三维网格模型的布尔运算方法

提出了一种基于三维网格模型的布尔运算方法。首先通过基于方向包围盒（OBB）层次包围盒树的碰撞检测算法,得到实体的相交三角形对;接下来求出两相交三角形之间的交线,建立与三角形的交线拓扑关系;通过分类处理三种交线类型来对相交三角形进行区域划分,得到一系列多边形,并对多边形进行三角剖分形成结果区域;最后根据体的包含关系构建关系邻接表,判断多边形区域的相对于其他实体的内外关系并通过网格模型的拓扑关系,定位表面三角网格区域;同时根据交、并、差等布尔操作,对结果区域进行取舍,得到最终结果。实验结果表明相交部分的岩性与实体的岩性相吻合,验证了该算法的正确性以及可行性。     

三维网格模型的稳定布尔运算算法

给出一种稳定、高效的三维网格模型的布尔运算算法。该算法首先,基于网格模型原始的拓扑关系,结合层次包围盒相交检测实现网格模型相交区域快速定位;然后,采用改进的空间三角形求交算法求解离散交线段数据,并对单个三角形重新进行Delaunay三角剖分;最后,通过建立交线段与相交三角形间的拓扑关系对交线快速跟踪提取,通过局部区域快速分类组合,实现三角网格模型的精确布尔运算。该算法能有效地处理各种特殊情况且运行稳定;程序实现简单,实例证明符合工程需求。     

基于空间分解的三角网格模型求交方法

三角网格模型间的求交问题是计算机辅助设计与制造领域的关键问题之一.分析了已有空间分解技术和包围盒方法等的优缺点,并在此基础上提出了改进的空间分解求交方法. 该算法能够精确定位三角形所占的空间网格,一定程度上减少了需要求交的三角形的数量.实验的结果表明,改进的算法提高了采用空间分解进行三角网格求交的计算效率.     

利用几何求交实现三角网格模型快速体素化

为解决现有的三角网格模型体素化算法存在的体素寻找不全或者体素化效率不高的问题,提出一种快速的三角网格模型体素化算法.该算法分为表面体素化和内部体素化2个步骤:表面体素化使用几何求交方法快速寻找三角形与全部体素的相交多边形顶点,并将这些顶点和与三角形相交的体素一一对应,得到每一个三角形的相交体素,从而得到与三角网表面相交的全部体素;内部体素化使用同时填充内部和外部体素的扫描线种子填充算法,填充过程中使用变长队列,在保持算法的正确性和效率的同时大幅减小算法的空间复杂度.使用三角形数量较多的模型进行高分辨率体素化的实验结果表明,文中算法耗时短,在三角形数量较多时体素化效率显著提高.     

自交有理参数曲面网格生成

针对现有网格生成算法在处理自交曲面时出现的缺少交线表示、误差大以及交线附近三角形质量差的问题,提出一种针对自交有理参数曲面的网格生成算法.首先,利用动平面法计算曲面的奇异因子;其次,利用奇异因子和曲面的第一基本形式定位交线上的拓扑关键点;再次,基于动平面法设计了一种交线网格点配对生成算法,以保证网格交线的邻域协调性;最后,使用基于粒子的网格生成法生成参数域网格.在具有不同拓扑的自交曲面上进行网格生成实验,所提算法可保证网格交线拓扑正确性,且与未进行交线网格点配对的各类代表性各向同性网格生成算法相比,网格三角形最小角平均值平均高0.6%.     

一种用于光线与三角形网格求交运算的有效剔除算法

提出一种用于光线与三角形网格求交运算中的有效剔除算法.算法中,一根光线被定义为两个非平行平面的交线.针对由稠密三角形网格组成的复杂场景,算法通过三角形和测试平面的相交判断剔除与投射光线不相交的绝大多数三角面片.利用该算法,光线跟踪中主光线在图像空间的相关性可以方便、直观地被利用.为了利用物体在景物空间的相关性,算法可以结合层次包围盒、八叉树等常见的场景划分方法.而且,该算法可以方便地扩展应用于一般多边形网格.     

复杂曲面加工精度检验中曲面法矢与刀具扫描体求交算法的研究

提出了一种用于实现矢量与扫描体（代表五轴数控加工铣刀的运动）求交的有效算法,该算法首先对曲面法矢和刀具扫描体进行预处理,将曲面法矢与刀具扫描体之间的求交问题转化为有向线段与三角网格之间的求交计算,然后建立有向线段和三角网格的求交子集,减少了不必要的求交计算,提高了乍法的效率。文中举例说明了该算法在复杂曲面NC精度检验中的应用。     

四边形网格间接生成方法

研究了基于背景三角网格的四边形网格间接生成算法,并针对三角形合并过程中容易残留三角形的缺陷提出了确定侧边的详细算法,该算法主要是依据背景三角网格中边的位置和前沿边的情形,通过背景三角网格中已存在的边、边交换或边分割确定侧边,以避免在三角形合并过程中残留三角形单元。最后给出实例验证了算法的有效性。     

曲面浮雕的高效表示及3D打印算法

针对3D浮雕网格点数、面数空间占用大,在打印过程中耗费内存等缺点,提出将凹凸贴图表示的浮雕模型直接进行切片完成打印,并提出基于凹凸贴图的浮雕网格的3D打印自适应细分切片算法.在切片过程中,先对输入的粗网格根据凹凸图深度信息进行自适应中点细分,并更新细分后三角网格顶点的几何位置;然后对生成的局部三角网格集合与切片进行求交运算,将所获得的交线段存储后释放此三角形集合的内存;最后将生成的交线段重组成闭合多边形,生成打印路径,交由打印机完成浮雕模型打印.实验结果证明,将凹凸贴图推广到3D打印中,与传统的打印过程进行对比,该方法的空间利用率得到显著性提高.     

基于重新划分的三角形网格简化的一种改进算法

基于重新划分的三角形网格简化方法能自动生成多细节层次模型，它的基本思想是:根据三角形网格的局部几何和拓扑特征将一定数量的点分布到原网格上,生成一个中间网格,移去中间网格中的老顶点,并对产生的多边形区域进行局部三角化,最后形成以新点为顶点的三角形网格.本文在已有算法的基础上,提出了一种分布新点的算法,从而克服了原有方法的局限性.它利用三角形顶点的曲率和三角形的面积两个因素来反映网格在每个三角形处的特征.文中给出的一组实例说明了算法的有效性.     

Mesh Draping: Parametrization-Free Neural Mesh Transfer

Despite recent advances in geometric modelling, 3D mesh modelling still involves a considerable amount of manual labour by experts. In this paper, we introduce Mesh Draping: a neural method for transferring existing mesh structure from one shape to another. The method drapes the source mesh over the target geometry and at the same time seeks to preserve the carefully designed characteristics of the source mesh. At its core, our method deforms the source mesh using progressive positional encoding (PE). We show that by leveraging gradually increasing frequencies to guide the neural optimization, we are able to achieve stable and high-quality mesh transfer. Our approach is simple and requires little user guidance, compared to contemporary surface mapping techniques which rely on parametrization or careful manual tuning. Most importantly, Mesh Draping is a parameterization-free method, and thus applicable to a variety of target shape representations, including point clouds, polygon soups and non-manifold meshes. We demonstrate that the transferred meshing remains faithful to the source mesh design characteristics, and at the same time fits the target geometry well.     

Random Accessible Mesh Compression Using Mesh Chartification

Previous mesh compression techniques provide decent properties such as high compression ratio, progressive decoding, and out-of-core processing. However, only a few of them supports the random accessibility in decoding, which enables the details of any specific part to be available without decoding other parts. This paper proposes an effective framework for the random accessibility of mesh compression. The key component of the framework is a wire-net mesh constructed from a chartification of the given mesh. Charts are compressed separately for random access to mesh parts and a wire-net mesh provides an indexing and stitching structure for the compressed charts. Experimental results show that random accessibility can be achieved with competent compression ratio, which is only a little worse than single-rate and comparable to progressive encoding. To demonstrate the merits of the framework, we apply it to process huge meshes in an out-of-core manner, such as out-of-core rendering and out-of-core editing.     

Quasi-Developable Mesh Surface Interpolation via Mesh Deformation

We present a new algorithm for finding a most "developable" smooth mesh surface to interpolate a given set of arbitrary points or space curves. Inspired by the recent progress in mesh editing that employs the concepts of preserving the Laplacian coordinates and handle-based shape editing, we formulate the interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, such as a planar figure, to a final mesh surface that interpolates the given points and/or curves. During the deformation, the developability of the intermediate mesh is maintained by means of preserving the zero-valued Gaussian curvature on the mesh. To treat the high nonlinearity of the geometric constrains owing to the preservation of Gaussian curvature, we linearize those nonlinear constraints using Taylor expansion and eventually construct a sparse and over-determined linear system which is subsequently solved by a robust least-squares solution. By iteratively performing this procedure, the initial mesh is gradually and smoothly "dragged" to the given points and/or curves. The initial experimental data has shown some promising aspects of the proposed algorithm as a general quasi-developable surface interpolation tool.     

Mesh blending

A new method for smoothly connecting different patches on triangle meshes with arbitrary connectivity, called mesh blending, is presented. A major feature of mesh blending is to move vertices of the blending region to a virtual blending surface by choosing an appropriate parameterization of those vertices. Once blending is completed, the parameterization optimization is performed to perfect the final meshes. Combining mesh blending with multiresolution techniques, an effective blending technique for meshes is obtained. Our method has several advantages: (1) the user can intuitively control the blending result using different blending radii, (2) the shape of cross-section curves can be adjusted to flexibly design complex models, and (3) the resulting mesh has the same connectivity as the original mesh. In this paper, some examples about smoothing, sharpening, and mesh editing show the efficiency of the method.     

Mesh massage

We present a general framework for post-processing and optimizing surface meshes with respect to various target criteria. On the one hand, the framework allows us to control the shapes of the mesh triangles by applying simple averaging operations; on the other hand we can control the Hausdorff distance to some reference geometry by minimizing a quadratic energy. Due to the simplicity of this setup, the framework is efficient and easy to implement, yet it also constitutes an effective and versatile tool with a variety of possible applications. In particular, we use it to reduce the texture distortion in animated mesh sequences, to improve the results of cross-parameterizations, and to minimize the distance between meshes and their remeshes.     

Mesh Simplification

Mesh simplification is an important stage after surface reconstruction since the models produced can contain a large number of polygons making them difficult to manipulate. In this paper we present a mesh simplification algorithm to reduce the number of vertices in a dense mesh of triangles. The algorithm is based on edge operations that are performed in the inside of independent clusters distributed over the entire mesh. The clusters are well-characterized regions that can successfully accept simplification operations. The simplification operations produce only local transformations on the mesh. This region-based, distributed approach permits to easily track and control the changes in the triangulation and avoids the appearance of particular cases that would require a special handling. The algorithm uses two user-specified parameters to guide the operations. These parameters allow various simplification strategies that are illustrated on several dense triangulations.     

结合网格分割和边折叠的网格简化算法

传统网格简化算法简化效率较低,且在大幅度简化时难以保持网格模型的外形特征。为此,提出一种结合网格分割和边折叠的网格简化算法。采用分水岭算法对网格模型进行分割,以提高网格模型的简化效率。在Garland算法折叠代价函数的基础上,加入三角形形状和相邻曲面弯曲程度的相关因子,从而更好地保持网格模型的外形特征。实验结果表明,该算法在网格模型的简化速度和外形特征保持方面性能较好。     

骨骼蒙皮动画中网格优化的研究与实现

在骨骼蒙皮动画中需要处理大量的网格三角形,而在很多骨骼蒙皮动画的应用中都需要很高的动画实时性,为了提高骨骼蒙皮动画的实时性,对网格的优化是其中一项重要的工作.本文提出了一种优化网格的方法,并予以实现.     

墙式网孔

提出了一种新的网孔－墙式网孔．墙式网孔是一种三度网孔,它通过从普通四度网孔的每个节点删去一度而获得,其节点度节省了２５％,但其直径同普通四度网孔几乎一样．它在计算能力上同普通四度网孔是等价的,因为四度网孔可以有效地嵌入到墙式网孔中,其伸张度为３,拥塞度为４．于是所有现存的基于四度网孔的并行算法都可以毫不费力地移植到三度网孔中且只有常数的减速比．墙式网孔可以通过边界节点回卷相连而产生墙式环托,它是点     

保持视觉外观特征的网格简化

针对附有纹理属性的网格模型,提出并实现了一种保持模型基本外观和形状特征的多分辨率网格简化算法.采用半边折叠操作,综合考虑了网格模型半边的几何重要性和纹理属性重要性,将其作为各半边的折叠代价来确定模型中所有边的折叠顺序.预先对网格模型中的边界边和纹理边进行标记,并在简化过程中进行加权处理.实验结果表明,即使在急剧的模型简化后,该方法仍能很好地保持原有模型的视觉外观和形状特征.