基于弹簧-质点模型的不规则曲面纹理映射

针对三角网格表示的不规则曲面的纹理映射问题,提出一种基于弹簧-质点模型的简单、高效、失真小的纹理映射算法。结合调和映射的参数化方法以及弹簧-质点模型的复杂平面展开方法,保持拓扑关系地将三维曲面投影于平面内;通过建立三角网格表示的投影面的弹簧-质点模型,将不规则曲面参数化于给定大小的矩形域;利用参数化的结果计算不规则曲面各顶点的纹理坐标,进行纹理贴图。实验结果表明,该算法能够实现纹理高效、均匀、变形小地映射于任意不规则曲面上。     

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．     

三角网格表面近似测地线的计算

为了有效地计算三角网格表面任意两点间的近似测地线,将三角网格模型表示成带权图,计算带权图上两点间的最短路径,并迭代细分最短路径邻域内的边以构造新的带权图求解.改进了细分顶点的生成策略,提出了邻域扩展的方法,提高了迭代运算速度,有效地解决了迭代细分算法容易陷入局部最优的问题;并把测地线距离应用于径向基函数,实现了一种曲面变形算法.实验表明该算法达到了较好的效果.     

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.     

基于弹簧-质点模型曲面展开的改进算法

为了提高现有弹簧-质点模型曲面展开算法的速度和稳定性,提出了自适应时间步长方法.通过计算模型中各质点的惩罚力,实现了三角片翻转区域的整体调整;同时结合了考虑初速度和忽略初速度2种方法的优点;最后对一些参数的计算方法做了改进.实验结果表明,该算法能够有效地消除初始展开及优化过程中出现的翻转三角片,提高了复杂曲面的展开质量.     

基于两步的网格平滑

在三角网格的生成过程中,不可避免地会出现噪声,如何有效地消除这些噪声已经成为当前计算机图形学领域的一个重要课题,提出了一个简单的,能有效去除噪声,同时能很好的保持网格尖边特征的算法.该算法通过两步来实现,第一步对三角网格的三角面面法矢量进行平滑,第二步依据面法矢量调整新的顶点坐标.此算法在伪三角的帮助下,能很好保持曲面的几何特征,防止曲面收缩.实验结果说明了实验的有效性.     

三角网格的能量优化参数化方法

三角网格参数化是纹理映射、曲面拟合与曲面重构、网格编辑等工作的基础和环节,参数化变形的大小是衡量参数化好坏的标准.为此提出一种基于变形能量优化的三角网格参数化方法.采用区域增长算法逐层展平空间三角网格,得到空间三角网格曲面的自由边界的参数化结果,并利用保形变换将自由边界的参数化结果变换为规则边界的参数化结果;同时兼顾了参数化的角度变形和面积变形,使得参数化结果具有整体变形较小的特点,并能够避免三角形折叠的现象.将该方法应用于纹理映射中的数值实验表明,其比常见的几种参数化方法具有更好的纹理映射效果.     

曲率约束的隐式曲面三角网格化

提出一种有效的隐式曲面三角网格化算法。从隐式曲面上的一个种子点开始,生成网格的边界作为扩张多边形,且该多边形最小角对应的顶点为扩张点,计算从扩张点处欲生成的三角网格,为了防止新生成的三角网格和已经存在的三角网格重叠,要进行冲突检测。在隐式曲面三角网格化的过程中,扩张多边形是不断变化的,需要重复上述步骤,直至没有扩张多边形时结束。该算法分别应用于解析隐式曲面和变分隐式曲面的三角网格化。实验结果表明,该算法不需要重新网格化的步骤,生成的三角网格具有较高的质量,且三角网格随曲率适应性变化,因此说明了该算法的有效性。     

基于三角面网格细化策略的改进种子填充算法

区域填充染色的一般解决方法并不适用于空间曲面.为解决该问题,提出一种适用于空间三角面网格的种子填充算法.通过改变种子点的判定方法,将平面种子填充算法扩展到空间三角面网格上,在细分三角面网格结构时,使用以轮廓线为引导的细分策略,并利用凸包的一些特殊性质对轮廓点进行筛选.实验结果表明,该算法可以较好地完成三角面网格的区域填充染色,在效率和填充效果方面都可以满足实际应用.     

单位化建模衰减变形新方法

针对软组织自由变形中调整控制顶点难以准确控制物体变形的问题,提出了一种基于单位化建模的衰减变形算法。该算法利用三角网格进行单位化建模,将变形软组织碰撞点的三维世界坐标转换为三角网格二维顶点坐标,通过确定以碰撞点所在顶点为中心的自适应变形区域,控制区域内顶点偏移量发生衰减变化,从而直接作用于物体顶点进行形变,同时通过设计合适的衰减函数使偏移量呈抛物线衰减。通过实验证明该算法所建模型具有通用性,变形在局部区域内可取得准确的抛物线衰减效果。     

改进的布尔方法及其在虚拟ACL手术中的应用

为了实现在虚拟ACL手术中对骨骼模型进行钻孔操作的动态模拟,提出了一种针对面网格模型的改进布尔操作方法.首先对与切割曲面相交的三角形进行细分,并移动切割曲面附近的网格顶点使其位于曲面上,实现模型表面上的布尔操作;然后对切割曲面附近的模型表面进行平滑处理,以消除在顶点移动操作中带来的模型表面锯齿状现象;最后采用前沿推进方法生成模型的内壁网格,并利用基于时间的钻孔深度控制函数实现对钻孔操作过程的动态模拟.该方法消除了近似布尔方法中的"T"型点问题,能够保持模型表面平滑效果和切割边缘尖锐特征,实现了对布尔操作的动态模拟,满足实时性的要求.该方法适用于实时系统中针对面网格模型的动态、交互式布尔操作模拟.     

Conformal Flattening by Curvature Prescription and Metric Scaling

We present an efficient method to conformally parameterize 3D mesh data sets to the plane. The idea behind our method is to concentrate all the 3D curvature at a small number of select mesh vertices, called cone singularities, and then cut the mesh through those singular vertices to obtain disk topology. The singular vertices are chosen automatically. As opposed to most previous methods, our flattening process involves only the solution of linear systems of Poisson equations, thus is very efficient. Our method is shown to be faster than existing methods, yet generates parameterizations having comparable quasi‐conformal distortion.     

A highly solid model boundary preserving method for large-scale parallel 3D Delaunay meshing on parallel computers

In this paper, we propose a novel parallel 3D Delaunay triangulation algorithm for large-scale simulations on parallel computers. Our method keeps the 3D boundary representation model information during the whole parallel 3D Delaunay triangulation process running on parallel computers so that the solid model information can be accessed dynamically and the meshing results can be very approaching to the model boundary with the increase of meshing scale. The model is coarsely meshed at first and distributed on CPUs with consistent partitioned shared interfaces and partitioned model boundary meshes across processors. The domain partition aims at minimizing the edge-cuts across different processors for minimum communication cost and distributing roughly equal number of mesh vertices for load balance. Then a parallel multi-scale surface mesh refinement phase is iteratively performed to meet the mesh density criteria followed by a parallel surface mesh optimization phase moving vertices to the model boundary so as to fit model geometry feature dynamically. A dynamic load balancing algorithm is performed to change the partition interfaces if necessary. A 3D local non-Delaunay mesh repair algorithm is finally done on the shared interfaces across processors and model boundaries. The experimental results demonstrate our method can achieve high parallel performance and perfect scalability, at the same time preserve model boundary feature and generate high quality 3D Delaunay mesh as well.     

反求工程中的隐式曲面快速自适应性多边形算法

论文给出一种反求工程中基于三角形细分的隐式曲面快速自适应性多边形化方法。该文先由输入的三维扫描数据点利用空间延展的MarchingCubes方法得到隐式曲面较为粗糙的三角形表面网格形状,再利用该文的自适应性优化方法对粗糙网格从三个方面自适应性调整,即调整网格顶点法向,控制曲率,再补偿网格抽样率。从而生成的三角网格和采样点具有局部适应性,能随着曲率的变化自动控制采样点的疏密程度,消除了逼近网格中的T-形边。实验表明,恢复的隐式曲面能很好地反映形状特征,能满足反求工程的实时需求。     

Interpolation by geometric algorithm

We present a novel geometric algorithm to construct a smooth surface that interpolates a triangular or a quadrilateral mesh of arbitrary topological type formed by n vertices. Although our method can be applied to B-spline surfaces and subdivision surfaces of all kinds, we illustrate our algorithm focusing on Loop subdivision surfaces as most of the meshes are in triangular form. We start our algorithm by assuming that the given triangular mesh is a control net of a Loop subdivision surface. The control points are iteratively updated globally by a simple local point-surface distance computation and an offsetting procedure without solving a linear system. The complexity of our algorithm is O(mn) where n is the number of vertices and m is the number of iterations. The number of iterations m depends on the fineness of the mesh and accuracy required.     

A pipeline for computer aided polyp detection

We present a novel pipeline for computer-aided detection (CAD) of colonic polyps by integrating texture and shape analysis with volume rendering and conformal colon flattening. Using our automatic method, the 3D polyp detection problem is converted into a 2D pattern recognition problem. The colon surface is first segmented and extracted from the CT data set of the patient's abdomen, which is then mapped to a 2D rectangle using conformal mapping. This flattened image is rendered using a direct volume rendering technique with a translucent electronic biopsy transfer function. The polyps are detected by a 2D clustering method on the flattened image. The false positives are further reduced by analyzing the volumetric shape and texture features. Compared with shape based methods, our method is much more efficient without the need of computing curvature and other shape parameters for the whole colon surface. The final detection results are stored in the 2D image, which can be easily incorporated into a virtual colonoscopy (VC) system to highlight the polyp locations. The extracted colon surface mesh can be used to accelerate the volumetric ray casting algorithm used to generate the VC endoscopic view. The proposed automatic CAD pipeline is incorporated into an interactive VC system, with a goal of helping radiologists detect polyps faster and with higher accuracy.     

Drawing on air: input techniques for controlled 3D line illustration

Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch, which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.     

Computing length-preserved free boundary for quasi-developable mesh segmentation

Stretch-free surface flattening has been requested by a variety of applications. At present, the most difficult problem is how to segment a given model into nearly developable atlases so that a nearly stretch-free flattening can be computed. The criterion for segmentation is needed to evaluate the possibility of flattening a given surface patch, which should be fast computed. In this paper, we present a method to compute the length-preserved free boundary (LPFB) of a mesh patch which speeds up the mesh parameterization. The distortion on parameterization can then be employed as the criterion in a trial-and-error algorithm for segmenting a given model into nearly developable atlases. The computation of LPFB is formulated as a numerical optimization problem in the angle space, where we are trying to optimize the angle excesses on the boundary while preserving the constraints derived from the closed-path theorem and the length preservation.     

Similarity based interpolation using Catmull–Clark subdivision surfaces

A new method for constructing a Catmull–Clark subdivision surface (CCSS) that interpolates the vertices of a given mesh with arbitrary topology is presented. The new method handles both open and closed meshes. Normals or derivatives specified at any vertices of the mesh (which can actually be anywhere) can also be interpolated. The construction process is based on the assumption that, in addition to interpolating the vertices of the given mesh, the interpolating surface is also similar to the limit surface of the given mesh. Therefore, construction of the interpolating surface can use information from the given mesh as well as its limit surface. This approach, called similarity based interpolation, gives us more control on the smoothness of the interpolating surface and, consequently, avoids the need of shape fairing in the construction of the interpolating surface. The computation of the interpolating surface’s control mesh follows a new approach, which does not require the resulting global linear system to be solvable. An approximate solution provided by any fast iterative linear system solver is sufficient. Nevertheless, interpolation of the given mesh is guaranteed. This is an important improvement over previous methods because with these features, the new method can handle meshes with large number of vertices efficiently. Although the new method is presented for CCSSs, the concept of similarity based interpolation can be used for other subdivision surfaces as well.