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。     

SWEEP曲面的NURBS逼近

提出了一种ＳＷＥＥＰ曲面用ＮＵＲＢＳ逼近的方法，对于截面线的定位，提出了一种定位方法，对于逼近误差控制，可转化为对插值曲线的误差估计。本文算法已在具有自主版权的Ｇｅｍｓ５．０中实现。     

规则二次曲面壳密度可变的全四边形网格剖分

本文提出了一种规则二次曲面壳上密度可变的全四边形网格剖分方法。利用二次曲面壳的标准参数方程，在二次曲面块Ｒ与参数平面的一个等参面Ｐ之间建立一种一对一映射关系。根据曲面壳上网格划分的密度要求，先在等参面Ｐ上剖分网格，然后将其精确映射到二次曲面Ｒ上。本方法消除了网格剖分时曲面上极点可能出现的奇异性，实现了二次曲面上的全四边形网格剖分，并可按网格划分的密度要求实现网格的疏密过渡。以球面，圆柱面为例，介绍     

嵌入参数空间的曲面控制自由变形方法

提出了一种新的通过控制参数曲面来实现物体的自由变形的方法，物体通过映射函数被嵌入到曲面的参数空间从而实现变形，同时映射函数的引入增加了变形的控制手段。实验表明该方法具有易于交互和控制的优点，适用于几何造型和计算机动画领域。     

流曲线曲面的概念和构造方法

给出了一种新的曲线曲面－流曲线曲面概念及其构造方法。给出了用多项式和Ｂｅｚｉｅｒ控制网构造流曲线曲面的基本方法和约束条件，这种流曲线曲面方法可用于计算机辅助几何设计和图形学中曲线表示和设计，特别是船体外型的造型和设计。     

一种应用参数曲面的动态自由变形方法

本文提出了一种动态自由变形方法，被变形物体首先附在两张参数曲面上，当参数曲面的形状发生变化时，物体会随之变形。这两张参数曲面分别被称为形状曲面和高度曲面，其中形状曲面用于控制变形物体的形状，高度曲面用于控制物体沿着形状曲面法向的高度。     

基于可控卷积曲面的三维神经元建模

在神经科学领域，大脑复杂神经行为的分析需要构造表面光滑且高质量的神经元模型。针对三维神经元形态数据的复杂性，现有三维神经元模型的研究在构造模型的过程中，骨架之间的折痕较大且表面光滑度较低。为解决支撑半径过大导致的卷积过渡混合问题，采用基于采样点密度和半径的算法进行数据预处理并结合骨架的抽象性和卷积曲面的光滑性，提出一种利用局部可变支撑半径控制的卷积曲面混合方法。采用基于VDB的稀疏体素自适应调整空间分辨率提高生成效率，用于解决提取不同半径神经元等值面的速度问题。为验证生成模型数据的有效性，利用MeshLab工具验证网格的水密性并基于Isotropic Remeshing算法重构网格，利用Loop算法细分神经元网格，使其表面更加光滑且包含更多细节信息。为构造在脑神经组织中进行光传播模拟实验的神经元模型，利用TetGen软件生成高质量的神经元四面体模型。实验结果表明，与现有神经元建模方法相比，该方法不仅能有效提高生成速率，而且能生成高阶光滑的网格模型。     

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。     

Loop细分曲面的等距曲面的逼近

提出了一种生成Loop细分曲面的等距曲面的逼近方法．通过让生成的等距曲面在对应于其控制网格顶点的地方是精确的等距，作者将等距曲面的逼近问题转化为求解一个线性方程组．文中提出了一个用于快速求解该线性方程组的改进的Gauss—Jacobi迭代法．另外，该文还考虑了逼近的误差控制和等距曲面的自交问题．     

Analytical solutions for sketch-based convolution surface modeling on the GPU

Convolution surfaces are attractive for modeling objects of complex evolving topology. This paper presents some novel analytical convolution solutions for planar polygon skeletons with both finite-support and infinite-support kernel functions. We convert the double integral over a planar polygon into a simple integral along the contour of the polygon based on Green’s theorem, which reduces the computational cost and allows for efficient parallel computation on the GPU. For finite support kernel functions, a skeleton clipping algorithm is presented to compute the valid skeletons. The analytical solutions are integrated into a prototype modeling system on the GPU (Graphics Processing Unit). Our modeling system supports point, polyline and planar polygon skeletons. Complex objects with arbitrary genus can be modeled easily in an interactive way. Resulting convolution surfaces with high quality are rendered with interactive ray casting.     

基于Metaball的曲面约束变形模型及应用

结合曲面变形技术和Metaball原理,提出了基于Metaball的曲面约束变形模型,将Metaball的势函数表达曲面变形的约束,用它去作用于待变形曲面,通过调整Metaball势函数的约束中心、作用半径、偏移等参数控制曲面的预期变形效果,利用骨架卷积获得平坦光滑的曲面.讨论了约束关系、单个约束的影响、控制约束的相互影响等问题,并举例说明了这个模型的机理和应用.     

Prototype Modeling from Sketched Silhouettes based on Convolution Surfaces

This paper presents a hybrid method for creating three‐dimensional shapes by sketching silhouette curves. Given a silhouette curve, we approximate its medial axis as a set of line segments, and convolve a linearly weighted kernel along each segment. By summing the fields of all segments, an analytical convolution surface is obtained. The resulting generic shape has circular cross‐section, but can be conveniently modified via sketched profile or shape parameters of a spatial transform. New components can be similarly designed by sketching on different projection planes. The convolution surface model lends itself to smooth merging between the overlapping components. Our method overcomes several limitations of previous sketched‐based systems, including designing objects of arbitrary genus, objects with semi‐sharp features, and the ability to easily generate variants of shapes.     

SCALe‐invariant Integral Surfaces

Extraction of skeletons from solid shapes has attracted quite a lot of attention, but less attention was paid so far to the reverse operation: generating smooth surfaces from skeletons and local radius information. Convolution surfaces, i.e. implicit surfaces generated by integrating a smoothing kernel along a skeleton, were developed to do so. However, they failed to reconstruct prescribed radii and were unable to model large shapes with fine details. This work introduces SCALe‐invariant Integral Surfaces (SCALIS), a new paradigm for implicit modelling from skeleton graphs. Similarly to convolution surfaces, our new surfaces still smoothly blend when field contributions from new skeleton parts are added. However, in contrast with convolution surfaces, blending properties are scale‐invariant. This brings three major benefits: the radius of the surface around a skeleton can be explicitly controlled, shapes generated in blending regions are self‐similar regardless of the scale of the model and thin shape components are not excessively smoothed out when blended into larger ones.     

Convolution surfaces for arcs and quadratic curves with a varying kernel

A convolution surface is an isosurface in a scalar field defined by convolving a skeleton, comprising of points, curves, surfaces, or volumes, with a potential function. While convolution surfaces are attractive for modeling natural phenomena and objects of complex evolving topology, the analytical evaluation of integrals of convolution models still poses some open problems. This paper presents some novel analytical convolution solutions for arcs and quadratic spline curves with a varying kernel. In addition, we approximate planar higher-degree polynomial spline curves by optimal arc splines within a prescribed tolerance and sum the potential functions of all the arc primitives to approximate the field for the entire spline curve. Published online: November 20, 2002     

基于卷积曲面的几何造型方法

卷积曲面是一种很有潜力的隐式曲面造型方法。由于卷积的可叠加性质,使得其生成的曲面很光滑,不会产生凸包和裂缝。卷积曲面造型是基于骨架的,其骨架可以是曲线或曲面,也可以以物体轮廓线为骨架原型来获取所需要的物体造型。在卷积造型的过程中,通过对骨架加权可以精细地控制结果曲面的形状。在介绍了卷积曲面造型的各类方法后,分析了其特点和发展方向。     

Computing multiscale curve and surface skeletons of genus 0 shapes using a global importance measure

We present a practical algorithm for computing robust, multiscale curve and surface skeletons of 3D objects. Based on a model which follows an advection principle, we assign to each point on the skeleton a part of the object surface, called the collapse. The size of the collapse is used as a uniform importance measure for the curve and surface skeleton, so that both can be simplified by imposing a single threshold on this intuitive measure. The simplified skeletons are connected by default, without special precautions, due to the monotonicity of the importance measure. The skeletons possess additional desirable properties: They are centered, robust to noise, hierarchical, and provide a natural skeleton-to-boundary mapping. We present a voxel-based algorithm that is straightforward to implement and simple to use. We illustrate our method on several realistic 3D objects.     

基于任意骨架的隐式曲面造型技术

给出了一个新的基于任意多面体网格骨架的构造性自由曲面造型算法.算法首先由每个给定骨架构造出一个距离场,然后利用隐函数光滑过渡技术和CSG(constructive solid geometry)表示技术将所构造的隐式曲面自由地两两粘合成一张光滑曲面.隐式曲面的多边形化算法则用来生成最终曲面网格.以任意骨架作为基本体素,突破了传统隐式曲面以点为基本骨架的限制.而且,距离曲面很好地逼近了原骨架形状,使用户可直观地对复杂曲面进行交互设计.而形变函数的引入,则极大地丰富了此方法的造型能力.实验结果表明,基于该算法的原型系统能够方便、直观地构造复杂的自由曲面.     

A novel stroke-based feature extraction for handwritten Chinese character recognition

A stroke-based approach to extract skeletons and structural features for handwritten Chinese character recognition is proposed. We first determine stroke directions based on the directional run-length information of binary character patterns. According to the stroke directions and their adjacent relationships, we split strokes into stroke and fork segments, and then extract the skeletons of the stroke segments called skeleton segments. After all skeleton segments are extracted, fork segments are processed to find the fork points and fork degrees. Skeleton segments that touch a fork segment are connected at the fork point, and all connected skeleton segments form the character skeleton. According to the extracted skeletons and fork points, we can extract primitive strokes and stroke direction maps for recognition. A simple classifier based on the stroke direction map is presented to recognize regular and rotated characters to verify the ability of the proposed feature extraction for handwritten Chinese character recognition. Several experiments are carried out, and the experimental results show that the proposed approach can easily and effectively extract skeletons and structural features, and works well for handwritten Chinese character recognition.     

隐式曲面在三维植物建模中的应用研究综述

分别从BlobTree结构、融合、精确接触造型、具有多项式密度分布的直线骨架卷积曲面和植物表面纹理等方面,介绍并分析了隐式曲面在三维植物建模中的基本思想和关键技术,并对应用隐式曲面得到三维模型的可视化方法进行了总结。最后对这一研究课题进一步的发展趋势进行了讨论。