The feasibility of the algorithm is verified by numerical examples.
引文
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[5] LEE I K,KIM M S,ELBER G.Planar curve offset based on circle approximation[J].Computer-Aided Design,1996,28(8):617-630.
[6] KLASS R.An offset spline approximation for plane cubic splines[J].Computer-Aided Design,1983,15(5):297-299.
[7] 金佳培,赵伟华,曾宇,等.G1约束下基于三次内点插值的曲线逼近方法[J].杭州电子科技大学学报(自然科学版),2017,37(5):38-43.
[8] 寿华好,王国瑾.区间Bézier曲线的边界[J].高校应用数学学报:A辑,1998,13(s1):37-44.
[2] AHN Y J,HOFFMANN C,KIM Y S.Curvature continuous offset approximation based on circle approximation using quadratic Bézier biarcs[J].Computer-Aided Design,2011,43(8):1011-1017.
[3] KHAN M A,CHEN Z C.Approximation of planar offset curves with globally bounded error for B-spline NC tool paths[J].International Journal of Production Research,2012,50(23):6811-6825.
[4] KIM Y J,LEE J,KIM M S,et al.Efficient offset trimming for planar rational curves using biarc trees[J].Computer Aided Geometric Design,2012,29(7):555-564.
[5] LEE I K,KIM M S,ELBER G.Planar curve offset based on circle approximation[J].Computer-Aided Design,1996,28(8):617-630.
[6] KLASS R.An offset spline approximation for plane cubic splines[J].Computer-Aided Design,1983,15(5):297-299.
[7] 金佳培,赵伟华,曾宇,等.G1约束下基于三次内点插值的曲线逼近方法[J].杭州电子科技大学学报(自然科学版),2017,37(5):38-43.
[8] 寿华好,王国瑾.区间Bézier曲线的边界[J].高校应用数学学报:A辑,1998,13(s1):37-44.