圆锥样条曲面拟合
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摘要
为了生成给定曲面模型的逼近圆锥样条曲面表示,提出一种圆锥样条曲面的逼近算法.对于给定的曲面模型,该算法首先计算一个逼近该目标模型的近似可展曲面;然后通过聚类可展曲面局部逼近圆锥的轴线对可展曲面进行区域分割;再通过求解带圆锥约束的曲面拟合问题,找到圆锥面的圆锥参数;最后通过将优化得到的圆锥面映射到精确圆锥样条曲面空间,构造精确圆锥样条曲面.实验结果表明,该算法能够将一个曲面形状转化为一个由圆锥面的光滑拼接表示,为曲面模型的加工制造带来了新的技术手段.
We propose an approach for computing a cone spline surface fitting to a given model. For a given surface, our algorithm first calculates an initial developable surface to approximate it, which is then segmented into a set of regions by clustering on axis lines of local fitting cones to the developable surface. Shape parameters of conical patches are determined by solving a surface fitting problem with geometric constraints of cones. A precise cone spline surface is constructed by mapping the optimized conical patches to the space of cone spline surfaces. The experimental results demonstrate the capability of the proposed method to convert a surface into a smooth composition of conical patches which facilities the manufacturing of surface models.
We propose an approach for computing a cone spline surface fitting to a given model. For a given surface, our algorithm first calculates an initial developable surface to approximate it, which is then segmented into a set of regions by clustering on axis lines of local fitting cones to the developable surface. Shape parameters of conical patches are determined by solving a surface fitting problem with geometric constraints of cones. A precise cone spline surface is constructed by mapping the optimized conical patches to the space of cone spline surfaces. The experimental results demonstrate the capability of the proposed method to convert a surface into a smooth composition of conical patches which facilities the manufacturing of surface models.
引文
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[9]Maekawa T,Chalfant J S.Design and tessellation of B-spline developable surfaces[J].Journal of Mechanical Design,1998,120(3):453-461
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[11]Pottmann H,Wallner J.Approximation algorithms for developable surfaces[J].Computer Aided Geometric Design,1999,16(6):539-556
[12]Tang C C,Bo P B,Wallner J,et al.Interactive design of developable surfaces[J].ACM Transactions on Graphics,2016,35(2):Article No.12
[13]Zheng Yujian,Bo Pengbo.Quasi-developable surface construction based on boundary curves and its application in ship hull design[J].Journal of Computer Aided Design&Computer Graphics,2018,30(7):1243-1250(in Chinese)(郑玉健,伯彭波.基于边界曲线的拟可展曲面构造方法及在船体造型中的应用[J].计算机辅助设计与图形学学报,2018,30(7):1243-1250)
[14]Fernández-Jambrina L.Bézier developable surfaces[J].Computer Aided Geometric Design,2017,55:15-28
[15]Goldapp M.Approximation of circular arcs by cubic polynomials[J].Computer Aided Geometric Design,1991,8(3):227-238
[16]Pottmann H,Schifner A,Bo P B,et al.Freeform surfaces from single curved panels[J].ACM Transactions on Graphics,2008,27(3):Article No.76
[2]Andrews J,Séquin C H.Type-constrained direct fitting of quadric surfaces[J].Computer-Aided Design and Applications,2014,11(1):107-119
[3]Andrews J,Séquin C H.Generalized,basis-independent kinematic surface fitting[J].Computer-Aided Design,2013,45(3):615-620
[4]Leopoldseder S,Pottmann H.Approximation of developable surfaces with cone spline surfaces[J].Computer-Aided Design,1998,30(7):571-582
[5]Yang X N,Yang W P.Cone spline approximation via fat conic spline fitting[J].Computer-Aided Design,2006,38(6):703-712
[6]Aumann G.Interpolation with developable Bézier patches[J].Computer Aided Geometric Design,1991,8(5):409-420
[7]Aumann G.A simple algorithm for designing developable Bé-zier surface[J].Computer Aided Ceometric Design,2003,20(8/9):601-619
[8]Aumann G.Degree elevation and developable Bézier surfaces[J].Computer Aided Geometric Design,2004,21(7):661-670
[9]Maekawa T,Chalfant J S.Design and tessellation of B-spline developable surfaces[J].Journal of Mechanical Design,1998,120(3):453-461
[10]Bodduluri R M C,Ravani B.Design of developable surfaces using duality between plane and point geometries[J].Computer-Aided Design,1993,25(10):621-632
[11]Pottmann H,Wallner J.Approximation algorithms for developable surfaces[J].Computer Aided Geometric Design,1999,16(6):539-556
[12]Tang C C,Bo P B,Wallner J,et al.Interactive design of developable surfaces[J].ACM Transactions on Graphics,2016,35(2):Article No.12
[13]Zheng Yujian,Bo Pengbo.Quasi-developable surface construction based on boundary curves and its application in ship hull design[J].Journal of Computer Aided Design&Computer Graphics,2018,30(7):1243-1250(in Chinese)(郑玉健,伯彭波.基于边界曲线的拟可展曲面构造方法及在船体造型中的应用[J].计算机辅助设计与图形学学报,2018,30(7):1243-1250)
[14]Fernández-Jambrina L.Bézier developable surfaces[J].Computer Aided Geometric Design,2017,55:15-28
[15]Goldapp M.Approximation of circular arcs by cubic polynomials[J].Computer Aided Geometric Design,1991,8(3):227-238
[16]Pottmann H,Schifner A,Bo P B,et al.Freeform surfaces from single curved panels[J].ACM Transactions on Graphics,2008,27(3):Article No.76