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1.
INTRODUCTIONTheOSSI(OffsetSurface/SurfaceIntersection)problemisasub-problemofgeneralSSI.AlthoughtheOSSIproblemcanberesolvedbyapplyinggeneralSSIalgorithm,itiscomputationallyexpensiveandexhaustive.Inrecentdecades,effortshavebeenfocusedoncomputingSSIexactly,efficiently,androbustlyinageneralsetting(Abdel-MalekandYeh,1997;Changetal.,1994;BurkeandSabharwal,1996;Mullenheim,1991).Thesetechniquescanbeclassifiedmainlyintofivecategories:algebraic,latticeevaluation,marching(tracing)method,… 相似文献
2.
The problem of parametric speed approximation of a rational curve is raised in this paper. Offset curves are widely used in
various applications. As for the reason that in most cases the offset curves do not preserve the same polynomial or rational
polynomial representations, it arouses difficulty in applications. Thus approximation methods have been introduced to solve
this problem. In this paper, it has been pointed out that the crux of offset curve approximation lies in the approximation
of parametric speed. Based on the Jacobi polynomial approximation theory with endpoints interpolation, an algebraic rational
approximation algorithm of offset curve, which preserves the direction of normal, is presented.
Project supported by the National Basic Research Program (973) of China (No. 2002CB312101) and the National Natural Science
Foundation of China (Nos. 60373033 and 60333010) 相似文献
3.
A new algorithm is presented that generates developable Bézier surfaces through a Bézier curve called a directrix. The algorithm
is based on differential geometry theory on necessary and sufficient conditions for a surface which is developable, and on
degree evaluation formula for parameter curves and linear independence for Bernstein basis. No nonlinear characteristic equations
have to be solved. Moreover the vertex for a cone and the edge of regression for a tangent surface can be obtained easily.
Aumann’s algorithm for developable surfaces is a special case of this paper.
Project supported by the National Basic Research Program (973) of China (No. 2004CB719400), the National Natural Science Foundation
of China (Nos. 60373033 and 60333010) and the National Natural Science Foundation for Innovative Research Groups (No. 60021201),
China 相似文献
4.
A family of quasi-cubic blended splines and applications 总被引：4，自引：0，他引：4
SU Ben-yue TAN Jie-qing 《浙江大学学报(A卷英文版)》2006,7(9):1550-1560
INTRODUCTION Bézier curves and uniform B-spline curves are powerful tools for constructing free form curves and surfaces (FFC/FFS). But they cannot represent the arcs, hyperbola, sphere, cylinders and other transcendental curves and surfaces exactly. In order to avoid the in- conveniences, many bases are presented in other new spaces (Zhang, 1996; Pe?a, 1997; Walz, 1997; Sánchez-Reyes, 1998; Mainar et al., 2001). Note that, these existing methods can deal with both polynomial curve… 相似文献
5.
In this paper, a G1, C1, C2 PH-spline is employed as an approximation for a give Bézier curve within error bound and further renders offset which can
be regarded as an approximate offset to the Bézier curve. The errors between PH-spline and the Bézier curve, the offset to
PH-spline and the offset to the given Bézier curve are also estimated. A new algorithm for constructing offset to the Bézier
curve is proposed.
Project supported by the National Natural Foundation of China (No. 60073023) and the National Basic Research Program (973)
of China (No. 2002CB312101) 相似文献
6.
为了能快速作出多个曲面围成区域的简图,手工作图有时候很有必要.手工作曲面围成的立体图的难点是画出曲面的交线.先化简联立方程,结合投影和平行截割法,准确地描出交线.给出了作简图的数学原理和一般步骤.学生作图效果表明这种作图法操作性强,便于学生掌握. 相似文献
7.
We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data
points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an
approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates
of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that
reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D
Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further
research and improvements.
Project supported in part by the Special Funds for Major State Basic Research Projects (Grant No. G19990328) and Foundation
for University Key Teacher by the Ministry of Education(Grant No.CCR-9901986) 相似文献
8.
CAI Hong-jie WANG Guo-jin 《浙江大学学报(A卷英文版)》2007,8(10):1650-1656
Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduction for polynomial Bezier curves to the algorithms of constrained multi-degree reduction for rational Bezier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bezier curves, which are used to make uniform the weights of the rational Bezier curves as accordant as possible, and then do multi-degree reduction for each component in homogeneous coordinates. Compared with the two traditional algorithms of ＂cancelling the best linear common divisor＂ and ＂shifted Chebyshev polynomial＂, the two new algorithms presented here using reparameterization have advantages of simplicity and fast computing, being able to preserve high degrees continuity at the end points of the curves, do multi-degree reduction at one time, and have good approximating effect. 相似文献
9.
We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^2-continuity. Instead of moving the control points, we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve＇s discrete structure, where the approximation error is measured by L2-norm. We use geometric information about the curves to generate the merged curve, and the approximation error is smaller. We can obtain control points of the merged curve regardless of the degrees of the two original curves. We also discuss the merged curve with point constraints. Numerical examples are provided to demonstrate the effectiveness of our algorithms. 相似文献
10.
为提高城市主干道交通通行能力,通过建立多交叉口信号配时的优化模型,对主干道单点交叉口配时优化和相邻交叉口之间相位差的线性协调进行研究,并利用Matlab软件对模型进行求解。最后以福建省莆田市荔城南大道与国道G324、荔园西路两个相邻交叉口为优化对象,并利用Synchro软件对优化结果进行仿真。结果表明,优化方案使交叉口服务水平提高一个等级,两个交叉口总延迟时间降低20.1%。 相似文献
11.
复杂曲面笔式加工的直接插补算法 总被引：2，自引：0，他引：2
针对复杂曲面笔式加工时位于曲面上的空间曲线型刀具轨迹,给出一种直接插补算法.即对以投影方式形成的位于曲面上的空间曲线形式的刀轨,根据导动曲线和刀触点轨迹线之间的几何运动关系,通过泰勒展开近似得到刀触点轨迹线上插补点所对应的导动线的参数,再反求间接得到刀触点坐标,从而生成控制机床运动的指令.该方法的实现扩充了CNC系统的轨迹控制功能,提高了复杂曲面的加工效率.仿真结果表明算法可行而且有效.该算法也可以应用到整体曲面加工中. 相似文献
12.
INTRODUCTION Offset curves/surfaces, also called parallel curves/surfaces, are defined as the locus of the points which are at constant distance along the normal from the generator curves/surfaces. As for a planar gen- erator curve Γ:C(t)=(x(t),y(t)), the parametric speed and its norm σ(t) are defined respectively as (Farouki, 1992) C ′( t ) =( x ′( t ), y ′(t )),σ (t ) = x ′ 2 (t ) y ′2(t ). (1) Subsequently the offset curve of the generator curve, which is at constant distanc… 相似文献
13.
A method for computing the visible regions of free-form surfaces is proposed in this paper. Our work is focused on accurately
calculating the visible regions of the sequenced rational Bézier surfaces forming a solid model and having coincident edges
but no inner-intersection among them. The proposed method calculates the silhouettes of the surfaces without tessellating
them into triangle meshes commonly used in previous methods so that arbitrary precision can be obtained. The computed silhouettes
of visible surfaces are projected onto a plane orthogonal to the parallel light. Then their spatial relationship is applied
to calculate the boundaries of mutual-occlusion regions. As the connectivity of the surfaces on the solid model is taken into
account, a surface clustering technique is also employed and the mutual-occlusion calculation is accelerated. Experimental
results showed that our method is efficient and robust, and can also handle complex shapes with arbitrary precision.
Project supported by the National Basic Research Program (973) of China (No. 2002CB312106) and the National Natural Science
Foundation of China (Nos. 60533070, and 60403047). The third author was supported by the project sponsored by a Foundation
for the Author of National Excellent Doctoral Dissertation of China (No. 200342) and a Program for New Century Excellent Talents
in University (No. NCET-04-0088), China 相似文献
14.
WANG Yuan-jun CAO Yuan 《浙江大学学报(A卷英文版)》2006,7(9):1572-1577
INTRODUCTION In Computer Aided Design, fairness is one of the basic requirements for designing curves. If the curves are not fair, the design will be unsatisfactory and the producing process will be discommodious. In practice, there are all kinds of errors such as modelling error and measuring error. It means that the information on the data points may not be accurate. In order to obtain fair curves by interpolating these data points, we should fair the data points first. This is the so… 相似文献
15.
提出了一种新的离散点毛坯曲面重构算法。此算法是一种纯几何的构造方法，其基本出发点是首先在（u,w)参数平面内对实际测量所取得的离散数据点分别进行u向和w向排序，按照排序结果确定每一个实际测量点的矩形作用域，之后进行一种特殊的Hermite插值，再将重叠的作用域迭加即可。论文最后给出了一个计算实例，验证了此算法的正确性和有效性。 相似文献
16.
17.
FANG You-tong YAO Ying-ying 《浙江大学学报(A卷英文版)》2007,8(3):412-415
In this paper, a modified transient finite element (FE) algorithm for the performance analysis of magnetically levitated vehicles of electromagnetic type is presented. The algorithm incorporates the external power system and vehicle’s movement equations into FE model of transient magnetic field computation directly. Sliding interface between stationary and moving region is used during the transient analysis. The periodic boundaries are implemented in an easy way to reduce the computation scale. It is proved that this method can be used for both electro-motional static and dynamic cases. The test of a transformer and an EMS-Maglev system reveals that the method generates reasonable results at very low computational costs comparing with the transient FE analysis. 相似文献
18.
Novel MgCl2-supported Ziegler-Natta (Z-N) catalysts prepared using a new one-pot ball milling method can effectively control the amounts
of Ti-loading in the catalysts. Complex GPC data on polypropylene synthesized by these novel catalysts were analyzed using
the method of fitting the molecular weight distribution (MWD) curves with a multiple Flory-Schulz function. It was found that
multiple active centers exist in these novel catalysts. Detailed study of the effects of the Ti-loadings in the catalysts
on the distribution of the active centers showed that the Ti-loadings in the novel MgCl2-supported Z-N catalysts might affect the proportion of each type of active centers; and might be the main factor responsible
for the effect of the Ti-loadings on the microstructure, the molecular weight and molecular weight distribution width of the
resultant polymer, the catalytic activity and polymerization kinetics.
Project supported by the National Natural Science Foundation of China (No. 20172045), Science and Technology Plan Fund of
Zhejiang Province (No. 001101116) and Foundation for Doctors of Ningbo City (No. 2003A62012), China 相似文献
19.
YANG Cheng-lei QI Meng MENG Xiang-xu LI Xue-qing WANG Jia-ye 《浙江大学学报(A卷英文版)》2006,7(9):1522-1529
INTRODUCTION To compute the minimum distance between two convex polygons or polyhedrons is often a main step of many applications, such as collision detection (Choi et al., 2006; Li et al., 2003), path planning. In order to reduce the time complexity of the algorithm as much as possible, the convex property must be applied fully. Edelsbrunner (1985) proposed an algorithm for computing the minimum distance between two dis- joint convex polygons. The algorithm takes O(logm logn) time, and … 相似文献