基于法矢控制的B样条曲面逼近的PIA方法

提出了一种基于法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)算法。一方面该方法将离散数据点的切失、曲率、法矢等几何特征充分应用到离散数据点的逼近问题上,利用数据点两个方向的切矢构造出数据点的法矢约束来控制逼近曲面形状,相比于无法矢控制的 B 样条曲面逼近的渐进迭代逼近(PIA)方法,逼近曲面更光顺,可获得更好的逼近效果。另一方面由于该算法选取主特征点作为控制顶点,所以允许在曲面拟合中控制顶点的数目小于数据点的数目。而且PIA算法的每次迭代过程中的各个步骤都是独立的,很容易被应用到并行计算上,可提高计算效率。本文还给出了一些实例来验证该算法的有效性。     

基于散乱点的增量式曲面逼近

针对用接触式三维点数据获取设备快速输入的物体表面散乱点云数据，提出了增量式B样条曲面快速逼近算法．该算法首先要获得重建曲面的边界数据，以生成初始曲面；然后对输入的散乱数据点云用投影法计算出其参数值；再用模板子块在曲面上移动，反算出模块子块的控制点；最后更新整个曲面的相应控制点，实现边输入、边逼近，即增量式曲面逼近．在输入过程中可看到曲面逐渐逼近目标曲面的过程，在误差大的区域可以增加输入点来改善曲面逼近效果．对于复杂曲面进行多次投影计算散乱数据点参数及曲面逼近，可达到良好效果．     

散乱数据点集的三角划分算法研究

在对当前的三角网格划分方法进行比较分析后，提出了一种散乱数据点集的3D三角网格划分算法，该算法不需如同二维划分方法一样要对散乱点集对应的自由曲面分片投影，并可自然处理含有凹边界及孔域的曲面数据点集，利用网格扩展、边界环分裂和边界环封闭，根据曲面的变化逐层推进生成三角网格，使算法能方便地处理非封闭曲面、空间剪裁曲面、封闭曲面、空间多连通曲面等各种曲面的散乱数据。     

从点集重构曲面网格方法综述

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步;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。     

一种通用的trimmed曲面三角化算法

本文提出一种既可用于进行trimmed曲面求交,也可用于进行trimmed曲面显示的快速trimmed曲面三角化算法。算法主要基于本文首次提出的对trimmed曲面的空间及参数trimmed边界进行相关离散的思想和入边、出边、跨边三角形等新概念。算法已经成功地应用于雕塑立体造型系统MESSAGE中,进行trimmed曲面的求交与显示。     

一个利用法矢的散乱点三角剖分算法

曲面上散乱点的三角剖分在曲面重建中发挥着重要作用，借助于曲面上的法矢信息和三维Delaunay三角剖分算法，该文给出了一种新的散乱点三角剖分算法，输入一组散乱点以及所在曲面S在这些散乱点处的一致定向的法矢信息，该算法将产生一张插值散乱点的三角网格曲面M，并且曲面M可以近似地看成是曲面S的三角剖分，算法的主要步骤分为两步：首先通过曲面S的一致定向的法矢信息，在曲面S的同一侧添加辅助点，利用这些辅助点来剔除Delaunay三角剖分中产生的不需要的三角片；然后将剩余的三角片连接成一张完整的网格曲面，与基于中轴的三角剖分算法相比，该文算法需要更少和更简单的计算，与局部三角剖分算法相比，该文算法可以更有效地避免重建后的曲面产生自交，该文的算法可用于任意拓扑的光滑曲面重建。     

一种NURBS曲面拟合精度的量化评测算法

曲面重构是逆向工程中的核心技术之一,由于NURBS曲面在光顺性和局部可编辑等方面所具有的优点,使其成为点云数据自由曲面重构的常见形式。目前对NURBS曲面重构技术的研究上取得了一些成果,但各方法在拟合精度和效果上各有参差,因此有必要对NURBS曲面拟合精度评价算法进行研究。在采用NURBS实现曲面拟合的基础上,对拟合精度的量化指标进行研究,设计了一种基于区域划分的搜索迭代算法,可快速地计算得到原始点云与NURBS曲面的偏差。     

基于曲面精确表示的距离极值点的计算及在刀具干涉检测中的应用

针对基于曲面精确表示的刚体碰撞检测中裁剪曲面距离极值点的求解问题,提出了利用平面向量场估计初始曲面距离极值点的方法,避免了曲面过度细分,讨论了距离极值点满足的微分几何条件,给出了解析曲面/参数曲面、参数曲面/参数曲面、点/参数曲面和曲线/参数曲面的距离极值点迭代算法。实例验证分析了该算法的高效性和可靠性。     

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。     

结构光视觉三维点云逐层三角网格化算法

针对结构光视觉恢复的大规模三维点云的可投影特点,提出一种基于投影网格的底边驱动逐层网格化曲面重建算法。该算法首先将点云投影到一个二维平面上;然后基于点云投影区域建立规则投影网格,并将投影点映射到规则二维投影网格上,建立二维网格点与三维点云间的映射关系;接着对投影网格进行底边驱动的逐层网格化,建立二维三角网格;最后根据二维投影点与三维点的对应关系及二维三角网格拓扑关系获得最终的三维网格曲面。实验结果表明,算法曲面重建速度快,可较好地保持曲面细节特征。     

Self-intersections of offsets of quadratic surfaces: Part II, implicit surfaces

The paper investigates self-intersections of offsets of implicit quadratic surfaces. The quadratic surfaces are the simplest curved objects, referred to as quadrics, and are widely used in mechanical design. In an earlier paper, we have investigated the self-intersections of offsets of explicit quadratic surfaces, such as elliptic paraboloid, hyperbolic paraboloid and parabolic cylinder, since not only are they used in mechanical design, but also any regular surface can be locally approximated by such explicit quadratic surfaces. In this paper, we investigate the rest of the quadrics whose offsets may degenerate, i.e. the implicit quadratic-surfaces (ellipsoid, hyperboloid, elliptic cone, elliptic cylinder and hyperbolic cylinder). We found that self-intersection curves of offsets of all the implicit quadratic surfaces are planar implicit conics and their corresponding curve on the progenitor surface can be expressed as the intersection curve between an ellipsoid, whose semi-axes are proportional to the offset distance, and the implicit quadratic surfaces themselves.     

基于两视图的曲面重建方法

提出了一种利用曲面物体的两幅图像进行曲面重建的方法。从物体的正面和侧面拍摄两幅图像，而后利用用户交互获得这两幅图像中的侧影轮廓线。并通过最小化以这些侧影轮廓线作为约束二次目标函数，重建出最光滑的三维曲面。另外，在二次目标函数中增加一个系数，实现了曲面折痕。利用真实图像进行实验，验证了该方法的可行性和正确性。     

Meshing volumes with curved boundaries

This paper introduces a three-dimensional mesh generation algorithm for domains whose boundaries are curved surfaces, possibly with sharp features. The algorithm combines a Delaunay-based surface mesher with a Ruppert-like volume mesher, resulting in a greedy scheme to sample the interior and the boundary of the domain simultaneously. The algorithm constructs provably good meshes, it gives control on the size of the mesh elements through a user-defined sizing field, and it guarantees the accuracy of the approximation of the domain boundary. A notable feature is that the domain boundary has to be known only through an oracle that can tell whether a given point lies inside the object and whether a given line segment intersects the boundary. This makes the algorithm generic enough to be applied to domains with a wide variety of boundary types, such as implicit surfaces, polyhedra, level-sets in 3D gray-scaled images, or point-set surfaces.     

基于体数据的三维地质属性体建模

文章着重研究采用空间曲面构造三维地质属性体模型。首先,将空间曲面映射到三维体数据中,使用这些具有地质涵义的曲面对体数据进行空间划分,并在体数据中建立三维地质属性体模型。该文提出了一种适合于大数据量的标量体数据表示结构,并基于该结构,提出了一种基于种子填充算法的三维空间区域划分算法。     

Automatic mesh generation scheme for a two- or three-dimensional triangular curved surface

Two different methods of automatic mesh generation—the area system and the isoparametric coordinate system—both using quadratic shape function, have been introduced to generate meshes for curved triangular surfaces. Depending on geometrical and material variations, part of the region to be discretized is manually divided into a number of triangular zones. An algorithm is given to generate meshes of triangular elements with three or six nodes automatically using quadratic shape function and area-coordinate system for these zones. Any node number can be assigned to the vertices of a triangular zone. Different zones will be tied together automatically by using a merge algorithm. The application of the volume-coordinate system and quadratic shape function in generating solid elements for triangular prisms will also be discussed.     

A hidden line elimination method for curved surfaces

An algorithm for displaying curved surfaces with hidden lines eliminated is described. The surfaces are displayed as rectangular grids of straight segments which approximate those surfaces. The algorith is essentially one of brute force. However, it divides the screen space into small 3D boxes to reduce the number of subpatches to be checked to determine the visibility of each grid point. It turned out that this division process made this algorithm about 10 times faster than the algorithm which had no use of the division.Expanding the algorithm for making contour drawings is very easy. Some methods for drawing silhouette lines are considered.     

球面模型的逼近与数据压缩及推广

提出了一种三维物体表面的逼近表示与数据压缩方法.该方法可以在不增加表示物体表面的数据量(例如面片数量)的情况下,使逼近误差降低约1/2;在逼近误差不变的情况下,使表示物体表面的数据量大幅下降.提出了用与最基本的三维物体--球体表面相交的面片来表示球面的方法,将该方法扩展到了一般曲面.理论分析与实验数据表明,新算法与传统方法相比,其数据压缩比约为35%.该研究在虚拟现实技术和三维模型的数据压缩及传输等领域有较重要的学术及应用价值.     

A parallel algorithm for improving the maximal property of Poisson disk sampling

This paper presents a simple yet effective algorithm to improve an arbitrary Poisson disk sampling to reach the maximal property, i.e., no more Poisson disk can be inserted. Taking a non-maximal Poisson disk sampling as input, our algorithm efficiently detects the regions allowing additional samples and then generates Poisson disks in these regions. The key idea is to convert the complicated plane or space searching problem into a simple searching on circles or spheres, which is one dimensional lower than the original sampling domain. Our algorithm is memory efficient and flexible, which generates maximal Poisson disk sampling in an arbitrary 2D polygon or 3D polyhedron. Moreover, our parallel algorithm can be extended from the Euclidean space to curved surfaces in an intrinsic manner. Thanks to its parallel structure, our method can be implemented easily on modern graphics hardware. We have observed significance performance improvement compared to the existing techniques.     

A Rendering Equation for Specular Transfers and Its Integration into Global Illumination

In this paper, we present a rigorous theoretical formulation of the fundamental problem—indirect illumination from area sources via curved ideal specular surfaces. Intensity and area factors are introduced to clarify this problem and to rectify the radiance from these specular surfaces. They take surface geometry, such as Gaussian curvature, into account. Based on this formulation, an algorithm for integrating ideal specular transfers into global illumination is also presented. This algorithm can deal with curved specular reflectors and transmitters. An implementation is described based on wavefront tracing and progressive radiosity. Sample images generated by this method are presented.     

3D点云形状特征的二维主流形描述

首先,对空间分布不均匀且无序的三维点云构造其二维主流形,并以与球面同胚的封闭曲面网格形式给出其二维主流形的二次优化逼近,以主流形网格有序均匀的结点分布表示三维点云空间分布无序且不均匀的形状特征,降低了三维形状描述的难度;然后,以基本几何变换作为快速粗对齐、以迭代最近法向点(ICNP)方法作为精准对齐,确定两个主曲面网格之间最佳刚性变换,ICNP方法在寻找最近点时考虑法向夹角,利用了更多的几何信息,实现快速精准的刚性对齐,兼顾计算精度和速度;最后,以对齐误差作为两个3D点云之间形状差异测度.实验结果表明:所提出的基于主流形二次曲面网格优化逼近的三维点云模型形状描述方法对三维点云的分辨率和噪声等干扰因素具有较高的健壮性,可以用于三维检索的形状描述.