基于网格优化的隐式曲面自适应多边形化

隐式曲面多边形化是隐式曲面绘制的一种常用算法.基于网格优化的隐式曲面快速自适应多边形化算法,首先用多边形化算法生成一个粗糙的初始网格,再利用网格优化方法从网格顶点位置、规则性和网格法向三个方面对粗糙网格进行调整,最后根据网格的局部曲率用多边形细分策略细分优化后的网格.实验结果表明,该算法在网格生成速度和网格规则性上都胜于Marching Cubes的多边形化算法,恢复的隐式曲面能较好地反映形状特征.     

基于网格优化的隐式曲面自适应多边形化

隐式曲面多边形化是隐式曲面绘制的一种常用算法.基于网格优化的隐式曲面快速自适应多边形化算法,首先用多边形化算法生成一个粗糙的初始网格,再利用网格优化方法从网格顶点位置、规则性和网格法向三个方面对粗糙网格进行调整,最后根据网格的局部曲率用多边形细分策略细分优化后的网格.实验结果表明,该算法在网格生成速度和网格规则性上都胜于Marching Cubes的多边形化算法,恢复的隐式曲面能较好地反映形状特征.     

壳空间剖分的隐式曲面三角化

提出了一种曲率自适应的壳空间剖分隐式曲面三角形化新方法.新方法首先采用粒子系统对隐式曲面进行采样,通过高斯曲率约束粒子的生成,使生成的网格模型在曲率大的区域具有较多的小三角形,在曲率小的区域具有较少的大三角形,从而使网格模型更好地逼近隐式曲面.新方法在每个采样粒子处沿曲面法线正负方向延伸适当距离得到两个附加点,对所有附加点进行四面体化形成对隐式曲面逼近的壳空间四面体网格,在每个壳空间四面体中抽取三角形,所有抽取的三角形拼合得到隐式曲面的三角网格表示.与以往方法相比,新的三角网格化方法更具有鲁棒性,可一次性获得高质量的三角形网格.最后给出了对常用隐式曲面进行三角化的实例比较,显示了新方法的有效性.     

隐式曲面的快速适应性多边形化算法

通过将隐式曲面多边形化过程分为“构造”和“适应性采样”两个阶段，实现了隐式曲面多边形逼近网格的适应性构造．通过基于空间延展的Marching Cubes方法得到隐式曲面较为粗糙的均匀多边形化逼近，根据曲面上的局部曲率分布，运用适应性细分规则对粗糙网格进行细分迭代，并利用梯度下降法将细分出的新顶点定位到隐式曲面上；最终得到的多边形网格是适应性的单纯复形网格，其在保持规定逼近精度的前提下，减少了冗余三角形的产生，网格质量有明显改善．该算法可用于隐式曲面的交互式可视化过程．     

法向约束的隐式曲面多边形化

提出一种隐式曲面多边形化的方法,将隐式曲面的多边形化分为2个阶段:首先根据法向约束对隐式曲面进行采样,得到稳定的采样粒子表示;然后在每个采样粒子处沿法线正负方向分别在隐式曲面内部和外部延伸一段距离,得到2个曲面法向附加点.将法向附加点和采样顶点进行四面体化,删除法向顶点及其相关联的边,最终得到隐式曲面的三角形网格模型.最后用实例表明了该方法的有效性.     

隐式曲面的多分辨率法向网格逼近

法向网格是一种新型的曲面多分辨率描述方式，其中每个层次都可以表示为其前一个粗糙层次的法向偏移．文中提出一种基于法向网格表示的隐式曲面多分辨率网格逼近算法．首先通过基于空间剖分技术的多边形化算法获得隐式曲面的粗糙逼近网格，并利用网格均衡化方法对粗糙网格进行优化，消除其中的狭长三角形；然后利用法向细分规则迭代地对网格中的三角面片进行细分，并利用区间算术技术沿法向方向对隐式曲面进行逼近．最终生成的隐式曲面分片线性逼近网格为法向网格．该逼近网格为隐式曲面提供了一种多分辨率表示，网格具有细分连通性，其数据量较传统的多边形化算法所生成的网格有大幅度的压缩．该算法可用于隐式曲面的多级绘制、累进传输及相关数字几何处理．     

基于混合优化的快速隐式曲面采样方法

该文提出了一种新的隐式曲面快速采样方法,该方法首先提出了一种新的采样点互斥能量目标函数,基于该目标函数,通过一种混合优化方法来求解采样点的分布.第1步为采样点的局部优化,通过对采样点移动速度的控制参数调整,避免了大量Hessian矩阵的求逆操作,使得采样点能够根据互斥半径快速覆盖整个隐式曲面,得到初始采样点集;第2步为采样点的全局优化,采用L-BFGS方法对所有采样点进行优化,得到最终的高质量采样结果.通过实验表明,新方法的采样速度大大提高,并能够获得较好的隐式曲面采样点分布.     

隐式曲面快速多边形化

隐式曲面多边形化是隐式曲面绘制的常用算法。该文提出了一个隐式曲面快速多边形化算法。首先用Bloo-menthal的多边形化算法生成一个粗糙的初始网格,再进行网格优化提高网格规则性,最后用多边形细分策略细分优化后的网格。实验结果表明,该算法在网格生成速度和网格规则性上都胜于Bloomenthal的多边形化算法。     

三角网格模型的特征线提取

在反求工程中，散乱数据点云的曲面重构常采用三角网格模型，若将其转换成曲面实体模型则有更广泛的应用，从三角网格模型中提取特征线是转换过程中的重要步骤．在讨论反求工程中数据点云分块方法的基础上，采取“基于边”的方法来提取特征线：先提取特征点，再连接成特征线．根据相邻三角片的法矢夹角和各点主曲率是否为极值，分两次提取特征点，利用三角顶点加权和均匀化等方法减少狭长三角片对特征点提取的计算误差影响，再将特征点分组连接成B样条曲线．文中算法的结果可为B样条曲面分片拟合和建立B-rep曲面实体模型提供依据。     

曲率约束下的静态隐式曲面的粒子采样

针对隐式曲面绘制时参数不易确定、误差不易控制的问题,提出一种基于曲率的静态隐式曲面的粒子采样方法.首先选取一个种子粒子,依据转动法对其他粒子进行初始化;然后根据粒子之间的静电排斥力和粒子反投影旋转法更新所有粒子的位置,达到粒子系统的相对稳定状态;再依据采样点的曲率改变粒子间的相互作用力,实现对隐式曲面的基于曲率的粒子采样.实验结果表明,该方法简单易行,粒子位置更新的精度可控,避免了大量参数调节,并且可以适用于复杂曲面.     

Variational implicit surface meshing

In this paper, we propose a new algorithm to mesh implicit surfaces which produces meshes both with a good triangle aspect ratio as well as a good approximation quality. The number of vertices of the output mesh is defined by the end-user. For this goal, we perform a two-stage processing: an initialization step followed by an iterative optimization step. The initialization step consists in capturing the surface topology and allocating the vertex budget. The optimization algorithm is based on a variational vertices relaxation and triangulation update. In addition a gradation parameter can be defined to adapt the mesh sampling to the curvature of the implicit surface. We demonstrate the efficiency of the approach on synthetic models as well as real-world acquired data, and provide comparisons with previous approaches.     

Robust multi‐level partition of unity implicits from triangular meshes

This paper presents a new robust multi‐level partition of unity (MPU) method, which constructs an implicit surface from a triangular mesh via the new error metric between the mesh and the implicit surface. The new error metric employs a weighted function of inner points and vertices of a triangle to fit an implicit surface, which can control the approximation error between the surface and vertices of the triangle. Furthermore, it is applied to the MPU method by utilizing the dual graph of a triangular mesh, and the general quadric implicit surface is used for surface representation. Compared with the MPU method, the new method generates fewer subdivision cells with the same approximation error and performs more steadily especially when given triangular mesh with fewer vertices. Copyright © 2013 John Wiley & Sons, Ltd.     

A direct approach for subdivision surface fitting from a dense triangle mesh

This article presents a new and direct approach for fitting a subdivision surface from an irregular and dense triangle mesh of arbitrary topological type. All feature edges and feature vertices of the original mesh model are first identified. A topology- and feature-preserving mesh simplification algorithm is developed to further simplify the dense triangle mesh into a coarse mesh. A subdivision surface with exactly the same topological structure and sharp features as that of the simplified mesh is finally fitted from a subset of vertices of the original dense mesh. During the fitting process, both the position masks and subdivision rules are used for setting up the fitting equation. Some examples are provided to demonstrate the proposed approach.     

Multiresolution Isosurface Extraction with Adaptive Skeleton Climbing

An isosurface extraction algorithm which can directly generate multiresolution isosurfaces from volume data is introduced. It generates low resolution isosurfaces, with 4 to 25 times fewer triangles than that generated by marching cubes algorithm, in comparable running times. By climbing from vertices (0-skeleton) to edges (1-skeleton) to faces (2-skeleton), the algorithm constructs boxes which adapt to the geometry of the true isosurface. Unlike previous adaptive marching cubes algorithms, the algorithm does not suffer from the gap-filling problem. Although the triangles in the meshes may not be optimally reduced, it is much faster than postprocessing triangle reduction algorithms. Hence the coarse meshes it produces can be used as the initial starts for the mesh optimization, if mesh optimality is the main concern.     

参数平面二叉树剖分网格简化

为了快速地对3维网格模型进行简化,提出了一种曲率自适应的3维网格简化算法,该算法首先将原始网格投影至参数平面上,并构造反映原始网格曲率分布的平面曲率灰度分布,用以表征简化过程中对网格各部分不同的采样密度要求;然后根据等曲率灰度分割的原则来对参数平面进行二叉树剖分,以构造反映其不均匀分布的非均衡二叉树结构,并依此选取简化后的网格顶点集合,以构造简化的三角网格.该算法的优点是执行速度快,同时在简化过程中仍能充分保持原始网格的细节.     

Boolean operations with implicit and parametric representation of primitives using R-functions

We present a new and efficient algorithm to accurately polygonize an implicit surface generated by multiple Boolean operations with globally deformed primitives. Our algorithm is special in the sense that it can be applied to objects with both an implicit and a parametric representation, such as superquadrics, supershapes, and Dupin cyclides. The input is a constructive solid geometry tree (CSG tree) that contains the Boolean operations, the parameters of the primitives, and the global deformations. At each node of the CSG tree, the implicit formulations of the subtrees are used to quickly determine the parts to be transmitted to the parent node, while the primitives' parametric definition are used to refine an intermediary mesh around the intersection curves. The output is both an implicit equation and a mesh representing its solution. For the resulting object, an implicit equation with guaranteed differential properties is obtained by simple combinations of the primitives' implicit equations using R-functions. Depending on the chosen R-function, this equation is continuous and can be differentiable everywhere. The primitives' parametric representations are used to directly polygonize the resulting surface by generating vertices that belong exactly to the zero-set of the resulting implicit equation. The proposed approach has many potential applications, ranging from mechanical engineering to shape recognition and data compression. Examples of complex objects are presented and commented on to show the potential of our approach for shape modeling.     

基于力学模型的曲面展开通用算法

为了解决曲面展开算法实现复杂、累积误差和通用性不佳的缺点,提出一种在三维空间内基于能量模型的曲面展开算法,待展开的曲面以三角网格形式表示,将曲面简化为三角网格的顶点组成的质点系统,通过在每个质点上加上适当的力使得三角网格产生相应的变形,达到将曲面展开的效果.与现有算法相比,该曲面展开算法适用于任意形状曲面,不需要使用投影平面,整个变形完全由网格顶点受力来驱动,便于实现、适用面广、对于不可展曲面也能得到较好的展开效果,而不会出现裂纹现象.