Real-Time Volume Deformations

Real-time free-form deformation tools are primarily based on surface or particle representations to allow for interactive modification and fast rendering of complex models. The efficient handling of volumetric representations, however, is still a challenge and has not yet been addressed sufficiently. Volumetric models, on the other hand, form an important class of representation in many applications. In this paper we present a novel approach to the real-time deformation of scalar volume data sets taking advantage of hardware supported 3D texture mapping. In a prototype implementation a modeling environment has been designed that allows for interactive manipulation of arbitrary parts of volumetric objects. In this way, any desired shape can be modeled and used subsequently in various applications. The underlying algorithms have wide applicability and can be exploited effectively for volume morphing and medical data processing.     

基于伸缩因子的参数曲线自由变形

提出一种新的参数曲线自由变形方法：构造出特殊的伸缩因子函数，以此去作用（伸缩）待变形曲线方程，从而使曲线发生形变，通过交互改变控制参数，可达到预期的变形效果，实验表明，该方法数学背景简单，易于控制，重复使用可获得丰富的变形效果，适用于几何造型，计算机动画等领域。     

A statistical wisp model and pseudophysical approaches for interactive hairstyle generation

This work presents an interactive technique that produces static hairstyles by generating individual hair strands of the desired shape and color, subject to the presence of gravity and collisions. A variety of hairstyles can be generated by adjusting the wisp parameters, while the deformation is solved efficiently, accounting for the effects of gravity and collisions. Wisps are generated employing statistical approaches. As for hair deformation, we propose a method which is based on physical simulation concepts, but is simplified to efficiently solve the static shape of hair. On top of the statistical wisp model and the deformation solver, a constraint-based styler is proposed to model artificial features that oppose the natural flow of hair under gravity and hair elasticity, such as a hairpin. Our technique spans a wider range of human hairstyles than previously proposed methods and the styles generated by this technique are fairly realistic.     

Interactive Shape Control of Interpolating B-splines

This paper presents a new methodfor providing interactive shape control of interpolating B-splines. The CAD designer can directly interact with geometric entities defined on the B-spline at any interpolated data point; shape adjustments can be performed either globally or locally. Our approach is based on Bλ-splines of order k (λ,k ≥1), i.e. λ-reparametrized, classical B-splines. The method presented can be easily generalised to surfaces defined either as tensor products or by using the skinning technique; interactive shape control can be provided in both surface parametric directions.     

渐进迭代逼近方法在曲线变形上的应用

目的 随着几何造型、计算机动画等领域的快速发展,曲线的自由变形技术在近年来受到了广泛的关注。为了获得更多有趣、逼真的变形效果,提出基于渐进迭代逼近与主顶点方法的曲线局部变形算法。方法 给定数据点集,首先采用渐进迭代逼近方法或是基于最小二乘的渐进迭代逼近方法产生待变形曲线;其次对待变形区域使用延拓准则,基于主顶点方法与待变形曲线的形状信息选取控制顶点进行调整;最后对调整后的控制顶点运用局部渐进迭代逼近方法生成逼近曲线,得到期望的变形效果。结果 此变形操作借助于局部渐进迭代逼近方法,具有较好的灵活性。通过茶壶、面部轮廓、手等数值实例,表明了该方法可以得到良好的变形效果。进一步地,借助于叠加变形还可以得到整体的、周期的、伸缩的等各类更加丰富的变形效果。结论 本文研究渐进迭代逼近在曲线变形上的应用,将主顶点方法引入曲线的变形之中,把两者相结合提出了基于渐进迭代逼近与主顶点方法的曲线局部变形算法。该算法不仅具备渐进迭代逼近方法的收敛稳定性,且借助于主顶点方法,可以得到较好的变形效果。该方法适用于曲线的局部变形,丰富了曲线的变形效果。     

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。     

Locally Injective Mappings

Mappings and deformations are ubiquitous in geometry processing, shape modeling, and animation. Numerous deformation energies have been proposed to tackle problems like mesh parameterization and volumetric deformations. We present an algorithm that modifies any deformation energy to guarantee a locally injective mapping, i.e., without inverted elements. Our formulation can be used to compute continuous planar or volumetric piecewise‐linear maps and it uses a barrier term to prevent inverted elements. Differently from previous methods, we carefully design both the barrier term and the associated numerical techniques to be able to provide immediate feedback to the user, enabling interactive manipulation of inversion‐free mappings. Stress tests show that our method robustly handles extreme deformations where previous techniques converge very slowly or even fail. We demonstrate that enforcing local injectivity increases fidelity of the results in applications such as shape deformation and parameterization.     

三维试衣系统中的H-Anim格式人体模型构造

介绍了一种容易实现的、实用性强的人体模型构造方法，可以广泛应用于服装的三维试衣系统或其他CAD领域。根据用户输入的参数或者交互式的操作，对一个标准的VRML H-Anim 1．1格式人体模型先进行骨架变形，再使用水平和垂直两条NURBS曲线控制身体各部分的变形，从而达到用户需要的效果。     

A New Approach for Direct Manipulation of Free-Form Curve

There is an increasing demand for more intuitive methods for creating and modifying free-form curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters, such as control points, knots, and weights, but also on the user's specified constraints and shapes. This paper presents a new approach for directly manipulating the shape of a free-form curve, leading to a better control of the curve deformation and a more intuitive CAD modeling interface. The user's intended deformation of a curve is automatically converted into the modification of the corresponding NURBS control points and knot sequence of the curve. The algorithm for this approach includes curve elevation, knot refinement, control point repositioning, and knot removal. Several examples shown in this paper demonstrate that the proposed method can be used to deform a NURBS curve into the desired shape. Currently, the algorithm concentrates on the purely geometric consideration. Further work will include the effect of material properties.     

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。     

基于拉普拉斯网格变形的三维植物叶片建模

论文提出一种基于拉普拉斯网格变形的三维植物叶片交互式设计方法。该 方法以叶片轮廓及叶片主脉中轴点数据输入并生成网格曲面,通过拉普拉斯网格变形技术对 叶片的曲面网格进行交互式编辑。轮廓中轴数据点既可以通过三维数字化获得,也可以根据 叶脉形态计算得到。实验证明,该方法具有较好的普适性,变形计算快速,能够达到实时交 互设计的需要,所生成的叶片不仅能够很好地保持叶片的面积特征,同时在形态上具有较强 的真实感。     

Compactly-supported smooth interpolators for shape modeling with varying resolution

In applications that involve interactive curve and surface modeling, the intuitive manipulation of shapes is crucial. For instance, user interaction is facilitated if a geometrical object can be manipulated through control points that interpolate the shape itself. Additionally, models for shape representation often need to provide local shape control and they need to be able to reproduce common shape primitives such as ellipsoids, spheres, cylinders, or tori. We present a general framework to construct families of compactly-supported interpolators that are piecewise-exponential polynomial. They can be designed to satisfy regularity constraints of any order and they enable one to build parametric deformable shape models by suitable linear combinations of interpolators. They allow to change the resolution of shapes based on the refinability of B-splines. We illustrate their use on examples to construct shape models that involve curves and surfaces with applications to interactive modeling and character design.     

Image segmentation by pixel classification

A fast boundary finding algorithm is presented which works without threshold operation and without any interactive control. The procedure can be described as a hierarchical two-step algorithm. In the first step the image is divided into two disjunct regions, one of them including the whole object of interest.In the second step the problem of boundary finding is suggested as a classification problem, which means that for any pixel a four-dimensional feature vector is computed which allows classification of pixels into contour elements and any other pixels.The algorithm was tested on several thousand cell images and can be easily adapted to other problems by modification of a set of parameters.     

基于能量优化的NURBS曲面几何特征修改

NURBS作为曲面造型技术中的重要方法之一,在计算机辅助几何设计和计算机图形学领域中有着广泛的应用。针对NURBS曲面的几何特征修改,提出了基于能量优化的修改方法。通过对NURBS曲面的控制顶点进行扰动,以曲面的应力能改变为目标函数并使之最小化,实现了NURBS曲面上给定多个点处的位置、一阶偏导矢、二阶偏导矢和法矢等几何特征的修改。数值实例表明该方法用于微调时,可实现对曲面局部形状的多种修改效果,便于交互设计。     

基于外部能量约束的曲面形状修改

提出了一个基于外部能是约束的曲面形状修改ＮＵＲＢ曲面的开矿首先给出曲面内部变形能量的近似计算公式,然后将典面形状修改所需满足的约束条件转化为相应的外部能量约束荐项,并附加在曲面的内部能量项之上,最后通过求解一个使面面能量的变化量为最小的无约束优化问题,得到变形后的曲面,使曲面总能量近亿为最小,这种方法以统一的形式处理各种不同类型的约束条件,从而简化了约束条件下曲面形状修改的计算。     

三角域上带形状参数的三次Bézier曲面

张量积Bézier曲面被成功地应用于商业CAD系统中,然而实际工程中的某些外形却无法依靠张量积形式实现.因此在CAGD中,三角Bézier曲面成为外部形状设计的主要工具之一.为了更加灵活地控制三角曲面的形状,构造了一组带形状参数的三次多项式基函数,它们是三角域上三次Bernstein基的扩展.利用该组基函数定义了三角域上带形状参数的多项式曲面.基函数和曲面分别具有Bernstein基和Bézier曲面的性质.在形状参数的取值范围内,三次Bézier三角曲面是它的特例.由于含有可调的形状参数,该曲面在形状修改与变形中具有更大的灵活性.形状参数具有明确的几何意义,参数越大曲面越逼近控制网格.实例表明,通过改变形状参数的取值可以调整曲面的形状,在CAGD中该方法是有效的.     

Hierarchical feature subspace for structure-preserving deformation

This paper aims to propose a new framework for structure-preserving deformation, which is interactive, stable, and easy to use. The deformation is characterized by a nonlinear optimization problem that retains features and structures while allowing user-input external forces. The proposed framework consists of four major steps: feature analysis, ghost construction, energy optimization, and reconstruction. We employ a local structure-tensor-based feature analysis to acquire prior knowledge of the features and structures, which can be properly enforced throughout the deformation process. A ghost refers to a hierarchical feature subspace of the shape. It is constructed to control the original shape deformation in a user-transparent fashion, and speed up our algorithm while best accommodating the deformation. A feature-aware reconstruction is devised to rapidly map the deformation in the subspace back to the original space. Our user interaction is natural and friendly; far fewer point constraints and click-and-drag operations are necessary to achieve the flexible shape deformation goal. Various experiments are conducted to demonstrate the ease of manipulation and high performance of our method.     

插值Doo-Sabin表面形状调节

修改了插值的Doo-Sabin细分表面的初始控制网格，在第一次细分的同时加入了表面调节参数。这个方案具有以下特征：1）满足插值所有顶点或某些顶点的同时可以由参数调节极限表面；增加了对极限表面的调节自由度。2）整个的计算复杂度为O(k),其中k是顶点的数量。在最后也对结果表面的形状处理进行了讨论。     

A curve analyzer for micro-computers

A computer program is described that emulates a curve analyzer and fits a sum of up to 30 Gaussian components plus a straight background to any set of equi-spaced data points. The program allows interactive, real time curve fitting by the operator and/or objective curve fitting using a non-linear least squares fitting routine, or a combination of the two. The program is more robust in a micro-computer environment than subtractive or generalized non-linear least squares methods and faster than pattern searching methods. The program has been used over the last 4 years in my laboratory by a number of personnel without any previous experience of computers. It is written in BASIC and runs on a Hawlett-Packard series 200 model 16S (9816) computer or on a Hewlett-Packard model 9845S computer. The program is structured to allow use of any underlying curve shape with 3 parameters per component.