Novel method for exactly evaluating the energy of Catmull-Clark subdivision surfaces

A novel method is produced to evaluate the energy of the Catmull-Clark subdivision surface including extraordinary points in the control mesh. A closed-form analytic formula for thin plate energy of the Catmull-Clark subdivision surface of arbitrary topology is derived through translating the Catmull-Clark subdivision surface into bi-cubic B-spline surface pieces. Using this method, both the membrane energy and the thin plate energy can be evaluated without requiring recursive subdivision. Therefore, it is more efficient and more accurate than the existing methods for calculating the energy of the Catmull-Clark subdivision surface with arbitrary topology. The example of surface fairing demonstrates that this method is efficient and successful for evaluating the energy of subdivision surfaces.

ANN model of subdivision error based on genetic algorithm

According to the test data of subdivision errors in the measuring cycle of angular measuring system, the characteristics of subdivision errors generated by this system are analyzed. It is found that the subdivision errors are mainly due to the rotary-type inductosyn itself. For the characteristic of cyclical change, the subdivision errors in other measuring cycles can be compensated by the subdivision error model in one measuring cycle. Using the measured error data as training samples, combining GA and BP algorithm, an ANN model of subdivision error is designed. Simulation results indicate that GA reduces the uncertainty in the training process of the ANN model, and enhances the generalization of the model. Compared with the error model based on the least-mean-squared method, the designed ANN model of subdivision errors can achieve higher compensating precision.

CURVE AND SURFACE INTERPOLATIONBY SUBDIVISION ALGORITHMS

Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.

SMOOTH SURFACE INTERPOLATION OVER ARBITRARY TRIANGULATIONS BY SUBDIVISION ALGORITHMS

A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.

Improved non-uniform subdivision scheme with modified Eigen-polyhedron

In this study,a systematic refinement method was developed for non-uniform Catmull-Clark subdivision surfaces to improve the quality of the surface at extraordinary points(EPs).The developed method modifies the eigenpolyhedron by designing the angles between two adjacent edges that contain an EP.Refinement rules are then formulated with the help of the modified eigenpolyhedron.Numerical experiments show that the method significantly improves the performance of the subdivision surface for non-uniform parameterization.

A Ternary 4-Point Approximating Subdivision Scheme

In this paper, the author presents a class of stationary ternary 4-point approximating symmetrical subdivision algorithm that reproduces cubic polynomials. By these subdivision algorithms at each refinement step, new insertion control points on a finer grid are computed by weighted sums of already existing control points. In the limit of the recursive process, data is defined on a dense set of point, The objective is to find an improved subdivision approximating algorithm which has a smaller support and a higher approximating order. The author chooses a ternary scheme because the best way to get a smaller support is to pass from the binary to ternary or complex algorithm and uses polynomial reproducing propriety to get higher approximation order. Using the cardinal Lagrange polynomials the author has proposed a 4-point approximating ternary subdivision algorithm and found that a higher regularity of limit function does not guarantee a higher approximating order. The proposed 4-point ternary approximation subdivision family algorithms with the mask a have the limit function in C2 and have approximation order 4. Also the author has demonstrated that in this class there is no algorithm whose limit function is in C3. It can be seen that this stationary ternary 4-point approximating symmetrical subdivision algorithm has a lower computational cost than the 6-point binary approximation subdivision algorithm for a greater range of points.

Estimating Subdivision Depth of Catmull-Clark Surfaces

In this paper, both general and exponential bounds of the distance between a uniform Catmull-Clark surface and its control polyhedron are derived. The exponential bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Based on the exponential bound, we can predict the depth of subdivision within a user-specified error tolerance. This is quite useful and important for pre-computing the subdivision depth of subdivision surfaces in many engineering applications such as surface/surface intersection, mesh generation, numerical control machining and surface rendering.

Conjugate-Gradient Progressive-Iterative Approximation for Loop and Catmull-Clark Subdivision Surface Interpolation

Loop and Catmull-Clark are the most famous approximation subdivision schemes,but their limit surfaces do not interpolate the vertices of the given mesh.Progressive-iterative approximation(PIA)is an efficient method for data interpolation and has a wide range of applications in many fields such as subdivision surface fitting,parametric curve and surface fitting among others.However,the convergence rate of classical PIA is slow.In this paper,we present a new and fast PIA format for constructing interpolation subdivision surface that interpolates the vertices of a mesh with arbitrary topology.The proposed method,named Conjugate-Gradient Progressive-Iterative Approximation(CG-PIA),is based on the Conjugate-Gradient Iterative algorithm and the Progressive Iterative Approximation(PIA)algorithm.The method is presented using Loop and Catmull-Clark subdivision surfaces.CG-PIA preserves the features of the classical PIA method,such as the advantages of both the local and global scheme and resemblance with the given mesh.Moreover,CG-PIA has the following features.1)It has a faster convergence rate compared with the classical PIA and W-PIA.2)CG-PIA avoids the selection of weights compared with W-PIA.3)CG-PIA does not need to modify the subdivision schemes compared with other methods with fairness measure.Numerous examples for Loop and Catmull-Clark subdivision surfaces are provided in this paper to demonstrate the efficiency and effectiveness of CG-PIA.

Continuity of non-uniform recursive subdivision surfaces

Since Doo-Sabin and Catmull-Clark surfaces were proposed in 1978, eigenstructure, convergence and continuity analyses of stationary subdivision have been performed very well, but it has been very difficult to prove the convergence and continuity of non-uniform recursive subdivision surfaces (NURSSes, for short) of arbitrary topology. In fact, so far a problem whether or not there exists the limit surface as well as G1 continuity of a non-uniform Catmull-Clark subdivision has not been solved yet. Here the concept of equivalent knot spacing is introduced. A new technique for eigenanaly-sis, convergence and continuity analyses of non-uniform Catmull-Clark surfaces is proposed such that the convergence and G1 continuity of NURSSes at extraordinary points are proved. In addition, slightly improved rules for NURSSes are developed. This offers us one more alternative for modeling free-form surfaces of arbitrary topologies with geometric features such as cusps, sharp edges, creases and darts, while elsewhere maintaining the same order of continuity as B-spline surfaces.

Emergency airport site selection using global subdivision grids

The occurrence of large-magnitude disasters has significantly aroused public attention regarding diversified site selection of emergency facilities.In particular,emergency airport site selection(EASS)is highly complicated,and relevant research is rarely conducted.Emergency airport site selection is a scenario with a wide spatiotemporal range,massive data,and complex environmental information,while traditional facility site selection methods may not be applicable to a large-scale time-varying airport environment.In this work,an emergency airport site selection application is presented based on the GeoSOT-3D global subdivision grid model,which has demonstrated good suitability of the discrete global grid system as a spatial data structure for site selection.This paper proposes an objective function that adds a penalty factor to solve the constraints of coverage and the environment in airport construction.Through multiple iterations of the simulated annealing algorithm,the optimal airport construction location can be selected from multiple preselected points.With experimental verifications,this research may effectively and reasonably solve the emergency airport site selection issue under different circumstances.

Some Sufficient Conditions for Convergent Multivariate Subdivision Schemes with Nonnegative Finite Masks

It is well known that the convergence of multivariate subdivision schemes with finite masks can be characterized via joint spectral radius. For nonnegative masks, we will present in this paper some computable simply sufficient conditions for the convergence, which will cover a substantially large class of schemes.

CORNER-CUTTING SUBDIVISION SURFACES OF GENERAL DEGREES WITH PARAMETERS

As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves:vertex splitting plus repeated midpoint averaging.In this paper,we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting,and generalize the strategy to arbitrary topological surfaces of general degree.By adjusting the free parameter,the proposed method can generate subdivision surfaces with flexible shapes.Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.

基于三维网格卷积的布料仿真模拟

针对当前布料仿真中模拟成本高且耗时长的问题,提出一种直接对三维布料网格卷积的布料模拟方法。对三维布料网格进行螺旋卷积,使用点填充方法增加采样点,存储局部域;采用顶点抽取算法对局部块进行池化,使用基于Gauss-Bonnet定理曲率的惩罚因子对顶点抽取算法进行增强,当局部块数量小于开始时数量的60%时停止顶点抽取;最后训练神经细分网络对抽取后的整体网格进行上采样,其中使用改进的蝶形细分算法生成新顶点。实验结果表明,与目前已有方法相比,该布料模拟方法能够保留丰富真实的褶皱,减少模拟成本和时间,是一种高效的布料模拟方法。

交通规划导向的科技赋能交通小区划分方法

文章以手机信令、路网大数据为基础,提出了针对交通规划的科技赋能交通小区划分方法,以路网数据划分聚类单元,利用手机信令数据准确识别聚类单元内居民出行时空分布特征,基于改进耦合空间聚类算法进行聚类,借助现状路网对聚类结果进行修正得到交通小区划分结果。宁波市实例研究表明,科技赋能交通小区划分方法能兼顾居民出行时空特征和城市路网匹配,并能较好保证交通小区的整体连续性,该方法适用性强,可为交通规划的科学制定提供借鉴。

用于正弦波频率估计的修正I-Rife算法

对正弦波信号的频率估计是雷达领域常见的问题。当真实频率接近量化频点时,I-Rife算法的频移因子的计算会产生较大误差,为提高频率估计的精度,本文通过分析Rife及I-Rife算法的性能及误差产生的原因,利用频谱细化的方法,提出了一种修正I-Rife算法,即用峰值频点左右各0.5点处的频谱幅值来替代频谱峰值点的幅值和次大值频点处的幅值进行插值计算,对频率偏移值进行更为准确的估计,在计算量与I-Rife算法几乎相同的情况下,有效地提高了频率的估计精度。仿真结果表明,改进后的I-Rife算法整体性能优于I-Rife算法,且估计的均方根误差更接近于克拉美-罗下界。

非平均化自适应Catmull-Clark细分算法

提出一种基于网格边的光滑度计算来进行Catmull-Clark自适应细分的新算法。该方法能够在满足显示需求的前提下较好地减小细分曲面过程中的网格生成数,同时解决了由于采用网格顶点曲率计算,来实现自适应细分方法中平均化生成顶点曲率带来的不足。通过对比试验,算法能更好地区别当前细分网格中光滑与非光滑区域,增加对非光滑区域网格加密密度,并且该算法能够普遍适用于较复杂的细分模式中,具有一定的推广价值。

一种可调的Catmull-Clark细分曲面

通过在曲面细分过程中引入一个参数t(0≤t≤1),使得Catmull-Clark细分曲面可调,得出一种新的算法。这种算法简单直观,通过调节参数t值,可以得到一族细分曲面。该族细分曲面不但保留了许多Catmull-Clark细分曲面的特性,而且可以方便地解决在工程中经常遇到的调整曲面位置和形状的问题。同时,还可以将这种细分算法作为Catmull-Clark细分的前置处理方法。文中详细讨论了这一算法,并给出了验证实例。

融和并行CORDIC算法的编码器细分

为在外形尺寸与码盘刻线数的双重限制下提升小型光电编码器的精度与分辨率,提出了一种基于坐标旋转计算法(Coordinate Rotation Digital Computer,CORDIC)的编码器细分方法。对现阶段众多电子学细分方法优缺点进行剖析,在细分原理的基础上分析误差产生原因,运用改进型CORDIC算法对运动不满一周期内的信号进行高精度细分处理。实验结果表明,相较于其他方法,最大最小峰谷差值分别减少了60″、20″、10″,均方根误差分别下降了77.1%、59.2%、36.4%,实现了高精度化和小型化。

改进的自适应特征细分方法及其对Catmull-Clark曲面的实时绘制

传统的自适应特征细分(FAS)算法对曲面上的全部特征点进行统一深度的细分,影响算法的执行效率,针对这一问题,提出了一种自适应特征细分方法。首先,设计了一种模块,即特征块处理单元(FPU),用于计算不规则区域的细分因子,根据Catmull-Clark细分模式来处理特征区域的不规则块,同时减少了GPU渲染块的数目;然后,对FAS的数据结构进行扩充,将关键点数据存放在细分表和渲染表中,GPU对表中数据进行全局细分与绘制,提高了细分和绘制的速度。实验结果表明,改进后的细分表和渲染表结构能够保证细分的动态特性和渲染的实时性。与传统FAS方法相比,本文算法能够保证三维曲面的绘制精度的同时,提高了28%的绘制速度,在实时性方面优于传统FAS方法。

改进Catmull-Clark细分算法及其在船用螺旋桨设计中的应用

基于舰艇作战或巡航时隐身性能的需要,针对舰艇关键零件的设计和加工制造现状,结合应用日益广泛的细分曲面造型方法,以Catmull-Clark细分算法为基础,提出一种基于网格边光顺程度计算的自适应细分算法。将该算法应用于船用螺旋桨的设计数值实验,由建模软件3DS MAX及其内部编程语言MAXScript来实现,并将实验结果与原始的Catmull-Clark算法细分结果、传统的顶点或边曲率法自适应细分结果进行了比较。数值实验结果表明,在满足零件设计现实需求的前提下,该自适应细分算法能较好地减少网格数量:当边的光顺度阈值取为0.825时,网格数降低了约28.83%,可提高计算速度,减小存储空间。该算法能克服以往基于均值计算的自适应算法存在的区分能力不足的影响。