基于拓扑相似性的等距参数曲面求交算法

等距曲面求交算法通常采用曲面求交算法反复迭代计算交线,没有考虑不同Offset距离等距曲面交线的相似性进行求交简化.提出了一种基于拓扑相似性的等距曲面求交优化算法.算法首先求取曲面的拓扑特征点,根据拓扑特征点分布图,确定交线环拓扑结构,在交线拓扑结构信息的指导下,确定初始点的搜索策略.采用提出的方法可以有效解决等距曲面的子环、奇点遗漏、分支跳跃、乱序跟踪和初始点求取问题,精确、鲁棒地计算出交线.     

隐式曲面／参数曲面的求交算法

本文介绍了一种实用有效的隐式曲面／参数曲面求交算法。算法主要分为两部分：特征初始点的求取和单调段的跟踪。解双变量多项式方程求解特征初始点。跟踪在三维空间进行，易于控制跟踪步长和离散交点对交线的逼近精度。算法不离散参数曲面，不漏交。     

平面向量场与曲率分析在曲面求交中的应用

在曲面求交算法中，初始跟踪点的确定和交线分支的跟踪是最关键的两个问题．本文总结了用平面向量场确定初始跟踪点的算法，给出了使用曲率分析精确计算跟踪方向，并估计跟踪步长的方法．应用平面向量场和曲率分析，作者实现了高效可靠的ＮＵＲＢＳ曲面求交算法．     

雕塑实体的精确求交算法

提出了一个雕塑实体布尔操作中的精确求交算法．为了确保算法的高效率、精确性和鲁棒性,采用了先确定拓扑、再跟踪的策略来进行曲线－曲面求交,以及层次求交和交线跟踪的方法,来保证裁剪曲面片分割和区域分类的一致性,从而克服实践中常见的退化情况．该算法已经在一个基于Ｗｉｎｄｏｗｓ／ＮＴ平台的雕塑实体造型器ＴｉｇｅｒＳｕｒｆ上实现,并通过大量造型实体实例的测试．     

平面向量与曲率分析在曲面求交中的应用

在曲面求交算法中，初始跟踪点的确定和交线分布的跟踪是最关键的两个问题，本文总结了用平面向量场确定初始跟踪点的算法，给出了使用曲率分析精确计算跟踪方向，并估计跟踪步长的方法，应用平面向量场和曲率分析，作者实现了高效可靠的ＮＵＲＢＳ曲面求交算法。     

参数曲面求交算法

参数曲面求交是雕塑产体造型中的关键问题，为了提高曲面／曲面求交方法的稳定性，准确性以及拓扑一致性，本文提出了一种改进方法，它是［Ｈｏｕｇｈｔｏｎ ａｔ ａｌ．＇８５］和［Ｂａｒｎｈｉｌｌ ａｔ ａｌ．＇９０］的思想的延伸，在本算法中，提出了获取曲面临近点的新方法和确定分析支点的可靠方法，改进确定追踪步长的方法。此外，它可以方例地计算出等距曲顶交线而无需等距逼近，通过上述改进本算法可处理分支点，切环     

一种改进的基于微分方程的曲面求交跟踪算法

参数曲面求交是计算机辅助几何设计领域中的关键技术之一。针对传统跟踪算法 中曲面求交的漏交和法向共线点处难于处理的问题,提出一种改进的基于微分方程的跟踪算法。 首先选择边界点和拐点作为跟踪的起点,解决了漏交问题。并采用基于交线微分形式的跟踪公 式计算后继交点,解决了法向共线点处难于处理的问题。最后利用牛顿迭代得到精确交点。该 算法不仅正确地跟踪到交线的每个分支,而且易于处理法向共线点处的跟踪,不遗漏关键点, 解决了传统跟踪法在法向共线点处交线不连续的问题。与传统跟踪法对比,其鲁棒性和稳定性 更强,精度更高且收敛略快,适用于求解任意参数曲面求交问题。     

任意曲面间跟踪求交的有效算法

提出了一种基于微分方程的跟踪算法，该算法采用基于交线微分形式的跟踪公式，解决了求交中难于处理的分支问题，和已有跟踪法相比，该算法稳定性更强，效率更高，而且适用于任意参数曲面及解析曲面。     

步长自适应追踪法曲面求交技术的研究

对具有多种曲面特征的实体进行建模,必须对相邻的单面片进行拼接。传统曲面求交技术有很多缺陷,例如在求交精度、求交速度上不能同时满足要求。对此提出步长可自适应的追踪法进行曲面求交,将五次非均匀B样条作为拟合曲线,在求交过程中将追踪步长值与交线末端曲率相关联,可以使步长根据具体环境实时变化。限定精度阈值[ε]为0.001?mm,将曲面求交试验在自主研发的逆向系统Surface Reverse中进行,分别采用传统追踪法和基于步长自适应的追踪法进行曲面求交,结果表明,追踪步长可自适应的追踪法求取交线的计算量少、用时较短,且交线精度可达到μm级。这种相交算法稳定、准确且速度较快。     

反求工程中的混合切片技术

提出一种基于平面与“点云”、平面与NURBS曲面求交计算的混合切片方法．该方法可以保证切片曲线在点云和曲面的连接处达到G^1连续，在此基础上的重构曲面既能保证与相邻曲面的连续性要求，又能满足对点云的逼近精度要求，对反求建模尤其是过渡特征的重建有着重要意义．文中详细探讨了平面与曲面求交和点云切片两个核心算法，并对基于模型特征的混合切片方案的选择原则以及不同方法进行了论述和比较．最后用实例证明该方法在反求建模中是切实可行的．     

Detection of loops and singularities of surface intersections

Two surface patches intersecting each other generally at a set of points (singularities), form open curves or closed loops. While open curves are easily located by following the boundary curves of the two patches, closed loops and singularities pose a robustness challenge since such points or loops can easily be missed by any subdivision or marching-based intersection algorithms, especially when the intersecting patches are flat and ill-positioned. This paper presents a topological method to detect the existence of closed loops or singularities when two flat surface patches intersect each other. The algorithm is based on an oriented distance function defined between two intersecting surfaces. The distance function is evaluated in a vector field to identify the existence of singular points of the distance function since these singular points indicate possible existence of closed intersection loops. The algorithm detects the existence rather than the absence of closed loops and singularities. This algorithm requires general C² parametric surfaces.     

A ground truth based vanishing point detection algorithm

A Bayesian probability-based vanishing point detection algorithm is presented which introduces the use of multiple features and training with ground truth data to determine vanishing point locations. The vanishing points of 352 images were manually identified to create ground truth data. Each intersection is assigned a probability of being coincident with a ground truth vanishing point, based upon conditional probabilities of a number of features. The results of this algorithm are demonstrated to be superior to the results of a similar algorithm where each intersection is considered to be of equal importance. The advantage of this algorithm is that multiple features derived from ground truth training are used to determine vanishing point location.     

Computing the intersection of two ruled surfaces by using a new algebraic approach

In this paper a new algorithm for computing the intersection of two rational ruled surfaces, given in parametric/parametric or implicit/parametric form, is presented. This problem can be considered as a quantifier elimination problem over the reals with an additional geometric flavor which is one of the central themes in V. Weispfenning research. After the implicitization of one of the surfaces, the intersection problem is reduced to finding the zero set of a bivariate equation which represents the parameter values of the intersection curve, as a subset of the other surface. The algorithm, which involves both symbolic and numerical computations, determines the topology of the intersection curve as an intermediate step and eliminates extraneous solutions that might arise in the implicitization process.     

Direct boolean intersection between acquired and designed geometry

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data).We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method.Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.     

Visualizing nonmanifold and singular implicit surfaces with point clouds

We use octree spatial subdivision to generate point clouds on complex nonmanifold implicit surfaces in order to visualize them. The new spatial subdivision scheme only uses point sampling and an interval exclusion test. The algorithm includes a test for pruning the resulting plotting nodes so that only points in the closest nodes to the surface are used in rendering. This algorithm results in improved image quality compared to the naive use of intervals or affine arithmetic when rendering implicit surfaces, particularly in regions of high curvature. We discuss and compare CPU and GPU versions of the algorithm. We can now render nonmanifold features such as rays, ray-like tubes, cusps, ridges, thin sections that are at arbitrary angles to the octree node edges, and singular points located within plot nodes, all without artifacts. Our previous algorithm could not render these without severe aliasing. The algorithm can render the self-intersection curves of implicit surfaces by exploiting the fact that surfaces are singular where they self-intersect. It can also render the intersection curves of two implicit surfaces. We present new image space and object space algorithms for rendering these intersection curves as contours on one of the surfaces. These algorithms are better at rendering high curvature contours than our previous algorithms. To demonstrate the robustness of the node pruning algorithm we render a number of complex implicit surfaces such as high order polynomial surfaces and Gaussian curvature surfaces. We also compare the algorithm with ray casting interms of speed and image quality. For the surfaces presented here, the point clouds can be computed in seconds to minutes on atypical Intel based PC. Once this is done, the surfaces can be rendered at much higher frame rates to allow some degree of interactive visualization.     

A reliable triangular mesh intersection algorithm and its application in geological modelling

We introduce a reliable intersection algorithm for manifold surface meshes. The proposed algorithm builds conforming surface meshes from a set of intersecting triangulated surfaces. This algorithm effectively handles all degenerate triangle–triangle intersection cases. The key idea of the algorithm is based on an extensive set of triangle–edge intersection cases, combined with an intersection curve tracking method. The intersection operations do not rely on global spatial search operations and no remeshing steps are needed. The intersection curves are introduced into each surface mesh using a unique curve imprinting algorithm. The imprinting algorithm naturally handles degenerate intersection cases of many surfaces at an edge or at a point. The algorithm produces a consistent mesh data structure for subsequent mesh optimization operations. The mesh intersection algorithm is used within a general framework for modelling and meshing of geological formations, which are essential for reliable mathematical modelling of oil reservoirs.     

基于最佳圆弧样条逼近的快速距离曲面计算

距离曲面是一种常用的隐式曲面,它在几何造型和计算机动画中具有重要的应用价值,但以往往在对距离曲面进行多边形化时速较慢,为了提高点到曲线最近距离计算的效率,提出了一种基于最佳圆弧样条逼近的快速线骨架距离曲面计算方法,该算法对于一条任意的二维NURBS曲线,在用户给定的误差范围内,先用最少量的圆弧样条来逼近给定的曲线,从而把点到NURBS曲线最近距离的计算问题转化为点到圆弧样条最近距离的计算问题,由于在对曲面进行多边形化时,需要大量的点到曲线最近距离的计算,而该处可以将点到圆弧样条最近距离很少的计算量来解析求得,故该算法效率很高,该实验表明,算法简单实用,具有很大的应用价值。     

Isosurfaces Over Simplicial Partitions of Multiresolution Grids

We provide a simple method that extracts an isosurface that is manifold and intersection‐free from a function over an arbitrary octree. Our method samples the function dual to minimal edges, faces, and cells, and we show how to position those samples to reconstruct sharp and thin features of the surface. Moreover, we describe an error metric designed to guide octree expansion such that flat regions of the function are tiled with fewer polygons than curved regions to create an adaptive polygonalization of the isosurface. We then show how to improve the quality of the triangulation by moving dual vertices to the isosurface and provide a topological test that guarantees we maintain the topology of the surface. While we describe our algorithm in terms of extracting surfaces from volumetric functions, we also show that our algorithm extends to generating manifold level sets of co‐dimension 1 of functions of arbitrary dimension.     

基于正交投影约束的点模型去噪

传统点云消噪算法会削弱曲面特征.为此,提出一种基于正交投影约束的点模型去噪算法.利用移动最小二乘曲面投影的思想,根据采样点与其在MLS曲面上正交投影点之间的关系构建移动距离权重函数,为防止模型收缩,给出曲率权重函数,通过双边滤波器确定滤波方向,结合移动距离权因子与曲率权因子确定采样点滤波距离.实验结果表明,该算法在消除点云噪声的同时,能保持点云高频结构特征,避免模型的收缩和顶点漂移.