平面图形在NURBS曲面上的映射

针对现有曲面图形映射方法实用性不强的缺陷,提出了一种NURBS曲面图形映射方法。基于曲面外形设计或选取适当的平面图形,求出平面图形在坐标平面内的极限位置,根据曲面上映射图形的位置和大小对NURBS曲面的节点向量和首末参数进行调整,将平面图形嵌入NURBS曲面参数域的相应位置,利用NURBS理论将平面图形从曲面参数域映射到曲面。验证实例表明,算法原理简单、性能稳定,具有较强的适应性和实用性。     

双二次NURBS曲面间的最短距离

利用双二次Bezier曲面为非负的充要条件，给出了分别位于两张双二次NURBS曲面上的点是否为这两张曲面间距离最近的点的判别方法．曲面非负是指在此显式曲面上没有位于XOY平面下方的点．在这一基础上，得到了计算双二次NURBS曲面间最短距离的一个算法．最后，给出了实验结果并将文中算法与采用分层数据结构的常用算法进行了比较。     

等距曲面的NURBS放样插值方法

本文给出了等距曲面的一种NURBS放样插值生成方法，该方法主要是在原始NURBS曲面上取得一个能较好反映曲面特征的型值点阵，再交这个型值点阵按某种算法矢方向外推，从而得到原始曲面的等距曲面上的型值点阵，然后，再用NURBS放样插值曲面来逼近等距曲面，本文给出的算法几何意义明显，易于编程实现，且得到的等距曲面其u向和v向参数曲线仍是NURBS曲线，且具有C^2连续性，最后，给出了一个实例。     

NURBS边界曲面直接生成法

由于非均匀有理B样条(NURBS)曲面的复杂性,传统NURBS边界曲面的生成是先构造孔斯曲面,再由孔斯曲面向NURBS曲面转换得到,其操作过程比较烦琐。针对此问题,提出了NURBS边界曲面直接生成算法,该算法根据给定的四条NURBS边界曲线,结合孔斯曲面生成方法直接插值生成NURBS曲面,从而避免了通过孔斯曲面向NURBS曲面转换所带来的计算代价,因此同传统方法相比,具有较低的计算代价。实验结果表明:该算法简化了曲面生成步骤,减少了曲面转换过程的计算量,生成的曲面边界信息明确,且连续性好。     

逆向工程中NURBS曲面与直线交点快速计算

给出了一个能够方便地判断NURBS曲面片与空间直线的交点个数,并且超线性收敛的快速迭代算法。计算Krawczyk算子判断给定的NURBS曲面片和空间直线有无交点和有几个交点。再使用拟牛顿迭代法求出NURBS曲面片和空间直线上的交点。该算法在用点云数据检测曲面重构的误差时具有快速、准确的特点。     

NURBS扫描体的逼近算法研究

提供了一种NURBS扫描体的逼近方法。该方法主要步骤：(1)通过系列平面切割，把NURBS曲面(实体)进行降维处理，变成平面曲线；(2)为曲线设置局部标架；(3)在局部标架下求出每一曲线在每一时刻的极值点后将其转换成原曲线的奇异点；(4)使用marching cubes算法剔除扫描体内部点，保留扫描体边界上的奇异点；(5)由所有保留点拟合成奇异曲面。本算法能较好地逼近NURBS扫描体，其逼近精度可通过控制切割精度和扫描过程中时间间隔的选取而得到有效控制。     

插值边界曲线的NURBS 近似极小曲面设计

探索性地设计了一个插值给定边界曲线的NURBS 近似极小曲面算法,弥补了当前NURBS 系统无法有效地设计工程所急需的一般NURBS 极小曲面的缺陷.运用NURBS 曲面的节点插入、Hybrid 多项式逼近等多种技术,将NURBS 曲面转化为相对简单的分片Bézier 曲面求解,并运用各子曲面片的控制顶点优化、整体曲面不断更新的迭代方法,成功地得到高精度的近似分片Bézier 极小曲面.最后,可以按用户的各种要求选择运用相应不同的迭代逼近算法,求取插值给定边界曲线的近似NURBS 极小曲面.     

基于3D曲面模型的数字水印算法

本文给出了一种NURBS曲面模型的三维数字水印算法.该算法不直接将水印信息嵌入到NURBS曲面的参数中,而是对原始NURBS曲面模型进行修改,通过映射成虚拟2D图像,利用已有的DCT域图像水印嵌入算法将信息嵌入到2D图像中,再对2D图像进行提取产生新的NURBS曲面水印模型.该算法对于控制顶点、节点向量的改变以及模型表面的近似等操作具有鲁棒性.     

基于映射法和Delaunay方法的曲面三角网格划分算法

提出一种曲面三角网格划分算法，该算法在曲面参数域中生成Delaunay类型的网格，然后将其映射到空间曲面，为了抵消映射过程中变形的影响，采用空椭圆准则代替传统的空间准则，并给出椭圆的构造算法以及椭圆圆心的定位方法，这些方法充分考虑到映射变形和求解速度，实验结果表明，该算法生成满意的曲面网格，具有一定的应用价值。     

NURBS曲面生成算法及仿真研究

讨论了一种生成NURBS曲面的算法,用C语言实现了该算法,并利用MATLAB进行仿真对该算法进行验证。在算法中讨论了曲面及其等距面生成方法以及曲面生成技术中相关的一些技术,如曲线段间参数过渡、曲面生成模式、曲面生成的实时性、改变曲面的形状等。仿真结果证明了算法的有效性。     

同形映射下的曲面场景的匹配算法的性能分析

针对移动机器人在曲面场景的匹配问题中,同形约束用于解决极约束产生的匹配模糊性问题和发现新的匹配点.实际上是平面块对曲面进行近似逼近的过程.逼近程度和逼近性能需要有指标进行定性和定量的衡量.故提出了两种性能评价指标:平均映射误差和平均映射匹配对.仿真实验结果的分析证明,场景深度变化或者场景距离摄像机的距离变化,对立体匹配算法性能本身不受影响,但映射和建立匹配关系时所需要的同形矩阵的数量不同.而且,随着特征点的稠密度提高,曲面场景的稳定性降低.可随着迭代过程的进行,算法本身结果还趋于稳定.     

A scanline algorithm for displaying trimmed surfaces by using Bézier clipping

Displaying objects with high accuracy is necessary for CAGD (computer-aided geometric design) and for the synthesis of photo-realistic images. Traditionally, polygonal approximation methods have been employed to display free-form surfaces. They bring on low accuracy of display not only in shape, but also in intensity of objects. In this paper, a scanline algorithm to directly display parametric surface patches, expressed by trimmed Bézier surfaces, without polygonal approximation is proposed. In the method proposed here, curved surfaces are subdivided into subpatches with curved edges intersecting with a scanline, and the intersections of every subpatch and the scanline are calculated. This method is extremely robust for calculating the intersections, which can be obtained with only a few iterations; the Bézier clipping method is used for the iteration. Anti-aliased images with shadows and texture mapping are given to show the effectiveness of the method proposed.     

一类极小曲面的控制网格表示

给出了平面曲率线极小曲面的拟Bézier和拟B样条控制网格表示,以悬链面及Enneper曲面为特殊形式,实现了由悬链面到Enneper曲面的动态变形.该工作为将极小曲面引入CAGD/CAD造型系统,并利用拟de-Casteljau算法生成极小曲面提供了一个有力的工具.     

一种应用平面展开完成任意曲面纹理映射的新方法

本文提出一种新的纹理映射方法。该方法在任意曲面和它的平面展开之间定义映射,并用映射特征来评价映射精度,能有效地减少任意曲面纹理映射中的映射变形误差。     

Two-Part Texture Mappings

Most published techniques for mapping two-dimensional texture patterns onto three-dimensional curved surfaces assume that either the texture pattern has been predistorted to compensate for the distortion of the mapping or the curved surfaces are represented parametrically. We address the problem of mapping undistorted planar textures onto arbitrarily represented surfaces. Our mapping technique is done in two parts. First the texture pattern is embedded in 3-space on an intermediate surface. Then the pattern is projected onto the target surface in a way that depends only on the geometry of the target object (not on its parameterization). Both steps have relatively low distortion, so the original texture need not be predistorted. We also discuss interactive techniques that make two-part mapping practical.     

Computation of medial axis and offset curves of curved boundaries in planar domain

In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between two boundaries and its medial axis have been proposed based on the moving Frenet frames and Cesaro’s approach of the differential geometry. Two pairs of adjoint curves have been formed and the geometrical model of the medial axis transform of the planar domains with curved boundaries has been established. The relations of position mapping, scale transform and differential invariants between the curved boundaries and the medial axis have been investigated. Based on this model, a tracing algorithm for the computation of the medial axis has been generated. In order to get the accurate medial axis and branch points, a Two_Tangent_Points_Circle algorithm and a Three_Tangent_Points_Circle algorithm have been generated, which use the results of the tracing algorithm as the initial values to make the iterative process effective. These algorithms can be used for the computation of the medial axis effectively and accurately. Based on the medial axis transform and the envelope theory, the trimmed offset curves of curved boundaries have been investigated. Several numerical examples are given at the end of the paper.     

A numerical solution to the generalized mapmaker's problem:flattening nonconvex polyhedral surfaces

Methods are described to unfold and flatten the curved, convoluted surfaces of the brain in order to study the functional architectures and neural maps embedded in them. In order to do this, it is necessary to solve the general mapmaker's problem for representing curved surfaces by planar models. This algorithm has applications in areas other than computer-aided neuroanatomy, such as robotics motion planning and geophysics. The algorithm maximizes the goodness of fit distances in these surfaces to distances in a planar configuration of points. It is illustrated with a flattening of monkey visual cortex, which is an extremely complex folded surface. Distance errors in the range of several percent are found, with isolated regions of larger error, for the class of cortical surfaces studied so far     

基于两步法的交互式纹理映射研究

两步纹理映射方法将映射过程分解为S映射与O映射两步进行.针对两步纹理映射方法研究中复杂物体表面纹理映射时出现的变形问题,采用B样条曲面代替简单的中间映射媒介,用它近似地包裹在三维物体的外表面,将纹理通过某种方式映射到曲面上实现参数化.基于两步映射方法提出了一种交互式纹理映射的算法.该算法允许用户交互选择贴图范围,通过控制B样条曲面实现对映射效果的调整.实验结果表明,该算法可显著提高纹理映射质量,纹理贴图效果良好.     

Bounded Radiosity – Illumination on General Surfaces and Clusters

Traditionally, Radiosity algorithms have been restricted to scenes made from planar patches. Most algorithms for computing form factors and the subdivision criterion for hierarchical methods implicitly assume planar patches. In this paper, we present a new radiosity algorithm that is solely based on simple geometric information about surface elements, namely their bounding boxes and cone of normals. Using this information allows to compute efficient error bounds that can be used for the subdivision oracle and for computing the energy transfer. Due to the simple interface to geometric objects, our algorithm not only allows for computing illumination on general curved surfaces, but it can also be directly applied to a hieararchy of clusters. Several examples demonstrate the advantages of the new approach.     

Parting line formation by slicing a 3D CAD model

An effective computer-aided parting line/surface formation algorithm can increase the overall efficiency in the mould design and manufacturing processes. The presence of free-form surfaces in a product model imposes a burden on mould makers to determine the parting line and parting surfaces. Previously proposed algorithms, although available, are few, and mainly deal with product with planar or simple curved surfaces. A new algorithm, which adopts an uneven slicing on the product model, is proposed. The algorithm provides a quick and effective way to locate the parting line and parting surface of a free-form product model.