共查询到19条相似文献，搜索用时 140 毫秒
1.
Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduc- tion for polynomial Bézier curves to the algorithms of constrained multi-degree reduction for rational Bézier curves. The idea is introducing two criteria, variance criterion and ratio criterion, for reparameterization of rational Bézier curves, which are used to make uniform the weights of the rational Bézier 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
2.
LU Li-zheng WANG Guo-zhao 《浙江大学学报(A卷英文版)》2007,8(10):1657-1662
This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applica 相似文献
3.
This paper presents a quadratic programming method for optimal multi-degree reduction of Bézier curves with G1-continuity. The L2 and l2 measures of distances between the two curves are used as the objective functions. The two additional parameters, available from the coincidence of the oriented tangents, are constrained to be positive so as to satisfy the solvability condition. Finally, degree reduction is changed to solve a quadratic problem of two parameters with linear constraints. Applica- tions of degree reduction of Bézier curves with their parameterizations close to arc-length parameterizations are also discussed. 相似文献
4.
We decompose the problem of the optimal multi-degree reduction of Bezier curves with comers constraint into two simpler subproblems, namely making high order interpolations at the two endpoints without degree reduction, and doing optimal degree reduction without making high order interpolations at the two endpoints. Further, we convert the second subproblem into multi-degree reduction of Jacobi polynomials. Then, we can easily derive the optimal solution using orthonormality of Jacobi polynomials and the least square method of unequally accurate measurement. This method of ＇divide and conquer＇ has several advantages including maintaining high continuity at the two endpoints of the curve, doing multi-degree reduction only once, using explicit approximation expressions, estimating error in advance, low time cost, and high precision. More importantly, it is not only deduced simply and directly, but also can be easily extended to the degree reduction of surfaces. Finally, we present two examples to demonstrate the effectiveness of our algorithm. 相似文献
5.
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
6.
A new method in highway route design: joining circular arcs by a single C-Bézier curve with shape parameter 总被引：1，自引：1，他引：0
We constructed a single C-Bezier curve with a shape parameter for G^2 joining two circular arcs. It was shown that an S-shaped transition curve, which is able to manage a broader scope about two circle radii than the Bezier curves, has no curvature extrema, while a C-shaped transition curve has a single curvature extremum. Regarding the two kinds of curves, specific algorithms were presented in detail, strict mathematical proofs were given, and the effectiveness of the method was shown by examples This method has the following three advantages： （1） the pattern is unified; （2） the parameter able to adjust the shape of the transition curve is available; （3） the transition curve is only a single segment, and the algorithm can be formulated as a low order equation to be solved for its positive root. These advantages make the method simple and easy to implement. 相似文献
7.
Two kinds of B-basis of the algebraic hyperbolic space 总被引：15，自引：2，他引：15
In this paper, two new kinds of B-basis functions called algebraic hyperbolic (AH) Bezier basis and AH B-Spline basis are presented in the space (?)k=span{1,t,...,tk-3,sinht,cosht}, in which K is an arbitrary integer larger than or equal to 3. They share most optimal properties as those of the Bezier basis and B-Spline basis respectively and can represent exactly some remarkable curves and surfaces such as the hyperbola, catenary, hyperbolic spiral and the hyperbolic paraboloid. The generation of tensor product surfaces of the AH B-Spline basis have two forms: AH B-Spline surface and AH T-Spline surface. 相似文献
8.
Aiming at solving the problems of lacking listening skills practices in English class. The paper is written for two purposes. Firstly, it intends to drive the attention of present obstacles in English listening teaching. Most children in China have their English classes at schools, however, they don’t learn too much English they just learn about English. After years of learning the problems come up: the college students who have passed CET4(College English Test) and CET6 are unable to speak or listen to native speakers. Secondly, it tries to introduce the listening skills and the methods of teaching it. Language is not a knowledge but a skill, to learn language does not mean to know as many rules and information about it, but is to practice from the first day your learn it and do practice as much as possible. 相似文献
9.
YANG Xiao-hua HUANG Jing-feng WANG Jian-wen WANG Xiu-zhen LIU Zhan-yu 《浙江大学学报(A卷英文版)》2007,8(6):883-895
Hyperspectral reflectance (350~2500 nm) data were recorded at two different sites of rice in two experiment fields including two cultivars, and three levels of nitrogen (N) application. Twenty-five Vegetation Indices (VIs) were used to predict the rice agronomic parameters including Leaf Area Index (LAI, m2 green leaf/m2 soil) and Green Leaf Chlorophyll Density (GLCD, mg chlorophyll/m2 soil) by the traditional regression models and Radial Basis Function Neural Network (RBF). RBF emerged as a variant of Artificial Neural Networks (ANNs) in the late 1980’s. A large variety of training algorithms has been tested for training RBF networks. In this study, Original RBF (ORBF), Gradient Descent RBF (GDRBF), and Generalized Regression Neural Network (GRNN) were employed. Results showed that green waveband Normalized Difference Vegetation Index (NDVIgreen) and TCARI/OSAVI have the best prediction power for LAI by exponent model and ORBF respectively, and that TCARI/OSAVI has the best prediction power for GLCD by exponent model and GDRBF. The best performances of RBF are compared with the traditional models, showing that the relationship between VIs and agronomic variables are further improved when RBF is used. Compared with the best traditional models, ORBF using TCARI/OSAVI improves the prediction power for LAI by lowering the Root Mean Square Error (RMSE) for 0.1119, and GDRBF using TCARI/OSAVI improves the prediction power for GLCD by lowering the RMSE for 26.7853. It is concluded that RBF provides a useful exploratory and predictive tool when applied to the sensitive VIs. 相似文献
10.
During the decision-making process, especially in multi-disciplinary complex cases, assessment technique is needed to assist policy-makers in making the right decision. Many of such assessment techniques have been developed for policy-makers, but the inevitable subjectivity of policy-makers often becomes the main obstacle in making the right or proper policy. Interlink decision-making index （IDMI） is a newly proposed assessment method with the advantages of being simple to use and having less human interference over other methods, as it does not require a weighting process of each selection criterion. This paper implements IDMI to assist with decision-making in national or regional low-carbon development, using China as a case study. The Chinese government has annotmced its carbon emission reduction target along with other development targets by 2020. Many policy settings can be chosen in order to achieve those targets. The problem is how to determine the best setting and the means by which decision-makers can avoid subjectivity and extremes. A number of policy setting options are generated carefully by a system dynamic model under different policy scenarios. The IDMI demonstrates a perfect way to assist in selecting the ＂best＂ among all the options that can achieve the goals within the acceptable range. 相似文献
11.
By using some elementary inequalities, authors in this paper makes further improvement for estimating the heights of Bézier
curve and rational Bézier curve. And the termination criterion for subdivision of the rational Bézier curve is also improved.
The conclusion of the extreme value problem is thus further confirmed.
Project supported by the National Natural Science Foundation of China (No. 60173034) and the Foundation of State Key Basic
Research(973) Program (No. G1998030600), China 相似文献
12.
Based on rational Bézier curves given by Ron Goldman, a new fractional rational Bézier curve was first defined in terms of
fractional Bernstein bases. Moreover, some basic properties were dicussed and a theorem connected to Poisson curves was obtained.
Some examples in this paper were given by the visual results.
Project supported by the National Natural Science Foundation of China (Grant No. 10271074) 相似文献
13.
In this paper, Bézier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the
Bézier curves with shape parameter. The Bézier basis curves with shape parameter have most properties of Bernstein basis and
the Bézier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase
of the shape parameter, the Bézier curves with shape parameter approximate to the control polygon. In the last, the Bézier
surface with shape parameter is also constructed and it has most properties of Bézier surface.
Project supported by the National Natural Science Foundation of China (No. 10371110) and the National Basic Research Program
(973) of China (No. G2002CB12101) 相似文献
14.
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
15.
Applying homogeneous coordinates, we extend a newly appeared algorithm of best constrained multi-degree reduccomponent 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
16.
A novel reconstruction method from contours lines is provided. First, we use a simple method to get rid of redundant points
on every contour, then we interpolate them by using cubic Bézier spline curve. For corresponding points of different contours,
we interpolate them by the cubic Bézier spline curve too, so the whole surface can be reconstructed by the bi-cubic Bézier
spline surface. The reconstructed surface is smooth because every Bézier surface is patched with G2 continuity, the reconstruction speed is fast because we can use the forward elimination and backward substitution method
to solve the system of tridiagonal equations. We give some reconstruction examples at the end of this paper. Experiments showed
that our method is applicable and effective.
Project supported by the National Natural Science Foundation of China (Nos. 60373070 and 60573147), Postdoctor Foundation
of Shanghai (No. 05R214129), and Zhejiang Education Foundation of China (No. 20050786) 相似文献
17.
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
18.
INTRODUCTION The problem of minimal surface is an old and active problem in the field of differential geometry. The minimal surface has been employed in many areas such as architecture, material science, aviation, ship manufacture, biology, crystallogeny, and so on. The history of minimal surface began with La- grange in 1762 (Nitsche, 1989). Many literature on the minimal surface exist in the last two hundred years (Nitsche, 1989; Osserman, 1986), but few on the minimal surface from the… 相似文献
19.
You-dong Ding Ph. D. 《上海大学学报(英文版)》2001,5(1):20-28
With the help of several discriminants about the zero points of a quartic polynomial, the sufficient and necessary conditions
for the positivity and nonnegativity of the quartic polynomial over an interval I⊂(−∞, +∞) was derived. Based on these conclusions,
the sufficient and necessary conditions for the positivity and convexity of the 2×2 Bézier surface over a rectangle were obtained.
A simple sufficient condition was deduced also and finally several examples were given.
Supported by the National Natural Science Foundation of China (69603009) and the Younger Foundation of Shanghai Municipal
Commission of Education (2000QN73) 相似文献