自由曲面的平面映射原理及其算法

论述空间曲面的平面映射定义及其变形；分析了空间曲面的几种近似映射方法，并同时分析了各种映射方法的优缺点；针对在空间曲面应用最广泛的NURBS曲面，提出了NURBS曲面的混合映射算法；讨论了小曲率NURBS曲面平面映射的算法，并将该算法成功地应用于花纹鞋模的设计中。     

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。     

NURBS曲面C1连续参数优化算法

为了在NURBS曲面上生成满足C1连续的近似弧长参数化等参线,将NURBS曲面4条边界的积分能量函数作为目标函数,提出一种基于分段三次重新参数化的曲面参数优化算法.首先推导出NURBS曲面4条边界的参数表达式;然后使用Hermite基函数变换NURBS曲面u和v方向参数,重新计算参数化等参线,导出变换后的4条边界的积分能量函数;最后通过数值优化算法计算出曲面的最优参数表示.在MFC和OpenGL环境下实现了多个NURBS曲面的等参线分布和纹理映射实验,结果表明该算法是有效的.     

基于多边形转换函数与NURBS的雕刻型面建模

根据平面任意闭合图形的图像,用多边形到函数的转换方法确定雕刻型面的部分深度信息,并用非均匀有理B样条(NURBS)曲面对这些参数进行插值,实现了对雕刻型面的建模.     

点模型曲面的调和映射参数化

利用调和映射的平面和球面中值性质，提出了确定点模型曲面参数化映射中有关权因子的两种新方法，设计了能够达到内在变形较小的相应参数化方法，并将参数化方法应用于点模型曲面上的纹理映射．实验和统计结果表明，文中方法是比较有效的点模型曲面的参数化方法．     

复合材料模压成型计算机模拟

为了解和掌握纺织复合材料织物的三维曲面模压成型性能,本文利用NURBS方法,对织物的半球成型进行了模拟。由于NURBS插值曲面不能直接反映织物成型后纱线的空间位置,而且运算十分复杂,因此,提出利用NURBS插值曲线模拟织物成型的方案。由此得到的模拟效果图不但具有很强的三维立体感,而且可知织物中经纬纱交织点在织物成型后的空间位置,并实现成型疵点预测,为成型工艺设计提供理论指导。该方法同样可用于其它平面织物的成型模拟。     

NURBS 曲面自由型特征处理方法研究

NURBS曲面自由型特征因不具有确定的参数、准确的边界,使其表示、编辑及操作十分困难。基于一种新的小波多分辨率分析技术将NURBS曲面从单一尺度几何表示的空域变换为频域的表示形式,借助于滤波器组将模型的整体结构和局部细节变换为其全局和局部多分辨率自由型特征,实现了对NURBS曲面的自由型特征的编辑、操作和控制。该方法不仅能提高NURBS曲面几何建模的效率,而且可以克服传统NURBS曲面建模的繁琐和费时。     

基于波前法的参数曲面有限元网格生成算法

为克服参数曲面有限元网格生成中的单元形状映射畸变问题,提出一种曲面有限元网格自动生成算法.该算法由弹性矢量确定曲面上新节点的生成方向和空间位置,利用相应的参数域网格进行新单元拓扑相容性判断.在生成闭曲面网格时,通过添加参/虚边界棱边对闭曲面边界进行调整,确保闭曲面边界信息相对其参数域的完整性;在给出闭曲面极点初始化方法和适当设置单元边线段相等条件的基础上,该算法适用于各种不同形式闭曲面的网格自动生成.实验算例表明,文中算法可生成质量良好的参数曲面和组合面有限元网格.     

沿参数曲面的均匀变形方法

基于参数曲面控制的物体自由变形是一项实用的技术，在已有的方法中，待变形物体被直接主控制曲面的参数空间，由于映射的非线性，导致物体变形同扭曲现象，本提出了一种基于参数曲面控制的均匀变形方法，新方法中，变形控制曲面首先以等距或局部等怕方式展开为平面，然后经由平面的线性映射，将待为形物体嵌入控制曲面的参数空间中，从而产生符合控制曲面形状的局部均匀变形，实验结果表明，本方法所产生的结果是令人满意的。     

Direct boolean intersection between acquired and designed geometry

In this paper, a new shape modeling approach that can enable direct Boolean intersection between acquired and designed geometry without model conversion is presented. At its core is a new method that enables direct intersection and Boolean operations between designed geometry (objects bounded by NURBS and polygonal surfaces) and scanned geometry (objects represented by point cloud data).We use the moving least-squares (MLS) surface as the underlying surface representation for acquired point-sampled geometry. Based on the MLS surface definition, we derive closed formula for computing curvature of planar curves on the MLS surface. A set of intersection algorithms including line and MLS surface intersection, curvature-adaptive plane and MLS surface intersection, and polygonal mesh and MLS surface intersection are successively developed. Further, an algorithm for NURBS and MLS surface intersection is then developed. It first adaptively subdivides NURBS surfaces into polygonal mesh, and then intersects the mesh with the MLS surface. The intersection points are mapped to the NURBS surface through the Gauss-Newton method.Based on the above algorithms, a prototype system has been implemented. Through various examples from the system, we demonstrate that direct Boolean intersection between designed geometry and acquired geometry offers a useful and effective means for the shape modeling applications where point-cloud data is involved.     

Surface Graph Sketching

The production of patterns and designs upon surfaces has received only limited attention, with texturing techniques being accepted as adequate. Texturing, however, can be a very unsatisfactory and clumsy method of producing complex and accurate designs upon a surface, even more so with surfaces such as NURBS where a texture may appear very much distorted when mapped to a surface. This paper introduces a new approach called surface graph sketching which draws upon ideas from planar graph sketching for the construction of complex curve networks across parametrically defined surfaces. Surface curves can be created by a number of methods and stored in the parameter space of the surface thereby allowing intricate and more importantly accurate surface designs to be created. Regions of the surface may be assigned a property such as colour or texture, or cut away to produce holes. Surface graph sketching has a number of applications, in the design of trimming curves, surface patterning and texture map definitions.     

A novel plane extraction approach using supervised learning

This paper presents a novel approach for the classification of planar surfaces in an unorganized point clouds. A feature-based planner surface detection method is proposed which classifies a point cloud data into planar and non-planar points by learning a classification model from an example set of planes. The algorithm performs segmentation of the scene by applying a graph partitioning approach with improved representation of association among graph nodes. The planarity estimation of the points in a scene segment is then achieved by classifying input points as planar points which satisfy planarity constraint imposed by the learned model. The resultant planes have potential application in solving simultaneous localization and mapping problem for navigation of an unmanned-air vehicle. The proposed method is validated on real and synthetic scenes. The real data consist of five datasets recorded by capturing three-dimensional(3D) point clouds when a RGBD camera is moved in five different indoor scenes. A set of synthetic 3D scenes are constructed containing planar and non-planar structures. The synthetic data are contaminated with Gaussian and random structure noise. The results of the empirical evaluation on both the real and the simulated data suggest that the method provides a generalized solution for plane detection even in the presence of the noise and non-planar objects in the scene. Furthermore, a comparative study has been performed between multiple plane extraction methods.     

基于投影法的隐式曲面多边形化

绘制多边形可借助图形系统的硬件来实现,因此,隐式曲面的多边形化是隐式曲面绘制的主要方法,文中提出了基于投影法的隐式曲面多边形化的方法,先在平面进行网格划分,再把平面上所有多边形面片映射到隐式曲面上,该方法对隐式曲面上有全部投影,部分投影和没有投影的多边形面片分别进行了讨论,该方法也适用于绘制隐式载剪曲面。     

NURBS曲面上积分曲率线的B样条表示

对NURBS曲面的曲率线的积分进行了系统的公式推导，并利用NURBS曲面的离散法向量有效地简化了曲面第二基本量的计算，加速了Euler法迭代求解曲率线微分方程的过程；在求得曲率线上的离散点集以后，应用奇异混合插值技术，在可控精度内把曲率线用显式直接表示为位于NURBS曲面上的B样条曲线．文中的思想与算法有助于曲率线技术在计算机辅助几何设计及曲面造型中的使用与推广．     

Fitting NURBS spherical patches to measured data

Algorithms and empirical studies for fitting spherical and planar NURBS patches to random data are presented. Algebraic as well as geometric methods are discussed leading to efficient techniques for surface as well as patch fitting. An automatic fitter is also presented that determines whether a plane or a sphere fit is optimal, computes the appropriate entities, and clips the geometry to obtain a NURBS sphere or plane fit. It is argued that patch fitting is necessary in order to avoid numerical problems due to pole and seam problems.     

基于遗传算法的平面图平面正交直线画图算法

提出了一种基于遗传算法的新的平面图平面正交直线画图算法,算法将平面图画图问题转化为约束优化问题,根据画图问题选定的美观准则构造约束函数,用遗传算法求解目标函数的最优解的近似值,从而得到平面图的平面正交直线画法。新算法的优点是方法简单,易于实现,画出的图形美观,算法稳定性好。实验结果表明,画图算法的最终结果不依赖于图的初始状态。