管状组织的中轴-元球造型方法

传统的医学体数据造型方法往往局限于将体数据表达为镶嵌在轮廓线族中的三角片集合,或者是简单的三维体元阵列.实际上,生物体的结构相当复杂,采用这些简单的造型方法显然不能适应绘制的要求.文章探讨了适用于气管、血管等管状、多分枝结构的造型方法,采用离散的中轴点表达分枝的拓扑结构,结合基于元球（metaball）的隐式曲面造型方法构造管状组织的模型.这种造型方法不仅可以使管状组织复杂的拓扑结构得以保留,而且保证了分枝之间连接的光滑性.     

空间采样点的隐式曲面表示与优化

基于元球隐式曲面表示,提出一个对给定3维物体表面采样数据进行自动曲面重建的方法。首先由空间采样点获取它们的球逼近表示;然后使用这些球作为元球的初始估计,构造出一张初始的元球隐式曲面;最后通过一个能量优化过程调整每个元球的形状参数,得到最终的隐式曲面。球的位置与形状的有效估计和局部支撑的元球核函数的使用极大地加速了曲面优化过程。实验结果表明该方法是有效而实用的。     

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。     

基于C-B样条的Catmull-Clark细分曲面造型系统的开发

论文针对工程应用,根据C-B样条和Catmull-Clark细分曲面的特点可调因子使得生成曲面形状可调和一次细分操作以后所有的网格面片都为四边域,构造合理的数据结构,采用有效的实时交互式的用户界面,开发了基于C-B样条的Catmull-Clark细分曲面的造型系统.为细分曲面的形状调整提供了简单、实时而且直观的人机交互方法.该系统能处理任意拓扑结构,能够精确地表示二次曲面,所生成的曲面光滑可调.可以以软件包或插件的形式加入到现有的CAD系统中.     

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 .     

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。     

带形状参数的三次TC-Bézier曲线

针对自由曲线曲面设计中的形状控制问题,构造了带形状控制参数λ的三次TC-Bezier曲线.λ具有明确的几何意义,λ的值越大曲线越逼近控制多边形.同时证明了几种有实际应用价值的曲线(椭圆弧、花瓣)可以用带形状参数三次TC-Bezier曲线的形式精确表示.还给出了带参数三次TC-Bezier曲线间的G<1'>拼接条件及在曲面造型中的应用实例.造型实例表明,该曲线在计算机辅助几何设计中具有重要的应用价值.     

圆弧曲线段和球面曲面片的多项式逼近

鉴于现有的CAD/CAM造型系统不能处理圆和球面的隐式方程以及用三角函数所表示的参数方程,因此为了使现有的CAD/CAM造型系统能够处理圆弧、圆以及球面曲面片、球面,人们只能采用参数多项式和参数有理多项式来逼近它们。为了能更好地对圆弧曲线段和球面曲面片进行逼近,提出了一种基于最小二乘范数的参数Bézier多项式逼近方法。该方法根据在最小二乘范数L2下所定义的距离函数取最小值,首先得到了一个圆弧曲线段和球面曲面片的参数Bézier多项式逼近式,并把该逼近多项式表示成两个行列式的商的形式。如果所取圆弧曲线段或球面曲面片为圆或球面时,则可得到圆或球面的参数Bézier多项式逼近式。另外,用该方法也可得到椭圆弧曲线段和椭球面曲面片的参数Bézier多项式逼近式。最后给出了一些数值实例,数值实验结果表明,该方法是有效的。     

参数曲面多边形区域上变形的伸缩因子与实验

为了改进参数曲面自由变形方法,构造了凸多边形域上的伸缩因子函数,它具有已往文献所引入的伸缩因子的特性。可使用新的伸缩因子去作用待变形曲面的参数方程,从而使曲面发生形变。可通过交互改变控制参数来控制曲面的形状,使其能够更好地表示一些不规则实体的外型。实验表明,该方法的数学背景简单、易于控制、重复使用可以达到获得丰富变形效果的目的。可用于几何造型、计算机动画以及CAD/CAM等领域。     

计算机生成中国传统祥云动画

开展用计算机生成具有中国民族特色动画的研究,对弘扬我国传统艺术和提高中国动画片竞争力都有重要意义。祥云图案历史悠久,是最富有中国特色的吉祥图案之一,现有的大部分研究工作主要针对真实感烟云的模拟和绘制,而对生成中国传统风格祥云动画的研究工作还很少。为此提出一个祥云动画生成模型。首先利用椭圆来构造云朵的骨架曲线,沿着曲线上的非均匀分布点排列多个半径不同的基本圆,然后通过对这些基本圆进行求并运算来生成云朵内部区域和轮廓线;通过控制基本圆沿以分布点为圆心的圆周上运动,来生成连续变化的轮廓线和云朵形状;利用轮廓线上的运动点作为起点,沿中心点方向绘制云尾内卷线条。实验结果表明,利用该模型用户可以生成各类具有中国传统风格的祥云动画。     

Fitted BVH for Fast Raytracing of Metaballs

Raytracing metaballs is a problem that has numerous applications in the rendering of dynamic soft objects such as fluids. However, current techniques are either limited in the visual effects that they can render or their performance drops as the number of metaballs and their density increase. We present a new acceleration structure based on BVH and kd‐tree for efficient raytracing of a large number of metaballs. This structure is built from an adapted SAH using a fast greedy algorithm and allows the visualization of several hundreds of thousands metaballs at interactive‐to‐real‐time framerates. Our method can handle arbitrary rays to simulate any complex secondary effects such as reflections or soft shadows, and is robust with respect to the density of metaballs. We achieve this performance thanks to a balanced CPU‐GPU (using CUDA) implementation of the animation, structure creation, and rendering.     

GPU-based Fast Ray Casting for a Large Number of Metaballs

Metaballs are implicit surfaces widely used to model curved objects, represented by the isosurface of a density field defined by a set of points. Recently, the results of particle‐based simulations have been often visualized using a large number of metaballs, however, such visualizations have high rendering costs. In this paper we propose a fast technique for rendering metaballs on the GPU. Instead of using polygonization, the isosurface is directly evaluated in a per‐pixel manner. For such evaluation, all metaballs contributing to the isosurface need to be extracted along each viewing ray, on the limited memory of GPUs. We handle this by keeping a list of metaballs contributing to the isosurface and efficiently update it. Our method neither requires expensive precomputation nor acceleration data structures often used in existing ray tracing techniques. With several optimizations, we can display a large number of moving metaballs quickly.     

A volume-preserving approach for modeling and animating water flows generated by metaballs

This paper presents a volume-preserving approach for animating liquid flows modeled by metaballs. A volume of liquid can be adjusted to a previous volume by using the influence radius and the maximum density of metaballs as volume-controlling parameters. Recursive subdivision is used to efficiently calculate the volume of implicit surfaces. The criterion for subdivision is obtained by using the concept of interval analysis and the common property of metaball density functions. Providing a sequence of parameters, the volume-compensation region can be controlled according to the substance making up the object, resulting in local preservation of the volume. Set partition is used for determining isolated surfaces in order to apply local-volume preservation. Published online: 23 July 2002 Correspondence to: K. Kaneda     

Stable matching between a hand structure and an object silhouette

A method is proposed which determines the possible ways to grasp an object, defined by its silhouette. This method is quite general and versatile: the geometry of the object is arbitrary and a large class of grippers is allowed; no a priori information is needed, except the parameters of the gripper, and so the method applies, in particular, to all the automatic prehension problems when the object and/or its orientation are unknown. Suitable segmentation and parametrization of the silhouette yields an explicit solution and a very fast and simple algorithm.     

重建小凸多面物体面形的新方法

为实现小凸多面物体面形快速重建,提出了基于投影轮廓的新方法。首先处理被测小凸多面物体各平行旋转角度下纵投影轮廓图像,得到对应轮廓序列集及横截面切片投影长度曲线集,然后由该曲线集得到所有疑似被测物体表平面的索引,将该索引对照各轮廓序列进行筛选,最后经计算得到被测物体的各表平面参数,完成面形重建。实验表明,该方法能够精确恢复被测小凸多面物体面形,与现有方法相比具有设备精简、速度快等特点,适用于针对小凸多面体工件的工程应用。     

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.     

Metaball重叠区域作用效果混合

在表现隐式曲面或曲面变形时，多个Metaball作用的重叠区域常会出现肿胀、褶皱、撕裂等缺陷。前人虽曾通过调整Metaball参数、简单叠加、直接合并等来解决这些问题，但未能得到效果好，且效率高的满意结果，为此，在分析、研究了Metaball单独作用、作用范围重叠的基础上，分别针对点骨架、直线段、曲线段骨架，提出了线性加权和、代数混合、指数加权和方法，用以处理多个Metaball在重叠区域的作用效果混合。实验表明。这些混合方法不但可与曲面的表示方法以及Metaball势函数的形式无关，而且在边界处的过渡较平滑，其效果与效率也得到了实例验证。     

Silhouette coherence for camera calibration under circular motion

We present a new approach to camera calibration as a part of a complete and practical system to recover digital copies of sculpture from uncalibrated image sequences taken under turntable motion. In this paper, we introduce the concept of the silhouette coherence of a set of silhouettes generated by a 3D object. We show how the maximization of the silhouette coherence can be exploited to recover the camera poses and focal length. Silhouette coherence can be considered as a generalization of the well-known epipolar tangency constraint for calculating motion from silhouettes or outlines alone. Further, silhouette coherence exploits all the geometric information encoded in the silhouette (not just at epipolar tangency points) and can be used in many practical situations where point correspondences or outer epipolar tangents are unavailable. We present an algorithm for exploiting silhouette coherence to efficiently and reliably estimate camera motion. We use this algorithm to reconstruct very high quality 3D models from uncalibrated circular motion sequences, even when epipolar tangency points are not available or the silhouettes are truncated. The algorithm has been integrated into a practical system and has been tested on more than 50 uncalibrated sequences to produce high quality photo-realistic models. Three illustrative examples are included in this paper. The algorithm is also evaluated quantitatively by comparing it to a state-of-the-art system that exploits only epipolar tangents     

A Method for Displaying Metaballs by using Bézier Clipping

For rendering curved surfaces, one of the most popular techniques is metaballs, an implicit model based on isosurfaces of potential fields. This technique is suitable for deformable objects and CSG model. For rendering metaballs, intersection tests between rays and isosurfaces are required. By defining the higher degree of functions for the field functions, richer capability can be expected, i.e., the smoother surfaces. However, one of the problems is that the intersection between the ray and isosurfaces can not be solved analytically for such a high degree function. Even though the field function is expressed by degree six polynomial in this paper (that means the degree six equation should be solved for the intersection test), in our algorithm, expressing the field function on the ray by Bézier functions and employing Bézier Clipping, the root of this function can be solved very effectively and precisely. This paper also discusses a deformed distribution function such as ellipsoids and a method displaying transparent objects such as clouds.     

点云表面曲线的手绘构造方法

为了勾勒点云的骨架或在点云上标记符号,提出一种基于手绘的点云表面曲线构造方法．首先将手绘的二维草图识别成二次曲线;然后将其均匀离散化并分别投影到点云表面;最后判断投影点是否接近于同一平面,如果是,则将二次曲线重新投影到该拟合平面;否则,将投影点连接成B样条曲线并对其平滑去噪．实验结果表明,利用该方法可以快速勾勒出点云轮廓,并在点云表面高效地绘制出二次曲线或者平滑的B样条曲线．