基于网格模型的磨损区域边界提取方法研究*

针对磨损零件的修复问题,提出了一种基于网格模型的磨损曲面边界线提取方法。根据磨损情况的不同,设置特征角的值,通过计算相邻三角面片法矢夹角,并与给定特征角的值相比较来提取磨损边界点,将磨损边界点插值成三次非均匀有理B样条(NURBS)曲线。给出了磨损边界线内磨损区域网格的删除方法,为后续实现磨损区域的曲面重构提供所需的几何信息与模型。应用实例表明,此方法用于磨损边界线的提取和磨损区域网格的删除是有效、可行的。     

复杂模型的三角参数曲面构造研究与实现

本文介绍由任意设置的散乱数据点给定的复杂曲面模型，按整体ＶＣ~１连续的几何特征构造非平面域Ｂｅｒｎｓｔｅｉｎ－Ｂｅｚｉｅｒ三角参数曲面的一种方法。可处理非凸边界、孔洞或多值的曲面造型和空间三角网格自动剖分，并提供一个偏差比率不大的简单判别式，有效地提高了算法效率。     

从点集重构曲面网络方法综述

本文主要对三维数据点重构曲面网格模型方法进行了综述。从三维数据点集重构曲面一般遵循以下三个步骤：1）重构曲面网格模型；2）网格简化；3）拟合曲面（通常为Bezier,NURBS),其中重构曲面网格为关键的一点，三维数据点集由三维数字化仪采集得到，不同的数字化设备，得到的三维数据点集可能会有差别，重构曲面网格的算法也不尽相同，本文介绍了几种对于不同数据形式，有代表性的重构曲面网格算法。     

Catmull-Rom几何样条曲面的应用

本文讨论了Ｃａｔｍｕｌ－Ｒｏｍ样条族中的几何连续的Ｃａｔｍｕｌ－Ｒｏｍ样条的构造，算法，性质及（Ｇ１，Ｋ＝１）Ｃａｔｍｕｌ－Ｒｏｍ样条曲面和（Ｇ２，Ｋ＝２）Ｃａｔｍｕｌ－Ｒｏｍ样条曲面的算法，并给出了应用实例。     

Gatmull—Rom几何样条曲面的应用

本文讨论了Ｃａｔｍｕｌｌ－Ｒｏｍ样条族中的几何连续的Ｃａｔｍｕｌｌ－Ｒｏｍ样条的构造，算法，性质及（Ｇ＾１，Ｋ＝１）Ｃａｔｍｕｌｌ－Ｒｏｍ样条曲面和（Ｇ＾２，Ｋ＝２）Ｃａｔｍｕｌｌ－Ｒｏｍ样条曲面的算法，并给出了应用实例。     

隐式曲面的光滑逼近

给出了隐式曲面的光滑逼近和保凸逼近曲面的构造,所构造的曲面是分段三次的,其光滑度高于Ｃ＾１。     

散乱数据点的三次多项式插值

用分片三次多项式曲面对散乱分布数据点插值的方法把给定区域划分成三角形网格，在每个三角形上构造一个三次多项式曲面片，整体的Ｃ１曲面由各三角形上的曲面片拼合而成．讨论了整体Ｃ１曲面需满足的条件组成的方程组的性质，并给出了求解方程组的方法．插值方法的多项式准确集包括所有三次和小于三次的多项式．     

Catmull-Rom几何样条在曲面设计中的应用

本文讨论了Ｃａｔｍｕｌｌ—Ｒｏｍ样条族中的几何连续的Ｃａｔｍｕｌｌ—Ｒｏｍ样条的构造、算法,性质及（Ｇ１,Ｋ＝１）Ｃａｔｍｕｌｌ－Ｒｏｍ样条曲面和（Ｇ２,Ｋ＝２）Ｃａｔｍｕｌｌ－Ｒｏｍ样条曲面的算法,并给出了应用实例。     

基于边折叠和质点-弹簧模型的网格简化优化算法

通过边折叠实现网格曲面简化，提出了保持曲面特征的边折叠基本规则，引入边折叠顺序控制因子λ，给出了折叠点坐标获取方法，简化过程中网格边长度趋于均匀．在曲面简化基础上，利用质点-弹簧模型优化网格形状．将网格顶点邻域参数化到二维域上，在质点-弹簧模型中引入约束弹簧，约束调整网格顶点，并逆映射到三维原始曲面上，局部优化网格顶点的相邻网格；调整曲面上所有网格顶点，在全局上优化网格形状．在曲面简化优化过程中，建立原始模型曲面和简化优化后曲面之间的双向映射关系；曲面的网格顶点始终在原始模型表面上滑动，并以双向Hausdorff距离衡量、控制曲面间的形状误差．应用实例表明：文中算法稳定、高效，适合于任意复杂的二维流形网格．     

形状模型在混合建模环境中的映射研究

混合建模技术是ＣＡＤ研究继承参数化特征建模技术之后的又一研究热点,线框,曲面和实体模型３种模型间的转换是混合建模技术的核心,本文介绍了：１）实体模型到线框和曲面模型的映射;（２）线框模型到实体模型的映射,３）曲面框型到实体模型的映射,为混合建模技术做了一些有益的探讨,并将模型映射算法成功地应用于ＩＧＥＳ和ＳＴＥＰ的前后置处理器的设计中,取得了满意的结果。     

Controllable C1 continuous blending of time-dependent parametric surfaces

This paper proposes the concept of blending time-dependent varying surfaces, and develops a new method to create a controllable C1 continuous blending surface between primary parametric surfaces whose position and shape change with time. We treat it as a boundary-valued problem defined by the mathematical model of a vectored dynamic fourth-order partial differential equation subjected to time-dependent C1 continuous blending boundary constraints. High performance blending surface generation is achieved through the development of an approximate analytical solution of the mathematical model. We investigate the accuracy and efficiency of the solution, study the effective shape control of the blending surfaces, and apply the obtained solution to tackle surface blending problems. The applications demonstrate that our proposed approach is very effective and efficient in dealing with controllable C1 continuous surface blending between time-dependent varying parametric surfaces.     

INTEGRAL SURFACES WITH VARIABLE INTEGRAL NEIGHBORS ON N-SIDED REGIONS

ＩＮＴＥＧＲＡＬＳＵＲＦＡＣＥＳＷＩＴＨＶＡＲＩＡＢＬＥＩＮＴＥＧＲＡＬＮＥＩＧＨＢＯＲＳＯＮＮ－ＳＩＤＥＤＲＥＧＩＯＮＳＨｕａｎｇＺｈｅｎｇｄｏｎｇ；ＺｈｏｕＪｉＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｐｒｅｓｅｎｔｓａｎｅｗａｐｐｒｏａｃｈｔｏｃｏｎ...     

医疗机器人穿刺针避障可达作业空间边界解析描述

提出了适用于机器人辅助腹腔介入治疗系统的手术规划方案,通过分析机器人手术流程,提出将穿刺针简化为球铰单关节操作臂的物理模型.基于机器入学中对操作臂避障可达作业空间边界解析描述的研究,利用含参数的非线性方程组对穿刺针的工作空间进行了解析描述.用3阶连续可导超二次曲面方程对腹腔内的肋骨及血管进行了描述.用数值迭代连续法求解出了穿刺针避障可达工作空间边界的l维解流形,并用Matlab进行了3维显示.成功求解出了腹腔内存在肋骨及血管等障碍物情况下穿刺针的工作空间边界.通过仿真实验可知,在穿刺针工作空间边界包络的范围内选取进针点,可保证穿刺针路径不与血管、肋骨等障碍物相碰.本文为医生规划手术方案提供了有效依据,解决了目前系统需要医生凭借自身手术经验来确定进针点的问题,提高了手术的效率和成功率.     

A Roadmap to Well Posed and Stable Problems in Computational Physics

All numerical calculations will fail to provide a reliable answer unless the continuous problem under consideration is well posed. Well-posedness depends in most cases only on the choice of boundary conditions. In this paper we will highlight this fact, and exemplify by discussing well-posedness of a prototype problem: the time-dependent compressible Navier–Stokes equations. We do not deal with discontinuous problems, smooth solutions with smooth and compatible data are considered. In particular, we will discuss how many boundary conditions are required, where to impose them and which form they should have in order to obtain a well posed problem. Once the boundary conditions are known, one issue remains; they can be imposed weakly or strongly. It is shown that the weak and strong boundary procedures produce similar continuous energy estimates. We conclude by relating the well-posedness results to energy-stability of a numerical approximation on summation-by-parts form. It is shown that the results obtained for weak boundary conditions in the well-posedness analysis lead directly to corresponding stability results for the discrete problem, if schemes on summation-by-parts form and weak boundary conditions are used. The analysis in this paper is general and can without difficulty be extended to any coupled system of partial differential equations posed as an initial boundary value problem coupled with a numerical method on summation-by parts form with weak boundary conditions. Our ambition in this paper is to give a general roadmap for how to construct a well posed continuous problem and a stable numerical approximation, not to give exact answers to specific problems.     

Generation of Discrete Bicubic G1 B-Spline Ship Hullform Surfaces from a Given Curve Network Using Virtual Iso-Parametric Curves

We propose a method that automatically generates discrete bicubic G1 continuous B-spline surfaces that interpolate the curve network of a ship hullform. First, the curves in the network are classified into two types: boundary curves and "reference curves". The boundary curves correspond to a set of rectangular (or triangular) topological type that can be represented with tensor-product (or degenerate) B-spline surface patches. Next, in the interior of the patches, surface fitting points and cross boundary derivatives are estimated from the reference curves by constructing "virtual" isoparametric curves. Finally, a discrete G1 continuous B-spline surface is generated by a surface fitting algorithm. Several smooth ship hullform surfaces generated from curve networks corresponding to actual ship hullforms demonstrate the quality of the method.     

Using support vector machines for the computationally efficient identification of acceptable design parameters in computer-aided engineering applications

This paper addresses the problem of estimating continuous boundaries between acceptable and unacceptable engineering design parameters in complex engineering applications. In particular, a procedure is proposed to reduce the computational cost of finding and representing the boundary. The proposed methodology combines a low-discrepancy sequence (Sobol) and a support vector machine (SVM) in an active learning procedure able to efficiently and accurately estimate the boundary surface. The paper describes the approach and methodological choices resulting in the desired level of boundary surface refinement and the new algorithm is applied to both two highly-nonlinear test functions and a real-world train stability design problem. It is expected that the new method will provide designers with a tool for the evaluation of the acceptability of designs, particularly for engineering systems whose behaviour can only be determined through complex simulations.     

Constructing multi-looped surfaces by loop joining

The objective of this research is to develop a surface joining method for constructing multi-looped surfaces. Based on this method, surfaces can be self-joined or inter-joined on loops to construct multi-looped surfaces. A loop is a continuous and closed boundary on a surface. By constructing one or several single-looped B-spline surfaces, multi-looped surfaces are constructed through loop joining of boundary curve segments. Loop joining is completed by merging the control points on the surface boundaries of B-spline surfaces. With the merging of data structures simultaneously, the consistencies of geometry and topology are kept in the surface model.The proposed method for constructing multi-looped surfaces has the advantages that it is conceptually explicit, simple for user understanding and easy for system programming, and there is no computation of surface/surface intersections involved, thus no numerical solutions for nonlinear equations are required.     

A Blend of Subdivision Surfaces and NURBS

In present paper, the contour deletion method is developed both to blend surfaces and to fill N-sided holes, which is used for subdividing the NURBS surface. First, according to the non-uniform Catmull-Clark subdivision principle, surfaces are blended. The non-uniform Catmull-Clark subdivision method is constructed, which build the surface through interpolating corner vertices and boundary curves. Then the contour deletion method is adapted to remove the controlling mesh boundary contour in the process of segmentation iteration. Last, N sided-hole is filled to generate a integral smooth continuous surface. This method not only guarantee that the blending surface and base surface patches have C2 continuity at the boundary, but also greatly improve the smoothness of the N-side hole filling surface. The results show that, this method simplifies the specific computer-implemented process, broads the scope of application of subdivision surfaces, and solves the incompatible problem between the subdivision surface and classical spline. The resulting surface has both advantages of the subdivision surface and classical spline, and also has better filling effect.     

A biomolecular electrostatics solver using Python,GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson–Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe  that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe  code is on the order of 1–2% error, when running on one gpu  card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu  cores. PyGBe  achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.     

基于Mumford-Shah模型和开样条曲线的边界检测

受Cremers方法启发, 本文提出了一种新的开边界自动检测算法, 如图像中海岸线和天际线的检测. 这一算法的设计主要是基于样条函数、曲线演化理论和Mumford-Shah图像分割泛函模型. 由于所要检测的目标为图像区域中开曲线, 在一般Mumford-Shah模型中引入了两个约束条件. 这就将开边界的检测问题转化为一般的曲线最小分割问题. 通过样条曲线控制点所满足的微分方程和约束条件, 曲线将演化至所要求的边界. 如果图像中有一条开曲线将图像分为两个明显不同质区域, 这一算法将能有效地自动检测出该边界曲线, 且不需要边界的梯度信息. 即使在图像中有大量噪声情况下, 该算法同样有效. 此外, 通过两条曲线演化方程, 该算法可推广到图像中带状区域的(如河流、道路等)自动检测.