自由曲面可控性网格划分理论及量化综合评价研究

Free-form grid structure, with its strong visual impression, has attracted attention from decision makers and architects. However, it is still urgent and crucial to research on the methodology to generate controllable grids over a curved surface and followed naturally is on the development of comprehensive and quantitative evaluation index on the grid quality. Therefore, this project aims at the research on complex free-form curved surface at the first beginning, where modified and improved algorithms in the field of GIS will be adapted to provide numerical solution to the surface partitions, exploiting the use of curved partition lines and closed internal boundaries. Logical expressions on the relationships among points, lines and a curved surfaces as a system will be set up, which are thereby used for subdividing the surface into patched regions or areas. Initial triangular grids in a plane will be generated by minimizing the variation of rod lengths between a curved surface and a plane, a mesh on a plane without gap and overlap will be achieved by utilizing mapping and iteration algorithm, this will reveal the principle of curved surface during the unfolding process. On the basis of the formed unfolded surface, a systematic theory to generate controllable and adjustable grids will be established. This theory will be based on a series of sub-divided procedures or techniques such as guideline definition, dot matrix arrangement, rod length controlling function, point or line position constraints, initial guideline direction adjustment, simulated truss iterative optimization and interpolation algorithm for curved line tuning. Finally, the similarity of the generated curved surface, the structural robustness of the curved surface, grid fluency and grid uniformity will be investigated in order to obtain a comprehensive and quantitative evaluation on the free-form grid quality. It is expected that the outcomes from this research will significantly benefit the grid generation methodology and quantitative and comprehensive evaluation.

自由曲面网格结构以其强力的视觉冲击力，深受城市建设决策者和建筑师的青睐。而如何实现可控性网格划分，开展量化综合指标评价，仍是该类结构亟待解决的关键科学问题。据此，本课题针对复杂自由曲面，通过强化GIS领域中的算法功能，探索分区边界为曲线及闭合情形的处置途径，建立点、线、面间的逻辑表达，实现曲面的分区分块；以曲面和平面对应边长相等为优化目标，形成平面三角化初始网格，实施映射迭代，揭示无裂缝、无重叠的曲面展开本质；在曲面展开的基础上，通过设置引导线、布置均匀点阵、控制网格边长函数、锁定点线约束位置、调控初始网格走向、模拟桁架迭代优化、运用插值算法调整曲线等技术策略，为任意边界和形状的自由曲面，创建可控可调的网格划分理论；研究曲面形状的相似性、结构的鲁棒性、网格的流畅性及规整性，实现自由曲面网格结构的量化综合指标评价。通过本课题的研究，将极大地提升自由曲面网格划分及量化综合评价的技术水平。

自由曲面网格结构以其强力的视觉冲击力，深受城市建设决策者和建筑师的青睐。而如何实现可控性网格划分，开展量化综合指标评价，仍是该类结构亟待解决的关键科学问题，本项目对自由曲面网格划分及综合量化评价进行了系统研究。(1).针对条件不良的曲线、曲面，提出了曲线曲面调整等方法，改善曲线、曲面的几何性能，使之适应网格划分算法。(2).针对形状较为复杂的曲面，提出曲面分片及重构方法。(3).针对复杂参数曲面，基于半自动化半规整网格划分思想，提出基于细分的方法。(4).基于映射技术和拟桁架法，提出了一种自由曲面的三角形网格生成方法—映射拟桁架法。(5). 基于气泡运动模拟和Delaunay三角剖分，提出了另一种三角形网格生成方法—空间气泡法。(6). 为了更好地适应边界线，提出了基于映射法和双向等分技术的网格划分方法—映射等分法。(7) 以生成均匀网格的空间气泡法为基础，引入改进网格规则性为目标的拓扑优化算法，再结合弹簧网模拟的网格松弛方法，提出了一套三角形网格生成及优化的系统。该系统还引入了一个定量评价网格流畅性的新指标。最终由该系统得到兼顾均匀性、流畅性与规整性的网格。(8)提出基于曲面拟合的思想，将复杂自由曲面拟合成一个曲面，并利用映射法和测地线法进行网格划分，最后进行网格优化。基于NURBS的线面求交和基于NURBS的面面求交两种方法，获得复杂自由曲面的N×M点云，利用向心参数化方法获得节点矢量U、V后，将N×M点云作为控制点拟合NURBS曲面，然后根据原曲面情况裁剪拟合曲面。在裁剪后的拟合NURBS曲面基础上，运用映射法和测地线法划分网格。(9).针对特别复杂的多重参数曲面，提出基于离散的方法。首先将多重参数曲面表示方式离散为单个多面体曲面表示。然后提出基于细分的算法框架，得到满足几何性能需求的网格。且能够处理任意边界类型（裁剪、孔洞等）与任意曲面形态（环状、封闭等）。通过本课题的研究，极大地提升了自由曲面网格划分及量化评价水平。

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