共查询到20条相似文献，搜索用时 546 毫秒
1.
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
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In this paper, Bezier basis with shape parameter is constructed by an integral approach. Based on this basis, we define the Bezier curves with shape parameter. The Bezier basis curves with shape parameter have most properties of Bemstein basis and the Bezier curves. Moreover the shape parameter can adjust the curves' shape with the same control polygon. As the increase of the shape parameter, the Bezier curves with shape parameter approximate to the control polygon. In the last, the Bezier surface with shape parameter is also constructed and it has most properties of Bezier surface. 相似文献
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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
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本文介绍了线切割CAD/CAM系统的自由曲线生成方法.通过比较Bezier曲线、B样条曲线、非均匀有理B样条(NURBS)曲线等主要造型方法,选择了一种适合线切割CAD/CAM系统的简单、易用的几何造型方法,并阐述其算法. 相似文献
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给出圆锥曲线上的两个控制点,利用有理曲线升阶方法,求出有理三次B6zier曲线的另外两个控制顶点以及权因子γ的值,从而达到用有理三次B6zier曲线对已给定的圆锥曲线的精确表示,如双曲线弧、抛物线弧和椭圆弧的表示。并给出了数值实例。 相似文献
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Ball曲线在多项式空间中得到了广泛的研究,而且在CAD系统中也有着广泛的应用。在C-Bézier基的基础上构造的一组新的基称为C-Ball基,用这组基定义的曲线称为C-Ball曲线。讨论了三角混合多项式空间中的C-Ball基和C-Ball曲线,该曲线继承了Bézier曲线的良好的几何性质,在曲线的升降阶上比Bézier曲线更加方便,且可以通过形状参数对曲线进行形状控制。 相似文献
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Bezier曲线是计算机图形学中最基本、最重要的内容之一,本文从Bezier曲线的定义出发,结合deCasteljau递推定比分割法,给出了绘制Bezier曲线的递归算法,并就递归算法终止条件展开了讨论。 相似文献
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蒋莉 《衡阳师范学院学报》2011,32(6):10-12
研究了基于某种约束条件的有理Bezier曲线的形状修改,约束条件为曲线通过某个单点或多个点,或在端点处满足某种切矢条件。方法是修改控制点。目的是使得修改前后的曲线的控制点的改变量最小。给出了具体控制点的扰动的计算公式,且给出了具体实例。 相似文献
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空间曲线的方程未知,要依据曲线上有限个观测点的坐标,计算曲线的弯曲度。从曲率的原始定义出发,建立起直接利用原始坐标数据计算空间曲线各弧段弯曲度的方法,同时构造出具有最佳弯曲度逼近的光滑曲线,证明了直接方法的可靠性。经过深入剖析,厘清了某些流行算法的模糊认识,通过示例阐明了运用二次样条和三次样条插值方法计算曲线弯曲度的缺陷。 相似文献
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Bezier曲线的算法描述及其程序实现 总被引：3，自引：0，他引：3
Bezier曲线是图形学中最基本、最重要的内容之一,在CAD/CAM技术中得到广泛的应用。通常的绘制方法是用很多近似的直线段。本文描述了Bezier曲线的算法,给出了绘制曲线的程序算法。 相似文献
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由于Bezier曲线与曲面的特性,它在计算机的辅助几何设计方面得到广泛的应用。本文在分析Bezier曲线与曲面的基础上,提出了Bezier曲线与曲面极值问题,即最短Bezier曲线与最小Bezier曲面问题,并提出了用模式搜索法与在matlab中用变量极值函数来解决该问题的解法,最后通过实例验证了该解法。 相似文献
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徐雨明 《衡阳师范学院学报》1997,(3)
从Bezier曲线的数学表达式、二次三次Bezier曲线的矩阵表示、Bezier曲线的性质等出发，组合SPDOS曲线字库内部结构和TURBOC语言程序，来具体说明Bezier曲线在轮廓字中的应用。 相似文献
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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
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INTRODUCTION Curve generating algorithms are important incomputer graphics and CAD/CAM. For some simplecurves such as line, circle, ellipse, etc., we have somerendering algorithms such as DDA algorithm for line,Bresenham algorithm and midpoint algorithm forcircle, Pitteway’s algorithm for ellipse, etc. (Bresen-ham, 1977; Pitteway, 1985; Ammeraal, 1987; Foleyet al., 1990; 1993). For rendering parametric curves and surfaces, apopular method is to compute a set of points along thecurv… 相似文献
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We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier curves with G2-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
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T-B样条基函数是具有B样条基函数性质的三角基函数。基于T-B样条基函数,构造了一类与给定多边形相切的闭三角多项式曲线,逼近效果好,计算量小,且编程统一,实验表明,具有较好的应用效果。 相似文献
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研究了曲线拟合方法的特点,讨论了三次样条曲线和参数三次样条曲线的拟合方法在螺杆截面廓形拟合中的应用,给出了拟合的方程,并用实例验证了拟合的效果.同时解决了拟合过程中的单调性、失真、端点切向量的确定方法等一些关键技术问题.该方法为精确地生成刀具轨迹提供了光滑的型线方程. 相似文献
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为简化伸缩变形计算过程,针对代数曲线和参数曲线,提出一种具有区域峰值的伸缩因子曲线变形方法。首先基于 Hermite 插值基函数构造一种多项式伸缩函数,然后建立带有伸缩参数的伸缩因子,最后将伸缩因子作用于曲线,促使曲线沿指定方向产生变形。在变形过程中,通过改变伸缩因子中的形状控制参数,实现曲线整体、局部以及周期变形效果。大量数值实例证明,该方法计算量小,便于理解和操作,可获得适用于不同设计要求的旋转曲面和外形轮廓线。与其它方法相比,该方法不仅可用于参数型曲线,还可用于隐式表示的代数曲线,丰富了隐式曲线的变形效果。 相似文献