基于凸四边形曲率的三角剖分优化准则

由3D散乱点集构造三角剖分在曲面造型中有着十分重要的作用，而剖分所采用的优化准则决定了最终的剖分结构。从曲率这一曲面内在特性入手，提出了一种空间凸四边形的曲率估计算法，据此还提出了一种新的基于该曲率的优化准则，即一种曲率最小优化准则，并通过一个例子详细地将这一新的优化准则与几种常用的优化准则做了比较，实验结果的分析表明，运用该优化准则得到的三角剖分具有较好的几何特性，在曲面重构和曲面设计等方面有很好的实用价值。     

一种快速三维散乱点云的三角剖分算法

改进了一种三维散乱点云三角剖分算法。三角剖分是点云数据曲面重构的主要算法之一,但针对三维散乱点云的三角剖分存在剖分效率不高,剖分得到的三角曲面形状无法控制,细节特征表现不足的问题。提出了基于空间栅格划分的三角剖分算法,并提出了一个新的评价函数,以控制三角网格曲面的生长。实验证明,改进后的算法极大的提高了剖分效率,而且能保证最终生成的三角网格曲面平滑而保有丰富的细节特征,适用于在虚拟现实、曲面重构等领域推广使用。     

基于曲面局平特性的散乱数据拓扑重建算法

提出了一种基于曲面局平特性的,以散乱点集及其密度指标作为输入,以三角形分片线性曲面作为输出的拓扑重建算法.算法利用曲面的局平特性,从散乱点集三维Delaunay三角剖分的邻域结构中完成每个样点周围的局部拓扑重建,并从局部重建的并集中删除不相容的三角形,最终得到一个二维流形拓扑曲面集作为重建结果.该算法适应于包括单侧曲面在内的任意不自交的拓扑曲面集,并且重建结果是相对优化的曲面三角形剖分,可以应用于科学计算可视化、雕塑曲面造型和反求工程等领域.     

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。     

针对密集点云的快速曲面重建算法

为了能够快速地从高密度散乱点云生成三角形网格曲面,提出一种针对散乱点云的曲面重建算法.首先通过逐层外扩建立原始点云的近似网格曲面,然后对近似网格曲面进行二次剖分生成最终的精确曲面;为了能够处理噪声点云,在剖分过程中所有网格曲面顶点都通过层次B样条进行了优化.相比于其他曲面重建方法,该算法剖分速度快,且能够保证点云到所生成的三角网格曲面的距离小于预先设定容限.实验结果表明,文中算法能够有效地实现高密度散乱点云的三角剖分,且其剖分速度较已有算法有大幅提高.     

一种散乱点云空间直接剖分算法

散乱点云的三角剖分在曲面重建中发挥着重要作用。在对三角剖分基本方法深入分析的基础上对此类点云提出了一种高效的重构算法。本算法将基于动态球策略的搜索算法引入到曲面重建中,源于增量式计算的思想,结合约束准则和设计的顶点度量函数,从基础三角面片开始扩展到覆盖整个物体表面。分析及实验结果表明,该算法能有效地对点云数据进行三角网格化,同时剖分后的三角网格曲面最大限度地保持了原有曲面的特性,证明了提出的基于动态球的曲面重构算法应用于散乱点云曲面重构问题的可行性。     

散乱点集Delaunay三角剖分的分布并行算法

为了加快大数据集Ｄｅｌａｕｎａｙ三角剖分的速度,提出了一种能对任意散乱点集进行Ｄｅｌａｕｎａｙ三角剖分的分布并行算法,算法具有容错性和自动负载平衡的能力,文中对其设计和实现方法进行了详细讨论,对算法的复杂性进行了分析,实验结果表明该算法的加速效果明显。     

离散插值曲面

散乱插值在实际应用中有重要作用.本文通过Vornonoi图构造了一张具有点插值和法 向插值的曲面.本文的方法优于目前散乱插值中常用的Shepard方法和三角剖分方法.本 文还给出了一种求离散插值曲面的算法,算法的时间复杂性为O(Nlog N),N为散敌点数.     

边界保持的隐式曲面三角化方法

隐式曲面三角化是隐式曲面绘制的常用算法.对于开区域上散乱点数据重建的隐式曲面,常用的隐式曲面三角化方法得到网格模型不能很好地保持散乱点数据的边界.针对该问题,提出了一种边界保持的隐式曲面三角化方法.根据散乱点数据的空间分布,控制等值面的抽取范围,实现了边界保持.实验结果表明,该算法能够产生和散乱点数据边界一致的三角网格.     

任意形状平面域的通用三角化算法

基于平面上散乱数据点的Ｄｅｌａｕｎａｙ三角剖分准则，提出了任意形状平面域的通用三角剖分算法。该算法不仅能用于Ｔｒｉｍｍｅｄ曲面的消隐显示及加工，也能用于有限元网格自动生成及其它领域。该算法已经成功应用于ＨＵＳＴＣＡＤＭ曲面造型及加工系统。     

任意三角形网格的基于二元四次箱样条分片C1曲面

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C1连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.     

任意三角形网格的基于二元四次箱样条分片C1曲面

提出一种以任意三角剖分为控制网格的二元箱样条曲面算法.二元三方向剖分是方向最少的三角剖分,建立在其上的二元三向四次箱样条在CAGD等领域有着广泛的应用.其规范的箱样条曲面计算仅适用于控制点的价数均为6的网格.从规范的算法出发,提出了一种任意价数控制网格的曲面计算算法,并对算法的连续性等进行了详细的分析.生成的曲面具有保凸性,且是分片C¹连续的.该算法可进行3D离散点全局或局部插值,并可应用于3D曲面重构等领域.     

一种三维表面重构中的轮廓集拼合新方法

针对切片级三维表面重构中的难点，提出了一种拼合轮廓集的新方法：通过对待拼合的轮廓集首尾轮廓进行平面三角剖分方向的判别，将空间轮廓集拼合的三维问题转化为平面多连通域三角剖分的二维问题，并改进了现有的平面多连通域三角剖分算法，巧妙地解决了切片级重构中的轮廓分支对应问题。实验表明，谊方法能准确完成复杂轮廓集的表面拼合，具有良好的适应性。     

SMOOTH SURFACE INTERPOLATION OVER ARBITRARY TRIANGULATIONS BY SUBDIVISION ALGORITHMS

ＳＭＯＯＴＨＳＵＲＦＡＣＥＩＮＴＥＲＰＯＬＡＴＩＯＮＯＶＥＲＡＲＢＩＴＲＡＲＹＴＲＩＡＮＧＵＬＡＴＩＯＮＳＢＹＳＵＢＤＩＶＩＳＩＯＮＡＬＧＯＲＩＴＨＭＳＲｕｉｂｉｎＱｕＳＭＯＯＴＨＳＵＲＦＡＣＥＩＮＴＥＲＰＯＬＡＴＩＯＮＯＶＥＲＡＲＢＩＴＲＡＲＹＴＲ...     

Robust uniform triangulation algorithm for computer aided design

This paper presents a new robust uniform triangulation algorithm that can be used in CAD/CAM systems to generate and visualize geometry of 3D models. Typically, in CAD/CAM systems 3D geometry consists of 3D surfaces presented by the parametric equations (e.g. surface of revolution, NURBS surfaces) which are defined on a two dimensional domain. Conventional triangulation algorithms (e.g. ear clipping, Voronoi-Delaunay triangulation) do not provide desired quality and high level of accuracy (challenging tasks) for 3D geometry. The approach developed in this paper combines lattice tessellation and conventional triangulation techniques and allows CAD/CAM systems to obtain the required surface quality and accuracy. The algorithm uses a Cartesian lattice to divide the parametric domain into adjacent rectangular cells. These cells are used to generate polygons that are further triangulated to obtain accurate surface representation. The algorithm allows users to control the triangle distribution intensity by adjusting the lattice density. Once triangulated, the 3D model can be used not only for rendering but also in various manufacturing and design applications. The approach presented in this paper can be used to triangulate any parametric surface given in S(u,v) form, e.g. NURBS surfaces, surfaces of revolution, and produces good quality triangulation which can be used in CAD/CAM and computer graphics applications.     

多连通多边形三角化找桥算法的研究及实现

已有的多边形三角化剖分算法,对多连通任意多边形的处理方法不一,算法大多复杂,可靠性低,而且往往只适合于特定的多边形剖分。本文结合现有的多边形三角剖分算法,提出了一个简洁高效、高可靠性的多连通任意多边形三角化剖分的找桥算法,该算法可用于各种多连通任意多边形的三角化剖分处理,并且成功运用于本单位研制开发的城市三维数码景观系统中,收到了较好的效果。     

Efficient Suboptimal Solutions to the Optimal Triangulation

Given two images, the optimal triangulation of a measured corresponding point pair is to basically find out the real roots of a 6-degree polynomial. Since for each point pair, this root finding process should be done, the optimal triangulation for the whole image is computationally intensive. In this work, via the 3D cone expression of fundamental matrix, called the fundamental cone, together with the Lagrange’s multiplier method, the optimal triangulation problem is reformulated. Under this new formulation, the optimal triangulation for a measured point pair is converted to finding out the closest point on the fundamental cone to the measured point in the joint image space, then 3 efficient suboptimal algorithms, each of them can satisfy strictly the epipolar constraint of the two images, are proposed. In our first suboptimal algorithm, the closest point on the generating cone to the measured point is used as the approximation of the optimal solution, which is to find out the real roots of a 4-degree polynomial; in our second suboptimal algorithm, the closest point on the generating line to the measured point is used as the approximation of the optimal solution, which is to find out the real roots of a 2-degree polynomial. Finally, in our third suboptimal algorithm, the converging point of the Sampson approximation sequence is used as the approximation of the optimal solution. Experiments with simulated data as well as real images show that our proposed 3 suboptimal algorithms can achieve comparable estimation accuracy compared with the original optimal triangulation, but with much less computational load. For example, our second and third suboptimal algorithms take only about a 1/5 runtime of the original optimal solution. Besides, under our new formulation, rather than recompute the two Euclidian transformation matrices for each measured point pair, a fixed Euclidian transformation matrix is used for all image point pairs, which, in addition to its mathematical elegance and computational efficiency, is able to remove the dependency of the resulting polynomial’s degree on the parameterization of the epipolar pencil in either the first image or in the second image, a drawback in the original optimal triangulation.     

Creating non-minimal triangulations for use in inference in mixed stochastic/deterministic graphical models

We demonstrate that certain large-clique graph triangulations can be useful for reducing computational requirements when making queries on mixed stochastic/deterministic graphical models. This is counter to the conventional wisdom that triangulations that minimize clique size are always most desirable for use in computing queries on graphical models. Many of these large-clique triangulations are non-minimal and are thus unattainable via the popular elimination algorithm. We introduce ancestral pairs as the basis for novel triangulation heuristics and prove that no more than the addition of edges between ancestral pairs needs to be considered when searching for state space optimal triangulations in such graphs. Empirical results on random and real world graphs are given. We also present an algorithm and correctness proof for determining if a triangulation can be obtained via elimination, and we show that the decision problem associated with finding optimal state space triangulations in this mixed setting is NP-complete.