截面线数据的曲面蒙皮重构技术研究

为了保持曲面形状的平滑性，在曲面重构过程中经常会出现曲面形状的变异，针对带有精确截面信息的截面线数据的三维曲面重构问题，提出了一种NURBS曲面蒙皮重构方法。该方法产生一个连续的NURBS曲面，改进了传统曲面蒙皮重构方法在处理非均匀截面数据点时出现的一系列问题，通过实际系统验证了该方法的有效性。     

基于边界采样技术的插值Loop细分方法

本文在分析了传统几何造型的弊端及开曲面造型中光滑边界曲线的插值要求后,针对细分曲面造型方法中较常用的Loop细分,提出了基于边界采样技术的插值细分曲面造型方法。该方法一方面利用了细分曲面造型的优点,如算法简单、可表达任意拓扑结构等;另一方面又满足了工程应用中插值边界曲线的要求。文中详细讨论该算法的步骤,并通过示例验证了该算法的有效性和实用性。     

基于四边形网格的可调细分曲面造型方法

提出了一种基于四边形网格的可调细分曲面造型方法。该方法不仅适合闭域拓扑结构，且对初始网格是开域的也能进行处理。细分算法中引入了可调参数，增加了曲面造型的灵活性。在给定初始数据的条件下，曲面造型时可以通过调节参数来控制极限曲面的形状。该方法可以生成C1连续的细分曲面。试验表明该方法生成光滑曲面是有效的。     

基于C—B样条的Catmull—Clark细分曲面

为了解决Catumull-Clark细分曲面在工程上难以推广的问题，给出了一种基于C－B样条的Catumull-Clark细分曲面的算法，C－B样条曲线是B样条曲线的拓广，但它们的形状依赖于参数α，由于新的曲面细分方法充分利用C－B样条能够精确表示圆，椭圆等规则形体的特性，因而使通过此方法生成的细分曲面，除了在奇异点处能保持二阶导数连续外，还能够像C－B样条曲线，曲面一样，精确地表示圆柱等常规曲面，统一工程曲面等的造型，同时它仍然保持细分曲面的造型特点，即能够解决NURBS曲面难以处理的任意拓扑结构的造型问题，另外，还可依赖控制参数α的调节作用来增加造型的自由度，而且当α→0时，它们就退化成Catmul-Clark细分曲面，在工程图形上的应用实例表明，这种算法简单，有效。     

基于双参数四点细分法的曲面造型

将双参数四点细分曲线方法进行推广，提出了基于双参数四点细分法的曲面造型方法，并对其收敛性进行了分析。该方法通过对两个参数的适当调节能够较容易地控制极限曲面的形状，极限曲面能够达到C4连续，可以应用到对曲面的连续性要求较高的曲面造型中去。在给定初始数据的条件下，可通过对形状参数的适当选择来实现对极限曲面的形状调整和控制，试验表明该算法生成光滑曲面是有效的。     

基于C-B样条的Catmull-Clark细分曲面

为了解决 Catum ull- Clark细分曲面在工程上难以推广的问题 ,给出了一种基于 C- B样条的 Catumull-Clark细分曲面的算法 .C- B样条曲线是 B样条曲线的拓广 ,但它们的形状依赖于参数 α.由于新的曲面细分方法充分利用 C- B样条能够精确表示圆、椭圆等规则形体的特性 ,因而使通过此方法生成的细分曲面 ,除了在奇异点处能保持二阶导数连续外 ,还能够像 C- B样条曲线、曲面一样 ,精确地表示圆柱等常规曲面、统一工程曲面等的造型 ;同时它仍然保持细分曲面的造型特点 ,即能够解决 NU RBS曲面难以处理的任意拓扑结构的造型问题 ,另外 ,还可依赖控制参数 α的调节作用来增加造型的自由度 ,而且当 α→ 0时 ,它们就退化成 Catm ul- Clark细分曲面 .在工程图形上的应用实例表明 ,这种算法简单、有效 .     

一种LOOP曲面细分算法研究

本文研究了曲面造型中的细分曲面造型方法,分析了细分曲面造型的优点。基于多边形网格的细分方法分析了基于三角形网格1-4分裂的Loop细分模式的优点,并实现了基于Loop细分模式的曲面造型。利用Loop细分模式进行两次细分,得到不同网格密度的数据,最后本文给出了细分前后的点数、边数以及面数,并显示了细分前后的点的效果图。     

蜂窝细分

给出了一类新颖的基于六边形网络的细分方法，该方法拓广了细分曲面的种类，被形象地称为蜂窝细分法，通过引入中心控制点的概念，使蜂窝细分具有参数选取灵活，形状控制容易，网格复杂性增长缓慢，适用范围广等优点，分析了蜂窝细分方法的极限性质以及参数选取规则，可保证细分曲面处处达到切平面连续，并在适当条件下具有插值能力，该方法适用于动画造型和工业造型设计。     

自适应细分方法进行曲面造型*

充分利用可调控CatmullClark细分规则与均匀的CatmullClark细分规则的优点,提出了自适应细分方法。该方法简单,比传统的单一细分方法有更好的灵活性,通过适当调节控制因子,可使得曲面造型比较灵活。通过分析曲面上点的曲率来控制细分,可以在较低的细分次数下达到良好的曲面造型效果,为曲面造型提供了一个新的方法。     

基于截面数据的C1插值融合曲面重建

为了避免NURBS曲面重建需要进行节点矢量相容的问题，提出了一种双方向融合插值的[C1]参数曲面重建方法，该方法先后分段插值截面上连续的数据点、截面曲线以构造样条曲线和曲面片，并引入融合算法进行曲线、曲面拼接，从而得到光滑的待建曲面。该方法不会产生由节点插入所带来的大量的数据冗余以及复杂的计算过程，同时采用了融合的思想来处理曲线、曲面的拼接，改良了传统参数曲线、曲面拼接方法需要满足边界条件的缺陷。     

Reconstruction of B-spline skinning surface from generalized cylinder mesh

We propose a novel method to reconstruct B-spline surfaces from generalized cylindrical meshes by skinning. Skinning is a well known surface creation technique and has been used in CAD and CG modeling. However, there are few papers which address the issue of automated creation and preparation of sectional curves for skinning. Although our method is only applicable to generalized cylindrical meshes, there are many real world objects which can be created or reconstructed by skinning. The proposed surface reconstruction method is fully automated with minimal user interventions. We have evaluated the validity of this method by reconstructing B-spline surfaces from various polygonal meshes varying in shapes and geometries. The final results show the effectiveness of our proposed method.     

自由曲线曲面的任意次非均匀细分

提出一种有效的建模自由曲线曲面的非均匀细分算法。首先在节点插入技术基础上推导出任意次自由曲线的非均匀细分规则,然后把它推广到张量积曲面得到任意次自由曲面的非均匀细分规则,最后对奇异点附近曲面采用类Doo-Sabin和Catmull-Clark的细分规则,从而使该算法可以实现建模任意次具有任意拓扑基网格的非均匀细分曲面。此外,该方法也实现了对传统细分格式的统一,例如,当次数为2并采用均匀节点矢量便转化为Doo-Sabin细分,当次数为3并采用均匀节点矢量便转化为Catmull-Clark细分。     

Fast character modeling with sketch-based PDE surfaces

Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly.

     

C-C细分曲面的交互形状修改

为了增强细分曲面的造型功能,讨论了C-C细分曲面的交互形状修改算法。通过实时建立局部坐标系定义C-C细分曲面上点、法向量和局部等参数线等约束并将其转化为对控制顶点的约束,得到全局线性系统,从而可以在满足不同类型的几何约束时修改曲面的形状。基于最小二乘法和能量优化法给出两种修改算法,前者可以保持控制顶点扰动量的总和最小,运行速度快,适合于局部、精确调整;后者利用罚函数法给出了能量极小意义下的最优解,适合于保持光顺性要求的全局修改。两种方法都可以利用广义逆矩阵求得显式解,具有可逆性、可交换性、结合性等优点,提高了曲面形状修改的效率和可控性。     

Sharp Features on Multiresolution Subdivision Surfaces

In this paper we describe a method for creating sharp features and trim regions on multiresolution subdivision surfaces along a set of user-defined curves. Operations such as engraving, embossing, and trimming are important in many surface modeling applications. Their implementation, however, is nontrivial due to computational, topological, and smoothness constraints that the underlying surface has to satisfy. The novelty of our work lies in the ability to create sharp features anywhere on a surface and in the fact that the resulting representation remains within the multiresolution subdivision framework. Preserving the original representation has the advantage that other operations applicable to multiresolution subdivision surfaces can subsequently be applied to the edited model. We also introduce an extended set of subdivision rules for Catmull–Clark surfaces that allows the creation of creases along diagonals of control mesh faces.     

Generating subdivision surfaces from profile curves

The construction of freeform models has always been a challenging task. A popular approach is to edit a primitive object such that its projections conform to a set of given planar curves. This process is tedious and relies very much on the skill and experience of the designer in editing 3D shapes. This paper describes an intuitive approach for the modeling of freeform objects based on planar profile curves. A freeform surface defined by a set of orthogonal planar curves is created by blending a corresponding set of sweep surfaces. Each of the sweep surfaces is obtained by sweeping a planar curve about a computed axis. A Catmull-Clark subdivision surface interpolating a set of data points on the object surface is then constructed. Since the curve points lying on the computed axis of the sweep will become extraordinary vertices of the subdivision surface, a mesh refinement process is applied to adjust the mesh topology of the surface around the axis points. In order to maintain characteristic features of the surface defined with the planar curves, sharp features on the surface are located and are retained in the mesh refinement process. This provides an intuitive approach for constructing freeform objects with regular mesh topology using planar profile curves.     

Interpolating an Unlimited Number of Curves Meeting at Extraordinary Points on Subdivision Surfaces*

Interpolating curves by subdivision surfaces is one of the major constraints that is partially addressed in the literature. So far, no more than two intersecting curves can be interpolated by a subdivision surface such as Doo‐Sabin or Catmull‐Clark surfaces. One approach that has been used in both of theses surfaces is the polygonal complex approach where a curve can be defined by a control mesh rather than a control polygon. Such a definition allows a curve to carry with it cross derivative information which can be naturally embodied in the mesh of a subdivision surface. This paper extends the use of this approach to interpolate an unlimited number of curves meeting at an extraordinary point on a subdivision surface. At that point, the curves can all meet with either C ⁰ or C ¹ continuity, yet still have common tangent plane. A straight forward application is the generation of subdivision surfaces through 3‐regular meshes of curves for which an easy interface can be used.     

A subdivision scheme for Poisson curves and surfaces

The de Casteljau evaluation algorithm applied to a finite sequence of control points defines a Bézier curve. This evaluation procedure also generates a subdivision algorithm and the limit of the subdivision process is this same Bézier curve. Extending the de Casteljau subdivision algorithm to an infinite sequence of control points defines a new family of curves. Here, limits of this stationary non-uniform subdivision process are shown to be equivalent to curves whose control points are the original data points and whose blending functions are given by the Poisson distribution. Thus this approach generalizes standard subdivision techniques from polynomials to arbitrary analytic functions. Extensions of this new subdivision scheme from curves to tensor product surfaces are also discussed.     

Algebraic pruning: a fast technique for curve and surface intersection

Computing the intersection of parametric and algebraic curves and surfaces is a fundamental problem in computer graphics and geometric modeling. This problem has been extensively studied in the literature and different techniques based on subdivision, interval analysis and algebraic formulation are known. For low degree curves and surfaces algebraic methods are considered to be the fastest, whereas techniques based on subdivision and Bézier clipping perform better for higher degree intersections. In this paper, we introduce a new technique of algebraic pruning based on the algebraic approaches and eigenvalue formulation of the problem. The resulting algorithm corresponds to computing only selected eigenvalues in the domain of intersection. This is based on matrix formulation of the intersection problem, power iterations and geometric properties of Bézier curves and surfaces. The algorithm prunes the domain and converges to the solutions rapidly. It has been applied to intersection of parametric and algebraic curves, ray tracing and curve-surface intersections. The resulting algorithm compares favorably with earlier methods in terms of performance and accuracy.