Calculus of nonrigid surfaces for geometry and texture manipulation

We present a geometric framework for automatically finding intrinsic correspondence between three-dimensional nonrigid objects. We model object deformation as near isometries and find the correspondence as the minimum-distortion mapping. A generalization of multidimensional scaling is used as the numerical core of our approach. As a result, we obtain the possibility to manipulate the extrinsic geometry and the texture of the objects as vectors in a linear space. We demonstrate our method on the problems of expression-invariant texture mapping onto an animated three-dimensional face, expression exaggeration, morphing between faces, and virtual body painting.     

隐含多项式曲线曲面拟合次数的确定研究

选用合适次数的隐含多项式曲线曲面描述目标物体是处理和识别目标物体的关键,因而需要在理论上解决隐含多项式曲线或者曲面的次数确定问题.根据目标物体本身的特征,从理论上得出隐含多项式曲线描述物体的次数确定定理,并给出了具体计算公式.该方法首先由给定物体边界的轮廓检测出其驻点数,然后根据驻点数得到拟合隐含多项式曲线方程次数的下界,进而推广到三维物体的隐含多项式曲面拟合次数的确定.最后给出的应用实例进一步验证了算法的有效性与可操作性.     

基于BP神经网络的隐式曲线构造方法

隐式曲线与曲面是当前计算机图形学研究的热点之一。通过把BP神经网络与隐式曲线构造原理相结合，提出了一种构造隐式曲线的新方法，即首先由约束点构造神经网络的输入与输出，把描述物体边界曲线的隐式函数转化为显式函数；然后用BP神经网络对此显式函数进行逼近；最后由仿真曲面得到物体边界的拟合曲线。该新方法不同于传统的对显式函数的逼近方法，因为传统方法无法描述封闭的曲线；也不同于基于优化的拟合隐式曲线方法，因为它无须考虑函数的形式或多项式的次数。实验表明，该新方法有很强的物体边界描述能力和缺损修复能力，因而在物体边界重建、缺损图像复原等领域有一定的应用前景。     

A Formal Approach to the Specification of Graphic Object Functions

Graphic objects are an abstract mathematical model for graphic systems. The model is an algebraic approach to represent graphic information, which include modelling operations. This formalism require some method to describe normal graphic procedures, such as changing the object colour or texture mapping, as these procedures are essential to represent graphic processes. This paper extends the theory by introducing the concept of graphic object functions. A graphic object function transforms one graphic object into another, changing its visual appearance or its geometric properties. A formal definition of graphic functions is given, with a characterization of two special kinds of graphic object functions: filters and object transference functions. These two kinds of functions can be used to perform normal graphic operations, such as changing colours, texture mapping or clipping. Equivalence relationships between graphic objects induced by functions are also studied. These relationships establish an hierarchical structure on the graphic object set.     

Reflection and Refraction on Implicit Surfaces

Implicit surfaces are often used in computer graphics. They can be easily modeled and rendered, and many objects are composed of them in our daily life. In this paper, based on the concept of virtual objects, a novel method of real-time rendering is presented for reflection and refraction on implicit surface. The method is used to construct virtual objects from real objects quickly, and then render the virtual objects as if they were real objects except for one more step of merging their images with the real objects＇ images. Characteristics of implicit surfaces are used to compute virtual objects effectively and quickly. GPUs （Graphics Processing Units） are used to compute virtual vertices quickly and further accelerate the computing and rendering processes. As a result, realistic effects of reflections and refractions on implicit surfaces are rendered in real time.     

Fur Shading and Modification based on Cone Step Mapping

This paper presents an algorithm for the real time rendering of fur without adding fur‐specific geometry, such as shells, to the object. It is based on Cone Step Mapping and introduces a local distortion of the view vector to simulate a deformation of the heightfield‐bound hair geometry. While this distortion enables a more realistic fur rendering, some limitations emerge and have to be dealt with. A local light reflectance model including approximations of global light interactions with hair and skin is proposed. We furthermore show how material and geometric properties can locally be influenced through standard texture mapping. This includes most notably the local modification of growth and streak direction of the hairs.     

Geometric texture modeling

Texture mapping has become an essential tool in any synthetic rendering scheme that aims at photorealism. Texture mapping typically associates any point on the surface of the rendered object with a location in the texture space. The surface point is then assigned rendering attributes, such as color or translucency from the respective location found in the texture space. Texture mapping techniques have also been used in attempts to emulate highly detailed geometry on the surfaces of objects. The proposed surface detail synthesis approach closes the loop from modeling to rendering using computer graphics texture mapping techniques, bringing them back into the geometric modeling phase. This article focuses primarily on texturing techniques that relate to shape modeling and surface geometry alteration.     

基于隐含多项式曲线的物体描述与对称性检测

物体的对称性检测是图像分析，计算视觉中一个重要研究课题，在形状匹配，基于模型的目标匹配，三维物体的重建，图像压缩和图像数据库检索等许多领域都有重要应用，但是，对称性检测一直是计算机视觉的难题，至今缺少通用性好，能同时检测各种对称性并且效率较高的算法，利用隐含多项式曲线对复杂物体的良好描述能力，提出了基于隐含多项式曲一的物体对称性检测方法，这将平面图形的对称性检测问题转化对隐含多项式曲线的研究，理论与实验表明该算法能检测物体的各种对称性，算法简单，而且还可以检测出有噪音和缺失部分信息的物体对称性     

合并纹理图像技术

该文在“CIG2000”基础上,提出了基于合并纹理图像的纹理映射技术。使用该技术可以解决为多个几何体制定同一幅纹理图像,以及一个几何体的不同面映射不同的纹理图像。因此提高了工作效率,大大影响处理速度。     

PC-based Real-time Texture Painting on Real World Objects

The problem of texture mapping on real world objects has attracted attention^11,8 recently. A work by Lensch et al. ⁹ addressed the problem of locating a camera position in the celestial sphere and then mapping the acquired pictures on a real world object. The entire process took a half hour to one hour to map 10 to 15 pictures. In this paper, we propose a new innovative algorithm to speed up the texture mapping or painting process in real-time. We built a PC-based system using a commonly available video card with a geometry engine. Mapping of a picture required about 20 seconds. It is successful in giving an illusion to the operator to paint a colorless real world object with a color texture brush.     

Texture Mapping Real‐World Objects with Hydrographics

In the digital world, assigning arbitrary colors to an object is a simple operation thanks to texture mapping. However, in the real world, the same basic function of applying colors onto an object is far from trivial. One can specify colors during the fabrication process using a color 3D printer, but this does not apply to already existing objects. Paint and decals can be used during post‐fabrication, but they are challenging to apply on complex shapes. In this paper, we develop a method to enable texture mapping of physical objects, that is, we allow one to map an arbitrary color image onto a three‐dimensional object. Our approach builds upon hydrographics, a technique to transfer pigments printed on a sheet of polymer onto curved surfaces. We first describe a setup that makes the traditional water transfer printing process more accurate and consistent across prints. We then simulate the transfer process using a specialized parameterization to estimate the mapping between the planar color map and the object surface. We demonstrate that our approach enables the application of detailed color maps onto complex shapes such as 3D models of faces and anatomical casts.     

基于物理模型的三维火焰实时渲染

火焰等无规则物体的模拟近年来成为计算机图形学中的一个研究热点。传统的基于粒子和纹理技术生成的火焰,并不能真实地反映物体的运动过程,生成的火焰效果图具有随机和生硬的特点。为了解决火焰模拟过程中难以实现的实时性和真实感的问题,文中采用一种基于物理模型的火焰实时渲染方法,应用有限差分法求解Navier-Stokes方程,采用半拉格朗日法求解平流项,扩散方程则利用隐式迭代方法进行求解,利用GPU强大的并行计算能力对求解过程进行加速,利用光线投射算法对火焰进行渲染,最后生成了逼真的火焰图像。实验结果表明该方法实现简单,渲染速度快,显示的效果真实。     

基于变分隐式曲面的网格融合

三维物体融合利用三维模型之间的剪贴操作从两个或多个现有的几何模型中光滑融合出新的几何模型.作为一种新的几何造型方法,它正受到越来越多的关注.提出一种基于变分隐式曲面的网格融合新方法.首先利用平面截面切出网格物体的待融合边界,然后通过构造插值待融合网格物体边界的变分隐式曲面并对其进行多边形化,得到待融合网格物体间的过渡曲面,最后通过剪切掉过渡曲面的多余部分及拓扑合并操作以实现过渡网格曲面与原始网格间的光滑融合与现有的直接连接待融合网格物体边界以实现网格融合的算法相比,该方法不仅突破了对待融合物体的拓扑限制,允许多个物体同时进行融合,而且算法计算快速、鲁棒,使用方便,展示出良好的应用前景.     

Fast and accurate texture placement

Mapping from parameter space to texture space separates textures from objects, enabling control of textured images without modifying the object or texture. Although conceptually straightforward, γ-mapping turns out to be very useful in practical texture mapping implementation. It logically separates the texture from the object and makes the texture mapping process flexible and easier to use. By modifying the γ-mapping, texture placement on the object is efficiently controlled without modifying either the texture image or the underlying geometry. We concentrate on efficiency issues related to γ-mapping, as well as its practical applications to parametric surfaces     

基于深度纹理的实时碰撞检测算法

结合层次包围盒和基于图形硬件的方法,以带深度纹理的包围盒替代物体的几何模型,利用图形硬件在纹理映射时进行深度比较,以实现碰撞检测.实验结果表明,与CULLIDE算法相比,文中算法执行效率更高且执行时间固定,具有较高的实时性.     

基于网格优化的隐式曲面自适应多边形化

隐式曲面多边形化是隐式曲面绘制的一种常用算法.基于网格优化的隐式曲面快速自适应多边形化算法,首先用多边形化算法生成一个粗糙的初始网格,再利用网格优化方法从网格顶点位置、规则性和网格法向三个方面对粗糙网格进行调整,最后根据网格的局部曲率用多边形细分策略细分优化后的网格.实验结果表明,该算法在网格生成速度和网格规则性上都胜于Marching Cubes的多边形化算法,恢复的隐式曲面能较好地反映形状特征.     

有真实感图形的纹理映射算法

本文讨论了计算机生成真实感图形的纹理映射技术，根据模拟现实物体的表面细节特征提出了三种纹理映射方法。     

Texture mapping on surfaces of arbitrary topology using norm preserving-based optimization

A simple and yet highly efficient, high-quality texture mapping method for surfaces of arbitrary topology is presented. The new method projects the given surface from the 3D object space into the 2D texture space to identify the 2D texture structure that will be used to texture the surface. The object space to texture space projection is optimized to ensure minimum distortion of the texture mapping process. The optimization is achieved through a commonly used norm preserving minimization process on edges of the surface. The main difference here is, by using an initial value approach, the optimization problem can be set up as a quadratic programming problem and, consequently, solved by a linear least squares method. Three methods to choose a good initial value are presented. Test cases show that the new method works well on surfaces of arbitrary topology, with the exception of surfaces with exceptionally abnormal curvature distribution. Other advantages of the new method include uniformity and seamlessness of the texture mapping process. The new method is suitable for applications that do not require precise texture mapping results but demand highly efficient mapping process such as computer animation or video games.     

Solid Texturing of Soft Objects

Since the shape of a soft object changes in response to its surroundings, it is difficult to give a single position in space as the location of the object. Indeed objects can and do break dynamically into subobjects. This means that you cannot map a solid texture onto such an object simply by using a function of the space coordinates. We have taken a different approach. Our soft objects are modeled as the volume enclosed by an isosurf ace of a field calculated from a set of key points. For each key point, we describe an abstract texture space. Any point on the surface of an object has, associated with each key point, a position in this space and a field contribution. A vector sum of these positions, weighted by the field contributions, is used to select a surface specification from the texture space. Textures mapped with this process retain their consistency during distortion and metamorphoses of objects, permitting a great variety of animation effects.     

基于特征约束点的纹理映射算法

纹理映射技术用于生成物体表面的纹理细节,是真实感图形技术的重要组成部分,也是计算机图形学的一个重要研究方向.针对目前很多纹理映射算法计算量大,方法比较复杂的缺点,应用Candide3作为三维网格模型,提出了一种快速有效的基于特征约束点的纹理映射算法.通过在三维网格模型和纹理图像上选取少量对应的特征约束点,利用三角网格剖分算法在纹理图像上建立选取特征点的三角网格.进而通过求取质心坐标的方法计算出三维网格模型上所有特征点的纹理坐标并完成整个三维网格模型的纹理映射.实验结果表明,提出的算法计算速度较快,能够得到高真实度的纹理映射效果,并且适用于不同纹理图像映射到同一三维网格模型上.