具有局部保形性的P曲线
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摘要
P曲线是由基函数和控制多边形生成的一类C~∞连续的端点插值型曲线。由于已有基函数设计自由度低,局部不保形,本文引入椭圆域多边形和菱形域多边形作为P曲线的新基函数,提高了它的全局保形性并且使其局部保形和局部可控。
P curve is a class of C~(∞ )continuous endpoints interpolation curves generated by basis functions and control polygons. Due to the low operability and the local non-conformality of the existing basis functions, the elliptic domain polygon and the rhombic domain polygon are introduced to P curve as new basis functions, improving the conformality of P curve globally and making it conformal locally and controllable partially.
P curve is a class of C~(∞ )continuous endpoints interpolation curves generated by basis functions and control polygons. Due to the low operability and the local non-conformality of the existing basis functions, the elliptic domain polygon and the rhombic domain polygon are introduced to P curve as new basis functions, improving the conformality of P curve globally and making it conformal locally and controllable partially.
引文
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[4] KOVáCS I, VáRADY T. P-curves and surfaces: Parametric design with global fullness control[J]. Computer-Aided Design, 2017,90(1):113-122
[5] MEYER M, BARR A, LEE H, et al. Generalized barycentric coordinates on irregular polygons[J]. Journal of Graphics Tools, 2002, 7(1):13-22.
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[2] 李军成, 刘成志. 带两个形状参数的同次Bézier曲线[J]. 计算数学, 2017, 39(2):115-128.
[3] BARSKY B A, BEATTY J C. Local control of bias and tension in beta-splines[C]// Conference on Computer Graphics and Interactive Techniques. ACM, 1983:193-218.
[4] KOVáCS I, VáRADY T. P-curves and surfaces: Parametric design with global fullness control[J]. Computer-Aided Design, 2017,90(1):113-122
[5] MEYER M, BARR A, LEE H, et al. Generalized barycentric coordinates on irregular polygons[J]. Journal of Graphics Tools, 2002, 7(1):13-22.
[6] HORMANN K, FLOATER M S. Mean value coordinates for arbitrary planar polygons[J]. ACM Transactions on Graphics(TOG), 2006, 25(4):1424-1441.