基于隐式曲面的三角网格模型等距算法

针对三角网格模型,提出了一种基于隐式曲面的等距算法.该算法首先对三角网格模型进行拓扑重建,然后对顶点进行八叉树采样,由采样点及采样点的单位法矢点来构建隐式曲面,将隐式曲面等距,最后将原模型的顶点投影到等距曲面得到投影点,根据先前建立的拓扑关系,将投影点三角网格化得到等距后的三角网格模型.该算法在一定数值范围内避免了等距模型自交问题,而且等距模型三角网格均匀,质量高.     

网格曲面数控加工编程分型线提取算法

针对复杂网格曲面分型线提取精度和效率不高的问题,根据非封闭自由曲面和封闭自由曲面的拓扑信息和几何特点,提出了2种基于投影方法的分型线提取算法. 对非封闭模型,首先将模型投影到平面并重新三角网格化,然后提取投影三角网格的边界,最后以平面三角网格的边界为检索信息在原始网格中检索得到自由曲面的分型线. 对封闭模型,根据模具分模的几何原理,提出通过建立封闭自由曲面凹模和凸模离散几何模型的方法提取封闭自由曲面的分型点,然后通过一环邻域点搜索法对分型点排序,得到分型线. 实验结果和数据分析表明,两种方法可以精确、高效地提取非封闭和封闭自由曲面的分型线,并可以确保分型点都是三角网格曲面的顶点.     

基于交互的B样条曲面重建与误差计算

基于三角网格模型的B样条曲面重建技术得到深入发展,计算与显示重建后的B样条曲面与原始测量三角网格之间的误差对分析曲面重建品质有重要作用。一种较为实用的B样条曲面重建方法是对三角网格模型进行四边界区域划分后进行栅格式采样,再根据采样点进行B样条曲面拟合。针对这种重建方法,研究了一种建立三角网格顶点与四边界区域对应关系的算法,再用离散的方法计算点到对应曲面的距离误差,最后用线性插值方法实现误差彩色．云图的显示。     

基于变分隐式曲面的三角网格孔洞修补

针对三角网格模型存在的孔洞问题提出一种基于变分隐式曲面的孔洞修补算法。首先，利用孔洞边界信息构造插值孔洞边界的变分隐式曲面并将其网格化，得到初始孔洞网格，再利用边界点裁剪初始孔洞网格，最后把裁剪后的孔洞网格与初始网格拓扑合并，完成孔洞修补。算法充分考虑了孔洞周围的信息，使得孔洞网格与原始网格光滑连接，取得了比较好的效果。     

反求工程中隐式曲面的三维网格自动精确恢复新算法

提出了一种基于点云数据的隐式曲面三维网格自动精确恢复新算法。该算法首先对恢复的初始三角形网格进行区域分割和边界重构,将隐式曲面的三角形网格分离出来,然后对恢复的隐式曲面表面的初始逼近网格从3个方面进行优化:即将初始逼近网格的曲率控制与网格面的拓扑一致性调整;调整网格顶点法矢与交互式分割;补偿网格抽样率。通过该算法能将隐式曲面的三角形网格自动精确恢复。然后进行网格光顺,输出优化的CAD模型。实例证明了该方法的正确性、可行性和实用性。     

全冠义齿网格过渡算法研究与应用

针对全冠义齿数字化设计时外冠和内冠过渡融合的问题,提出了一种新的网格过渡算法。首先提取外冠和内冠网格边界进行桥接形成封闭孔洞;然后根据定义的三角片插入规则插入新的三角片填充孔洞,构造初始过渡网格;最后投影到由边界顶点插值得到的隐式曲面上,投影点构成新的过渡网格,将其与外冠和内冠拓扑合并形成完整的全冠义齿修复体。用过渡算法得到的网格面片分布均匀,三角片质量较好,而且过渡边界光顺自然,具有较好的连续性。     

基于变分隐式曲面的三角网格孔洞修补

针对三角网格模型存在的孔洞问题提出一种基于变分隐式曲面的孔洞修补算法。首先,利用孔洞边界信息构造插值孔洞边界的变分隐式曲面并将其网格化,得到初始孔洞网格,再利用边界点裁剪初始孔洞网格,最后把裁剪后的孔洞网格与初始网格拓扑合并,完成孔洞修补。算法充分考虑了孔洞周围的信息,使得孔洞网格与原始网格光滑连接,取得了比较好的效果。     

任意拓扑三角网格模型的Loop细分曲面重建系统

提出一种从任意拓扑密集的三角网格模型拟合Loop细分曲面系统，包含对原网格模型进行特征识别，把保持了原有特征的简化网格和拓扑优化所获得的网格作为拟合初始控制网格。系统通过对控制网格顶点的循环修正和局部自适应细分来求解最终拟合细分曲面控制网格，避免了求解线性方程组，提高了拟合曲面的质量，实现了在给定精度下用较少的控制网格反映物体细节特征的分片光滑（片内除奇异点C^1外其余C^2连续）的Loop细分曲面重建。实例表明，Loop细分曲面重建系统对于任意拓扑海量三角网格测量数据的细分曲面重建是高效可行的。     

基于径向基函数的多种类型孔洞修补算法研究

利用径向基函数对散乱数据点进行曲面重建受到越来越多学者的关注,并被应用于解决网格模型中的孔洞修补问题。本文在实现径向基函数对简单孔洞进行修补的基础上,进一步研究了对多种类型孔洞的修补问题,提出了统一的修补算法:首先利用填充算法对孔洞进行填充,然后使用径向基函数建立孔洞区域的隐式曲面,最后将新增加的三角片顶点调整到建立的隐式曲面上,并给出了修补结果的优化处理。实例证明,该算法适用性好,对不同类型孔洞的修补效果理想。     

基于三角Bézier曲面的三角网格模型光顺算法

针对三角网格模型整体光顺效果较差的问题,提出一种基于三角Bézier曲面的三角网格模型光顺算法,该算法采用R*S树组织三角网格模型的动态索引,对三角网格模型进行精确保形精简,根据保形精简后三角网格模型型面几何特征构造整体G1连续三角Bézier曲面,将其作为三角网格模型的光顺参考曲面。通过将三角网格顶点映射于光顺参考曲面上,实现三角网格模型的光顺处理。实例证明该算法可对各种复杂型面的三角网格模型获得理想的整体光顺效果,并有效保留原模型的型面特征。     

A topological-free method for three-axis tool path planning for generalized radiused end milled cutting of a triangular mesh surface

A tool path generation method for a sculptured surface defined by a triangular mesh is presented. Existing tool methods require extensive computer processing power mainly because surface topology for triangular meshes is not provided. The three-axis tool path planning method presented in this paper for generalized radius end mills avoids this problem (and does not need topological information) by offsetting each triangular facet individually. Offsetting a single triangle results in many more triangles, many of which are redundant, increasing the time required for data handling in subsequent steps. To avoid the large number of triangles, the proposed method creates a bounding space to which the offset surface is limited. Applying the boundary space limits the size of the offset surface resulting in a reduction in the number of triangular surfaces generated. The offset surface generation may still result in unwanted intersecting triangles. The tool path planning strategy addresses this issue by applying hidden-surface removal algorithms. Simulation and machining tests are used to validate the tool paths generated using this method.     

General 3D offsetting of a triangular net using an implicit function and the distance fields

A novel approach which uses the distance fields based on cell subdivision and an implicit surface interpolation based on the radial basis function is proposed in order to get an accurate and error-free offset model of arbitrary shapes composed of a large number of triangle meshes. In the method, the space bounding the original model is divided into smaller cells. For the efficient calculation of distance fields, valid cells which will generate a portion of offset model are selected previously by the proposed detection algorithm. These valid cells are divided again into much smaller voxels which assure required accuracy. At each voxel, the distance fields are created by calculating the minimum distances between the corner points of voxels and the triangle meshes. For the more efficient calculation of distance fields, valid vertices among the triangle meshes which will generate minimum distances with current cell are selected by checking the intersection between current cell and a cone prism generated at each vertex of triangle meshes. In addition, a new approach based on an implicit surface interpolation scheme is proposed to perform two types of offsetting operations including uniform and non-uniform offsetting in the same framework. In the method, a smooth implicit surface is generated from the discrete offset distance values given by the user. After generating the whole distance fields, the offset surface was constructed by using the conventional marching cube algorithm together with mesh smoothing scheme. The effectiveness and validity of this new offset method was demonstrated by performing numerical experiments for the various types of triangle meshes.     

Surface offsetting using distance volumes

Proposed in this paper is a new approach for offset surface construction using three- dimensional (3D) distance volumes. After converting an original compound surface into a triangular mesh, the approach creates a distance volume of the triangular mesh. With this distance volume and a given offset value, it extracts the offset points in each slice to create a sequence of two dimensional (2D) cross-sections. The approach then performs offset surface construction using the serial cross-sections. For more accurate and efficient computation of the distance volume, the concept of space division is combined with the concept one of distance propagation to the whole space of interest. The resulting offset surface is a G¹ composite surface consisting of three kinds of surfaces: skinned, capped, andor branched surfaces. The proposed approach provides offset surfaces that are accurate and free of degeneracy. Some experimental results demonstrate its usefulness and quality.     

基于特征点的离散建模偏置技术研究

针对三角网格模型偏置过程中出现的自交和断裂等问题,提出了一种基于特征点的离散建模偏置方法。对网格模型顶点进行几何特征分类,并讨论了不同类型顶点的偏置规则。根据定义的顶点类型、法矢信息及给定距离,生成偏置点集。通过基于体素表示的条柄检验方法,滤除偏置点集中的内部点,实现自交处理。结果表明,生成的模型网格比较均匀,质量较高,在一定范围内能够满足偏置模型的自交处理要求。     

The development of a technique for 3D complex surface reconstruction from unorganized point cloud

In this paper, we propose a new neural network based on our two-level adaptive hierarchical clustering algorithm. The algorithm is to manage unorganized points, so that the triangular mesh models can be correctly obtained by applying the triangular mesh creation algorithm. We also develop adaptive self-flipping triangle edges to improve triangular mesh structure. Only one parameter, the maximal edge length of triangle, is needed in the neural network. The proposed two-level consists of the first level for clustering the cloud of points that has same order of the maximal edge length into a same cluster and the second level for generating triangular surface model or drape surfaces over the points of the same cluster. The normal vector for the generated triangular 3D surface model can be obtained from the second level. This helps to generate the STL file or stereolithography format. From the experimental results it can be shown that the proposed method is very effective for clustering unorganized point clouds for generating a triangular mesh of complex surfaces.     

自由曲面自适应数字化及应用研究

自由曲面的数字化是自由曲面重建的关键技术之一。如何合理地对自由曲面进行采样 ,将关系到曲面重建精度和测量效率等重要问题。通过引入初始曲面概念 ,提出了基于物体重心的采样算法模型。该算法具有保存曲面拓扑信息和网格自组的功能 ,能够较准确地反映曲面的形状特征。     

Generating Tool Paths for Free-Form Pocket Machining Using z-Buffer-Based Voronoi Diagrams

Voronoi diagrams for closed shapes have many practical applications, ranging from numerical control machining to mesh generation. Curve offsetting based on Voronoi diagrams avoids the topological problems encountered in traditional offsetting algorithms. In this paper, we present a new procedure for generating tool paths using z-buffer-based Voronoi diagrams specially to deal with free-form shaped pockets. Using a z-buffer, a proposed algorithm effectively extracts the topological information on the Voronoi diagram, and generates the geometric information on the Voronoi edges approximately. These Voronoi edges are refined using a numerical algorithm. This method is independent of curve type and is applicable to any pockets with parametric curve boundaries that are twice differentiable.     

曲面有限元网格引线织就生成法

离散曲面边界并初始化可出发构造新单元的单元边线段序列,依次从序列中的单元边线段出发,采用线段定向布点法或圆定向布点法,构造用于确定新节点生成位置的待选点集。从待选点集或曲面上已有的网格节点选择合适的点参与新单元的构造,并利用曲面参数域检查新单元的网格拓扑相容性。随节点、单元边线段和新单元交替生成,最终生成符合有限元分析要求的曲面网格。关键区域网格的自适应加密,则采取网格密度规划方式,通过构造曲面有限元自适应网格单元尺寸信息场来加以实现。