A high-accuracy method for filling voids and its verification

A new method for filling voids is developed by improving the approach to high- accuracy surface modelling (HASM), which is based on the first fundamental coefficients and the second fundamental coefficients of surfaces. The first fundamental coefficients are used to calculate the lengths of curves, angles of tangent vectors, areas of regions and geodesics on the surface. The second fundamental coefficients reflect the local warping of the surface, namely its deviation from the tangent plane at the point under consideration, which can be observed from outside the Earth. Nine regions with different landform complexities in hilly, plateau and mountainous areas are selected for testing the performance of HASM by comparing those ones of the classic methods such as triangulated irregular network (TIN), inverse distance weighted interpolation (IDW), advanced Spline method (ANUDEM), Spline and Kriging. The results demonstrated that the HASM void filling always has the highest accuracy regardless of the landform complexity, void area and auxiliary data.     

高精度曲面建模优化方案

目的 为了进一步提高高精度曲面建模（HASM）方法的模拟精度和计算速度,进而拓宽该模型的应用领域,提出了新的HASM模型算法。方法 采用新的差分格式计算HASM高斯方程中的一阶偏导数,以HASM预处理共轭梯度算法为例分析改进的差分格式对HASM的优化效果。结果 数值实验表明：在计算耗时及内存需求不变的情况下,采用新的差分格式的HASM算法可以显著提高单次迭代的模拟精度,同时能够降低关键采样点缺失对模拟结果精度的影响。进一步研究发现,当HASM采用新差分格式与原始差分格式（中心差分）交替迭代时,能够快速降低模拟结果的误差。结论 本文算法当达到指定的精度条时能够显著减小计算耗时,同时还能降低关键采样点缺失对模拟结果的影响。     

高精度曲面建模方法的系统构建

高精度曲面建模方法（HASM）是一种基于微分几何学曲面理论的曲面建模方法。大量数值实验表明,HASM的模拟精度高于Kriging、IDW、Spline等经典的插值方法,并已成功应用于土壤属性曲面建模、气温要素、DEM构建及生态系统变化趋势等领域。由于目前的HASM程序大多是用Matlab、C++、Fortran等语言开发的,受开发工具的限制,尚没有便于使用的图形界面,阻碍了方法的推广应用。针对这个问题,利用C#语言,在Visual Studio中构建了基于windows窗体的HASM模型系统,并做了一定的数值测试实验,结果表明了该系统的有效性。     

高精度曲面建模：HASM4

为了解决高精度曲面建模方法的速度问题,在大量数值实验的基础上,将模拟迭代方程HASM3改进为HASM4。分析结果表明,HASM4的CPU时间较HASM3有了大幅度的减少,而且随着计算域栅格总数的增加,这种减少幅度呈负幂指数规律;同时,随着计算规模的增大,HASM4达到收敛所需的迭代次数较HASM3达到收敛所需的迭代次数呈直线下降趋势。HASM4减少了模型计算量,提高了模型的运行速度,其模拟精度与HASM3相比也有一定幅度的提高。     

Markovian modelling and Fisher distribution for unsupervised classification of radar images

Statistical segmentation techniques based on hidden Markov field modelling have generated considerable interest in past years. They take contextual information into account in a particularly elegant and rigorous way. Although these models have been thoroughly tested, they can fail in some cases such as the non-stationary one. In this article, we propose use of the recently developed triplet Markov field, which models non-stationary images, and that of Fisher distribution, which is adapted to a wide range of surfaces for modelling synthetic aperture radar (SAR) image noise. Examples illustrate the difference between the approach proposed and classical ones. Various experiments indicate that the new model and its associated unsupervised algorithm perform better than classical ones.     

On bending invariant signatures for surfaces

Isometric surfaces share the same geometric structure, also known as the "first fundamental form." For example, all possible bendings of a given surface that includes all length preserving deformations without tearing or stretching the surface are considered to be isometric. We present a method to construct a bending invariant signature for such surfaces. This invariant representation is an embedding of the geometric structure of the surface in a small dimensional Euclidean space in which geodesic distances are approximated by Euclidean ones. The bending invariant representation is constructed by first measuring the intergeodesic distances between uniformly distributed points on the surface. Next, a multidimensional scaling technique is applied to extract coordinates in a finite dimensional Euclidean space in which geodesic distances are replaced by Euclidean ones. Applying this transform to various surfaces with similar geodesic structures (first fundamental form) maps them into similar signature surfaces. We thereby translate the problem of matching nonrigid objects in various postures into a simpler problem of matching rigid objects. As an example, we show a simple surface classification method that uses our bending invariant signatures.     

Hopf bifurcation via Volterra series

The Hopf bifurcation theorem gives a method of predicting oscillations which appear in a nonlinear system when a parameter is varied. There are many different ways of proving the theorem and of using its results, but the way which is probably the most useful, to control and system theorists, uses Nyquist loci in much the same way as the describing function method does. The main advantages of this method are dimensionality reduction, which eases the calculation, and the ability to cope with higher-order approximations than are used in the original Hopf theorem. This paper shows how such an approach to the Hopf bifurcation follows naturally and easily from Volterra series methods. Such use of Volterra series in nonlinear oscillations appears to be new. In many problems, the calculations involved are simplified when the Volterra series approach is taken, so the approach has practical merits as well as theoretical ones.     

A Compressed Data Structure for Surface Representation

One of the standard methods of simplifying the task of obtaining a shaded image of a solid object is to represent it by a polyhedron. Another method is to use sculptured surface modelling which represents surfaces by collections of surface patches. Using either method the surfaces can be approximated by facets, which are simple to shade according to photometry information.
To obtain a smooth image in regions of high curvature, the surface would typically be required to have hundreds or thousands of facets. Because of the large number of facets involved, it is extremely important that geometrical and topological information is stored in an efficient manner. This information must include all that is required for an unambiguous representation of the solid(s) in question.
The compressed data structure (CDS) is suitable for this purpose, and is capable of defining the majority of surfaces. The structure is intended to minimise the amount of data stored, with as much information as possible being implied. The CDS can be easily generated knowing the order of the vertices defining the surface.     

Non-Uniform Subdivision Surfaces with Sharp Features

Sharp features are important characteristics in surface modelling. However, it is still a significantly difficult task to create complex sharp features for Non-Uniform Rational B-Splines compatible subdivision surfaces. Current non-uniform subdivision methods produce sharp features generally by setting zero knot intervals, and these sharp features may have unpleasant visual effects. In this paper, we construct a non-uniform subdivision scheme to create complex sharp features by extending the eigen-polyhedron technique. The new scheme allows arbitrarily specifying sharp edges in the initial mesh and generates non-uniform cubic B-spline curves to represent the sharp features. Experimental results demonstrate that the present method can generate visually more pleasant sharp features than other existing approaches.     

Relief texture from specularities

In vision and graphics, advanced object models require not only 3D shape, but also surface detail. While several scanning devices exist to capture the global shape of an object, few methods concentrate on capturing the fine-scale detail. Fine-scale surface geometry (relief texture), such as surface markings, roughness, and imprints, is essential in highly realistic rendering and accurate prediction. We present a novel approach for measuring the relief texture of specular or partially specular surfaces using a specialized imaging device with a concave parabolic mirror to view multiple angles in a single image. Laser scanning typically fails for specular surfaces because of light scattering, but our method is explicitly designed for specular surfaces. Also, the spatial resolution of the measured geometry is significantly higher than standard methods, so very small surface details are captured. Furthermore, spatially varying reflectance is measured simultaneously, i.e., both texture color and texture shape are retrieved.     

New dominance concepts for multivariable control systems design

This paper sets out a revised view of the classical diagonal dominance method for multivariable feedback systems. The various types of dominance measure are unified by using one fundamental dominance theorem (FD)l. It is shown that the fundamental dominance condition yields the smallest dominance measure when compared with all the known classical diagonal dominance measures. In addition it is shown that the dominance measures such as row/column, generalized dominance and a few new ones are special cases and can be derived from this same FD theorem. This improved dominance criterion also provides the sufficient condition for a system to be approximated by a nominal one in the sense that the stabilization of this nominal system will assure the stability of the original one. Finally, a new type of dominance measure named L-dominance is presented. It has been shown that this new approach yields an even smaller dominance measure, and that when it is applied to matrices with non-positive off-diagonal elements, the L-dominant condition and the M-matrix condition are equivalent, but the testing of the former is easier and can be achieved via simple Gaussian eliminations     

Integrative 3D modelling of complex carving surface

Modelling of a complex carving surface is the most important process for digitization of art carving such as Chinese classical furniture carving, and it is difficult to be fulfilled. However, a complex 2D curve flower pattern can be easily acquired or drawn by handcraft or a drawing software. This paper presents a quick integrative 3D modeling method of complex carving surface based on a 2D curve flower pattern. The proposed method uses a scanning analysis algorithm, a normal distribution function and a distance function to model and create carving tracks. In this paper, the delamination, combination and interpolation of modelling process are described as well. The provided research method will make the modelling of complex carving surface more intelligent, agile, and will meet the requirement of integrative 3D modelling of digital art carving. Experimental results show that this method is of quick modelling and multi-model effective characteristics with realizable interactive designing and excellent practicability.     

KSpheres – an efficient algorithm for joining skinning surfaces

Besides classical point based surface design, sphere based creation of characters and other surfaces has been introduced by some of the recently developed modeling tools in computer graphics. ZSpheres^® by Pixologic, or Spore™ by Electronic Arts are just two prominent examples of these softwares. In this paper we introduce a new sphere based modeling tool, which allows us to create smooth, tubular-like surfaces by skinning a user-defined set of spheres. The main advantage of the new method is to provide a parametric surface with more natural and smoother shape, especially at the connection of branches than the surfaces provided by the existing softwares and methods.     

基于非均匀划分的分布式影像数据索引方法

本文介绍了现有的对影像数据管理和索引的方法及其存在的不足，提出了一种基于非均匀划分思想对分布式影像数据进行管理和索引的方法，避免了由于边缘补零带来的时间和空间开销。实验结果表明，本文方法能够支持对分布式多图幅的联合查询以及结果的无缝拼接，而且其时间和空间代价远小于现有方法。     

基于结式方法的代数曲面拼接

以同伦连续映射理论为基础,构造代数曲面拼接应该满足的代数方程组。然后,利用结式方法消去相关变元得到拼接曲面方程。两代数曲面拼接时,方程组是两个关于单位区间变元的方程。利用Sylvester结式消去该变元即可得到曲面拼接方程。对于多代数曲面,拼接过程可以考虑为不同种的连续映射。由此得到三种不同的曲面拼接方法,即串接法、过渡法和提升法。串接法可得到较低次的拼接曲面,但适用于代数曲面两两拼接且过渡曲面不相交的情况;过渡法适用于所有情况,但得到拼接曲面比较复杂;提升法是一种较好的算法,拼接时逐个将代数曲面并入拼接曲面中。该算法既可得到最低次拼接方程又适用于一般情况。上述方法的优点是无需考虑代数曲面方程中的变元,仅考虑对新增单位区间变元的处理。因此,算法的计算量小,并且能够预先得到拼接曲面时的计算量。     

Creating and Rendering Convolution Surfaces

Implicit surfaces obtained by convolution of multi-dimensional primitives with some potential function, are a generalisation of popular implicit surface models: blobs, metaballs and soft objects. These models differ in their choice of potential function but agree upon the use of underlying modelling primitives, namely, points. In this paper a method is described for modelling and rendering implicit surfaces built upon an expanded set of skeletal primitives: points, line segments, polygons, arcs and planes. An analytical solution to the convolution is described. This solution offers a more accurate and robust representation of the resultant implicit surface than previous methods. An algorithm for ray-tracing the surfaces formed through convolution of any combination of these primitives is also outlined.     

车身CAD/CAM扫描曲面的造型方法

本文介绍了与曲面造型方法有关的几个概念;从理论上阐述了扫描曲面的生成方法;重点论述了在汽车车身曲面造型中经常出现的各类扫描曲面的造型方法;最后介绍了扫描曲面的造型方法在实际车身零件曲面造型中的应用。     

基于画家算法的运动多面体的消隐方法

一般来说,画家算法（也称深度排序方法）适合于处理较为简单的多面体消隐问题。针对动态的复杂多面体,通过找出其在运动过程中的特点,提出了一种在画家算法的基础上减少重复排序,从而缩短运算时间的方法。在该方法提出之前,文中对其所基于的原理进行了证明。     

Geometric Modelling by Recursively Cutting Vertices

In this paper,a new method for curve and surface modelling is introduced which generates curves and surfaces by recursively cutting and grinding polygons and polyhedra.It is a generalization of the existing corner-cutting methods.A lot of properties,such as geometric continuity,representation,shape-preserving,and the algorithm are studied which show that such curves and surfaces are suitable for geometric designs in CAD,computer graphics and their application fields.