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基于共形几何的点云模型上加工轨迹规划研究
Alternative TitleConformal Geometry Based Tool Path Planning for Point Clouds
邹强1,2
Department装备制造技术研究室
Thesis Advisor赵吉宾
ClassificationTG659
Keyword点云 加工轨迹 共形几何 拉普拉斯算子 调和分析
Call NumberTG659/Z94/2014
Pages74页
Degree Discipline机械电子工程
Degree Name硕士
2014-05-28
Degree Grantor中国科学院沈阳自动化研究所
Place of Conferral沈阳
Abstract随着几何测量设备在精度和成本等方面的成熟,点云作为一种数据格式和三维物体描述方式在计算机辅助设计与制造,计算几何和计算机图形学等领域中得到了广泛的应用。而基于点云的几何处理研究已经成为上述领域重要的研究方向之一。同时随着测量的引入,点云不管在正向工程还是在逆向工程中都扮演着重要的角色。本文基于共形几何提出了一种在点云上直接规划加工轨迹的方法。该方法免除了从点云到网格或者参数曲面的重建过程。这一过程不仅计算耗时、复杂,而且缺少鲁棒性。至今曲面重建问题仍然是一个尚未完全解决的问题。同时与网格相比,点云无需拓扑关系,这大大简化了三维模型的存储及表示;而与参数曲面相比,其无需过多的预处理,例如 B-样条要求插值点为张量型点阵,这大大简化了几何处理的流程。故而在点云上直接规划加工轨迹具有极大的理论和应用意义。点云这一表示方式虽然相较其它表示方式有诸多优势,但是目前针对点云的几何处理理论和技术非常有限,点云数据的一些固有属性,如无拓扑信息和无测地信息等等,使得多数传统的算法难以适用于该领域。本文从点云上的拉普拉斯算子出发实现了规划加工轨迹所必需的一系列算法,从而形成系统、完备的算法框架。由于这一算子无需拓扑信息,故而可以有效地直接在点云上实现这些算法。本文的主要研究内容有: (1) 共形几何及微分属性估计; (2) 点云的去噪,点云边界的提取以及点云的共形参数化; (3) 点云上的加工轨迹直接规划方法。其中点云上的共形几何及微分属性估计是后续研究内容的基础,是贯穿全文的研究方法和工具。本文的主要贡献分为两部分。第一,本文首次实现了点云上的等参型加工轨迹的直接规划。传统方法首先从点云拟合出参数曲面或者网格,然后直接利用已有的针对样条曲面的轨迹规划方法来生成加工路径。与之相比,本文所提出的方法直接从点云得到加工轨迹,因而效率更高,在实际加工中具有重要的应用意义。第二,本文首次将共形几何引入到加工轨迹的规划中,将各种类型的加工轨迹统一到同一框架下,同时利用共形几何的局部相似性和保角性大为简化了加工轨迹几何参数的计算,在计算机辅助设计和制造中具有重要的理论意义。
Other AbstractDue to the increasing availability of highly accurate and affordable 3D geometric acquisition devices, the point cloud, as a representation ( or a data structure ) of 3D objects, has been more and more appealing in applications such as computer aided design and manufacturing ( CAD/CAM ), computational geometry and computer graphics etc.. And the point-based geometric processing algorithms has been receiving a growing attention in these disciplines. With the introducing of measurement into CAD/CAM, the point cloud now plays a significant role in both forward and reverse engineering.This thesis introduces a direct tool path planning approach for point clouds in three dimensions via the conformal geometry, which is free from the procedure of reconstructing meshes or surfaces from point clouds. Due to the compute-intensiveness and the lack of robustness of the algorithms for such reconstructions, which still remains an open issue, there is a need for further research in the topic of direct tool path planning based on point clouds. Compared with other representations, e.g., meshes and B-splines, the lack of topological information simplifies the representation and storage of surfaces. Therefore, direct planning of tool-path for point clouds is of great significance. Yet, when it comes to geometric processing, things become rather tough. To date, there has been no clearly stated and consistent theory of point-based computational geometry that can be used to develop high level geometry processing algorithms, e.g., tool path planning. In contrast, the proposed methods in this thesis are mainly based on point-based Laplacian which makes the topology information unnecessary, furthermore makes high level point-based geometric processing algorithms, e.g., tool path planning, possible and satisfying.In this thesis, the conformal geometry and approximation of differential properties are first introduced, and then the methods of denoising and boundary extraction from point clouds are presented, following which the conformal parameterization of point clouds is described, and finally the direct tool path planning for point clouds are proposed. The first part, i.e., the conformal geometry and approximation of differential properties are fundamental for sequential sections. It's the core research basis in this thesis.The main contributions of this thesis include: proposing a novel approach for planning iso-parametric tool path from a point cloud. Conventional method generate tool path for point clouds by first reconstructing a spline surface or mesh and then employing the traditional spline-based methods. In contrast, the proposed method leap from point clouds to tool paths directly resulting in higher efficiency in machining. In addition, this is the first work trying to introduce the conformal geometric processing method which is a cutting-edge technique in computational geometry into tool path planning. A unified framework for generating tool path of different path patterns is presented with the free boundary property of the conformal geometry. And the angle-preserving and local similarity properties of the conformal geometry are exploited to simplify the formulas of computing the tool path's parameters, i.e., the normal curvature, forward step curvature and side step, which play a theoretically important role in tool path planning.
Language中文
Contribution Rank1
Document Type学位论文
Identifierhttp://ir.sia.cn/handle/173321/14782
Collection智能产线与系统研究室
Affiliation1.中国科学院沈阳自动化研究所
2.中国科学院大学
Recommended Citation
GB/T 7714
邹强. 基于共形几何的点云模型上加工轨迹规划研究[D]. 沈阳. 中国科学院沈阳自动化研究所,2014.
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