高斯投影下的人机交互式物体仿真算法研究

基于物体表面的离散三维数据点,提出了一种人机交互式物体仿真建模算法。使用概率统计中均值与方差的知识对数据点进行去噪处理,借助地球地理经度、纬度坐标的概念采用高斯投影的方法对数据点进行初始网格的构建,借助Bezier曲面寻找新的控制点来对初始网格进行插值细分。在物体的整个仿真过程中使用OpenGL中的键盘控制函数实现人机交互式的建模,并且对建模后的物体进行光照、材质等的设置。实验结果表明提出的仿真建模算法是真实有效的,可以直接应用于古建筑物的修复、3D打印等领域中。     

融合QPSO算法的多精度布料仿真建模方法

在布料建模领域，如何快速模拟布料形变之后的褶皱细节是研究的热点。通过使用多精度布料建模方法，在布料的不同形变区域使用不同精度的网格，可以有效平衡建模的精度和速度，已有的工作主要是在布料形变过程中，动态计算出布料质点邻域的曲率，依据人为设定的阈值，划分出布料的多精度区域，而在大部分场景中，布料的变形模式没有规律，固定不变的阈值可能会影响布料的仿真效果。针对该问题，首先将基于量子行为的粒子群算法引入建模过程，通过粒子群算法对布料表面的搜索，提高了布料弯曲部位的搜索效率，优化了多精度布料的建模速度和精度，其次针对布料仿真运动过程进行研究，参考布料受空气阻力的数学模型，以及粒子动力学中的数值积分方法，优化布料运动的仿真计算方法。实验证明，与现有布料多精度方法相比，该方法能较快检测到布料褶皱区域并判断是否需要细化，且能较好地表现出布料仿真过程中空气阻力对布料造成的形变。     

耕地养分空间插值技术与合理采样密度的比较研究

土壤养分连续空间分布数据是土壤信息系统工作的基础,土壤养分空间插值的研究因此变得尤为重要.对湖北省鄂州市进行土壤养分采样调查,以对作物生长作用较为密切的有效氮、有效磷、有效钾、pH为研究对象,运用克里格法(Kriging)、样条函数法(spline)、距离权重倒数法(IDw)3种插值方法对数据进行栅格化处理,分析比较3种插值方法所得结果的特性以及对耕地养分数据插值的适宜性.通过调整空间采样点密度,比较几种空间采样密度对插值结果的影响,总结3种插值方法在不同空间尺度下的插值精度,并在不同土壤类型内进行不同采样密度的插值分析.     

粒子系统基本理论及其应用

粒子系统是一种应用广泛而实用的物体建模方法。文章介绍了粒子系统的相关基本理论,讨论了粒子系统在非整体物体模拟和整体物体表面建模以及可形变物体建模中的应用。     

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。     

基于点采样的三维动画研究*

建立了一种对高弹性、高塑性物体进行动画模拟的新方式。本算法利用点采样的方式表现表面,使用采样分裂和聚合以适应动画中采样密度的变化。将弹性力学中的理论应用到三维动画中,使用MLS法计算应力、张力、弹性体力,使用可变张力来模拟塑性变化,利用向量位移进行了动画模拟,并使用了多种曲面表示提高表面质量。动画可表现融化、流动、分裂、融合等弹性、塑性变化,可用于实时交互也可用于高质量的离线渲染。     

GPU加速的高精度数字地面模型建模方法

以曲面轮为基础发展的高精度曲面建模方法（HASM）可以建立具有高精度的数字高程模型,但使用该方法需要求解偏微分方程离散产生的大规模线性方程组,计算量巨大,严重制约了对大规模数据的模拟应用;而现代GPU技术的发展使GPU越来越广泛地应用于通用计算加速。为了提高HASM方法的模拟速度,把高精度曲面模拟与GPU通用技术相结合,提出了GPU加速的高精度曲面建模方法。把HASM模拟过程中的有限差分离散、离散后的大规模线性系统求解分别使用GPU进行分解,使用共轭梯度（CG）和预处理共轭梯度方法（PCG）将求解任务分解为可以并行处理的独立的多任务,使得计算任务并行化,同时并行运行大规模线程,每个线程执行一个独立的任务,充分利用了现代GPU强大的通用计算能力,并行处理以获得加速。利用并行化加速的高精度曲面建模算法使用英伟达公司的统一计算开发架构（CUDA）编程实现,GPU采用该公司的Quadro 2000。分别应用该算法进行了数值实验和实际项目区数字高程模型（DEM）模拟实验。实验结果表明,充分利用GPU的并行处理能力加速后的HASM方法,在保证达到相同曲面模拟的精度条件下,和传统的CPU方法相比,算法可以获得超过一个数量级的加速。     

基于水平集的3D动画

将水平集方法引入3D动画中，提出了一种新的动画方法，用一形变模型表示物体的表面，由模型的变形来实现动画，为了使模型能自适应改变其拓扑结构，将模型的进化问题转化为函数的水平集进化问题，同时采用了一种新颖的速度延伸方法来实现水平集进行化提高建模精度，为了加快建模的速度，结合狭窄区域技术和多分辨率方法，提出了基于水平集方法的3D动画快速算法，实验结果表明该方法能用于复杂拓扑结构的物体动画。     

新型软土沉降监测仪的研制

为解决目前我国对土体沉降监测方面存在的自动化程度低、测量精度不高等问题,提出一种新型基于霍尔效应的软土沉降监测方法,设计出一款高精度实时在线监测仪器.选用多个霍尔器件组成阵列固定在假设不发生沉降位移的参考面上.土沉降带动沉降磁环的跟随沉降,根据霍尔效应原理,霍尔器件会输出变化的电信号.采用RS-485总线将阵列电信号实时上传至主机,经主机对实验数据进行科学建模处理,建立沉降位移与输出电信号的对应关系,从而实现对土沉降实时在线监测.搭建模拟测试平台,测试结果表明:对沉降磁环的定位测试,误差在1.2544 mm内,相比较于利用接近原理的传统测量仪器测量精度更高,数据稳定性更好,可以实现实时在线测量.     

径向基函数网络的隐式曲面方法

将径向基函数网络与隐式曲面构造原理相结合,提出一种构造隐式曲面的方法．首先以描述物体曲面的隐式函数为基础构造三元显式函数,然后用径向基函数网络逼近显式函数,最后从神经网络的仿真超曲面得到描述物体的封闭曲面;并证明了在理论上此等值面可以以任意精度逼近物体曲面．该方法具有光滑度高、稳定性好,尤其适用少量采样点情形等特点．实验表明,它具有很强的造型能力．     

Exploration of local surface geometry with minimum number of contact points and surface normal information

In this paper, we propose a method of exploring the surface geometry of an unknown object by touch. The method is based on the idea that a three-dimensional surface geometry can be reconstructed from two principal curvatures of the object which are estimated from three concurrent curves. First, the process to minimize the number of contact points is addressed for the approximation of an arbitrary curve, which uses normal vectors at the contact points. Then, an algorithm for reconstructing a three-dimensional local surface from four contact points, two of which can be used to compute a normal curvature, is presented. Lastly, our method is applied to cylindrical, spherical and planar objects in simulation and experiments for validation.     

Efficient circular arc interpolation based on active tolerance control

In this paper, we present an efficient sub-optimal algorithm for fitting smooth planar parametric curves by G¹ arc splines. To fit a parametric curve by an arc spline within a prescribed tolerance, we first sample a set of points and tangents on the curve adaptively as well as with enough density, so that an interpolation biarc spline curve can be with any desired high accuracy. Then, we construct new biarc curves interpolating local triarc spirals explicitly based on the control of permitted tolerances. To reduce the segment number of fitting arc spline as much as possible, we replace the corresponding parts of the spline by the new biarc curves and compute active tolerances for new interpolation steps. By applying the local biarc curve interpolation procedure recursively and sequentially, the result circular arcs with no radius extreme are minimax-like approximation to the original curve while the arcs with radius extreme approximate the curve parts with curvature extreme well too, and we obtain a near optimal fitting arc spline in the end. Even more, the fitting arc spline has the same end points and end tangents with the original curve, and the arcs will be jointed smoothly if the original curve is composed of several smooth connected pieces. The algorithm is easy to be implemented and generally applicable to circular arc interpolation problem of all kinds of smooth parametric curves. The method can be used in wide fields such as geometric modeling, tool path generation for NC machining and robot path planning, etc. Several numerical examples are given to show the effectiveness and efficiency of the method.     

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。     

Geometric accuracy analysis for discrete surface approximation

In geometric modeling and processing, computer graphics and computer vision, smooth surfaces are approximated by discrete triangular meshes reconstructed from sample points on the surfaces. A fundamental problem is to design rigorous algorithms to guarantee the geometric approximation accuracy by controlling the sampling density. This paper gives explicit formulae to the bounds of Hausdorff distance, normal distance and Riemannian metric distortion between the smooth surface and the discrete mesh in terms of principle curvature and the radii of geodesic circum-circle of the triangles. These formulae can be directly applied to design sampling density for data acquisitions and surface reconstructions. Furthermore, we prove that the meshes induced from the Delaunay triangulations of the dense samples on a smooth surface are convergent to the smooth surface under both Hausdorff distance and normal fields. The Riemannian metrics and the Laplace–Beltrami operators on the meshes are also convergent to those on the smooth surfaces. These theoretical results lay down the foundation for a broad class of reconstruction and approximation algorithms in geometric modeling and processing.Practical algorithms for approximating surface Delaunay triangulations are introduced based on global conformal surface parameterizations and planar Delaunay triangulations. Thorough experiments are conducted to support the theoretical results.     

Adaptive-feedrate interpolation for parametric curves with a confined chord error

Recently, modern manufacturing systems have been designed which can machine arbitrary parametric curves while greatly reducing data communication between CAD/CAM and CNC systems. However, a constant feedrate and chord accuracy between two interpolated points along parametric curves are generally difficult to achieve due to the non-uniform map between curves and parameters. A speed-controlled interpolation algorithm with an adaptive feedrate is proposed in this paper. Since the chord error in interpolation depends on the curve speed and the radius of curvature, the feedrate in the proposed algorithm is automatically adjusted so that a specified limit on the chord error is met. Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples are provided to verify the feasibility and precision of the proposed interpolation algorithm.     

The probability density of the total curvature of a uniform random Gaussian sea surface in the specular points

Assuming that sea surface is a random uniform Gaussian function, an analytical expression is developed for the probability distribution density of the total curvature of the surface in specular reflection points. The density can be expressed in terms of an integral, and its asymptotics acquire a simple form for large values of the total curvature. A numerical experiment to verify the probability distribution density is also given.     

中国西部地区积雪深度的空间插值比较

应用反距离加权法、样条函数法、Kriging法对中国西部地区(79.05°～103.57°E,27.17°～48.05°N)113个气象台站观测的年平均积雪深度进行空间插值比较研究。结果表明反距离加权法和样条函数法的插值结果与积雪深度的实际分布情况有一定的差异;普通Kriging法能够反映出研究区积雪深度分布的空间结构特征,与实际情况比较吻合。影响插值结果精度的主要原因是研究区内气象台站稀少且空间分布很不均匀。可以通过合理的采样设计,将确定性方法和随机方法相结合,并考虑地形、气候等影响积雪分布的因素来提高空间插值的精度。     

基于残差和密度网格的簇心自确认聚类算法

为了解决DPC（Clustering by fast search and ?nd of Density Peaks）算法中依赖截断距离、计算复杂度大和需要人工选取簇心的问题，提出了基于残差和密度网格的簇心自确认聚类算法。将数据对象映射到网格上，用网格对象作为聚类对象，删除不含任何信息的网格对象；用特定方式计算网格对象的密度值和距离值；接着通过残差分析确定含有簇心的网格对象；用与非边缘点的距离和自变动的阈值来处理网格边缘点和噪声点。仿真实验表明所提出的算法与一些其他聚类算法对比，有着较高的聚类精度和较低的时间复杂度。     

Optimal shape error analysis of the matching image for a free-form surface

When using an optical non-contact scanning system to measure an object that has a large surface, large curvature, or a full 360° profile, one can acquire only one set of sectional measurement points each time. For reconstructing the entire object, every set of sectional measurement points acquired at different positions must match. Therefore, the optimal shape error analysis for the matching image of two or more sets of sectional measurement points is desired. This paper presents a measurement system that combines two CCD cameras, one line laser and a three-axis motion stage. It forms an optical non-contact scanning system in association with the mathematical method of direct shape error analysis for the use in reverse engineering. This analysis and measurement system can be used for the profile measurements of free-form objects. It analyzes the matching image of a free-form surface with high efficiency and accuracy. The validity and applicability of this system are demonstrated by two practical examples.     

可展Bézier曲面的设计

通过引入移位算子,利用de Casteljau算法,得到了可展Bézier直纹面是单参数平面族的包络的结论,并简洁地导出了两条边界曲线分别为n次和m次的空间Bézier曲线的直纹面为可展曲面的充分必要条件。提出了二次Bézier可展曲面的设计方法：给定可展曲面的4个角点a0、b0、a2、b2和两个自由设计参数?姿、?滋,则待求的2个控制顶点a1、b1是在前2个控制顶点a0、b0的线性插值点a*与后2个控制顶点a2、b2的线性插值点b*的连线上,并且也是a*、b*这2个线性插值点的线性插值,即这4点a*、a1、b1、b*共线。该设计方法简单,可以通过2个自由设计参数?姿、?滋方便地控制曲面的形状。实例说明设计效果良好。