拓扑优化结果的多视图参数化几何重构方法
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摘要
针对拓扑优化结果表示为单元密度的等值面存在复杂的锯齿状边缘,不便后续参数化几何建模及零件加工的问题,提出了一种基于多方向视图的拓扑优化结果自动参数化重构方法。首先将单元密度等值面转化为均匀的点云;然后将多边形近似的边扩展为直线和圆弧,用扩展多边形近似重构点云在多个投影平面(包括三视图和局部方向视图)上的参数化二维轮廓,并构造选择和评价函数来选择最佳二维轮廓,平滑连接邻边;之后将二维轮廓沿投影方向(笛卡尔坐标或自然坐标)拉伸得到实体;最后通过坐标变换将构造实体变换到全局坐标系下,再通过布尔运算得到参数化三维实体模型。
The optimal topologic results are usually expressed as the isosurface in unit density. The complex zigzag edge of these isosurfaces are not suitable for the subsequent parametric modeling of the geometry or the manufacturing of the components. In this work, an automatic parametric reconstruction method based on multi-view is proposed.Firstly,the isosurfaces have been converted into homogeneous point cloud. Then, the parametric 2 D contour of point cloud on multiple projection planes(including three views and local direction views) is reconstructed by extending the polygons into straight line and circular arc. The best 2 D contour's adjacent edges are connected smoothly, which is selected by applying evaluating function. Thus, the entity can be constructed by extruding the 2 D contour along the projection direction(descartes or natural coordinates). The multi entity are then converted to global coordinates based on Boolean operations, thereby obtaining the 3 D parametric entity.
The optimal topologic results are usually expressed as the isosurface in unit density. The complex zigzag edge of these isosurfaces are not suitable for the subsequent parametric modeling of the geometry or the manufacturing of the components. In this work, an automatic parametric reconstruction method based on multi-view is proposed.Firstly,the isosurfaces have been converted into homogeneous point cloud. Then, the parametric 2 D contour of point cloud on multiple projection planes(including three views and local direction views) is reconstructed by extending the polygons into straight line and circular arc. The best 2 D contour's adjacent edges are connected smoothly, which is selected by applying evaluating function. Thus, the entity can be constructed by extruding the 2 D contour along the projection direction(descartes or natural coordinates). The multi entity are then converted to global coordinates based on Boolean operations, thereby obtaining the 3 D parametric entity.
引文
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[4] Yi G, Kim N H. Identifying Boundaries of Topology Optimization Results Using Basic Parametric Features[J]. Structural and Multidisciplinary Optimization, 2017,55(5):1641-1654.
[5] Lin C Y, Chao L S. Automated Image Interpretation for Integrated Topology and Shape Optimization[J]. Structural & Multidisciplinary Optimization, 2000,20(2):125-137.
[6] 覃琨,方宗德,卞翔,等.基于MATLAB的机械零件拓扑优化结果几何重构研究[J].机械科学与技术,2013,32(11):1620-1623.
[7] 陈思,陈浩,李寿涛.一种工业CT点云数据的NURBS曲面重构算法[J].CT理论与应用研究,2011,20(1):11-20.
[8] Tang P S, Chang K H. Integration of Topology and Shape Optimization for Design of Structural Components[J]. Structural & Multidisciplinary Optimization, 2001,22(1):65-82.
[9] William R B. Generating CAD Parametric Features Based on Topology Optimization Results[D]. Provo: Brigham Young University, 2008.
[10] Shane H Larsen. Recognizing Parametric Geometry from Topology Optimization Results[D]. Provo: Brigham Young University, 2008.
[11] Foley J D, Van Dam A, Feiner S K, et al. Computer Graphics: Principles and Practice[M].Boston: Addison-Wesley Publishing Company, 2008.
[12] 李鹏程,邢帅,徐青,等.关键点检测的复杂建筑物模型自动重建[J].遥感学报,2014,18(6):1237-1246.
[13] 张鸿宾,郭建军.遗传算法在曲线多边形近似中的应用[J].计算机学报,1999,22(10):1100-1104.
[2] Field D A. Laplacian Smoothing and Delaunay Triangulations[J]. Communications in Applied Numerical Methods, 1988,4(6):709-712.
[3] Koguchi A, Kikuchi N. A Surface Reconstruction Algorithm for Topology Optimization[J]. Engineering with Computers, 2006,22(1):1-10.
[4] Yi G, Kim N H. Identifying Boundaries of Topology Optimization Results Using Basic Parametric Features[J]. Structural and Multidisciplinary Optimization, 2017,55(5):1641-1654.
[5] Lin C Y, Chao L S. Automated Image Interpretation for Integrated Topology and Shape Optimization[J]. Structural & Multidisciplinary Optimization, 2000,20(2):125-137.
[6] 覃琨,方宗德,卞翔,等.基于MATLAB的机械零件拓扑优化结果几何重构研究[J].机械科学与技术,2013,32(11):1620-1623.
[7] 陈思,陈浩,李寿涛.一种工业CT点云数据的NURBS曲面重构算法[J].CT理论与应用研究,2011,20(1):11-20.
[8] Tang P S, Chang K H. Integration of Topology and Shape Optimization for Design of Structural Components[J]. Structural & Multidisciplinary Optimization, 2001,22(1):65-82.
[9] William R B. Generating CAD Parametric Features Based on Topology Optimization Results[D]. Provo: Brigham Young University, 2008.
[10] Shane H Larsen. Recognizing Parametric Geometry from Topology Optimization Results[D]. Provo: Brigham Young University, 2008.
[11] Foley J D, Van Dam A, Feiner S K, et al. Computer Graphics: Principles and Practice[M].Boston: Addison-Wesley Publishing Company, 2008.
[12] 李鹏程,邢帅,徐青,等.关键点检测的复杂建筑物模型自动重建[J].遥感学报,2014,18(6):1237-1246.
[13] 张鸿宾,郭建军.遗传算法在曲线多边形近似中的应用[J].计算机学报,1999,22(10):1100-1104.