共查询到10条相似文献，搜索用时 250 毫秒
1.
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
2.
有理Bézier曲线具有很多良好的性质,是曲线曲面设计的重要方法.根据给定的型值点,通过构造有理Bézier样条插值曲线的公式,给出了计算方法,并且分析了重节点情形曲线的形状和特点,最后通过数值实例验证了方法的有效性. 相似文献
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
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