共查询到20条相似文献,搜索用时 93 毫秒
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本文研究了调整一个节点对B样条曲线产生的影响。调整B样条曲线的一个节点,引起两个节点区间改变。讨论了这两个节点区间上有定义的B样条基函数所发生的变化,以及对B样条曲线产生的影响。研究表明,通过调整一个节点可以方便地调整B样条曲线的形状,为B样条曲线形状调整提供了一种简便有效的方法,这在很大程度上丰富了B样条曲
线形状调整的方法。 相似文献
线形状调整的方法。 相似文献
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提出了Bézier样条曲线利用分割技术近似弧长参数化的一种方法,并给出了相应的算法。通过求出曲线上所谓的‘最坏点’并在相应点处进行分割,可得到两条Bézier样条曲线。让这两条Bézier样条曲线具有与它们的近似弧长成比例的权,并对所得到的新的Bézier样条曲线进行同样的工作最终可得到一条由多条Bézier样条曲线所构成的新曲线。将这多条Bézier样条曲线合并成为一条Bézier样条曲线并通过节点插入技术将所得Bézier样条曲线转化为B-样条曲线的形式可得到全局参数域,其中各条Bézier曲线在全局参数域中所占子区间的长度与它们的权成比例,这样便得到了一条近似弧长参数化曲线。 相似文献
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B样条曲线降阶新方法 总被引:13,自引:1,他引:13
首先导出了 B样条曲线退化的条件 ,然后根据 B样条升阶恒等式提出了 B样条曲线降阶的新算法 .最后 ,对结果进行了简要的误差分析 .如果结合节点插入技术 ,还可以将降阶后的误差限定在给定的容差之内 .实践表明 ,该算法容易实现、效率高、逼近效果好 . 相似文献
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B样条曲线同时插入多个节点的快速算法 总被引:4,自引:0,他引:4
基于离散B样条的一个新的递推公式,提出B样条曲线同时插入多个节点的新算法。不同于Cohen等插入节点的Oslo算法,本算法用新的方法离算离散B样条,求每个离散B样条的值只需O(1)的运算量,从而使本算法高效,其时间复杂性为O(sk n),其中k为B样条曲线的阶,n k 1为原节点数,s为新插入节点的个数,本算法的通用性强,适用于端点插值的和非端点插值的B样条曲线,可同时在曲线定义域内外的任意位置上插入任意个节点。 相似文献
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为了构造逼近稠密有序点列的初始曲线,提出一种B样条曲线逼近的节点配置算法.以初始曲线的曲率极值点和点列的2个端点作为特征点的种子点,利用最小二乘法构造逼近种子点的B样条曲线,并根据B样条曲线段的复杂度进行特征点的细分和节点矢量的更新;重复这一过程,直到逼近的误差小于给定的阈值,实现B样条曲线的精确逼近.实例结果表明,在相同的给定阈值条件下,文中算法可比Park算法、Piegl算法和Li算法减少更多的控制顶点,逼近曲线的控制顶点数等于细分后的特征点数,且逼近曲线的节点分布合理. 相似文献
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B样条曲线曲面GC2扩展 总被引:2,自引:0,他引:2
提出了一个扩展B样条曲线曲面的新方法,扩展B样条曲线曲面的关键是为新增加的点确定节点值,新方法的基本思想是:首先,B样条曲线和扩展部分在连接点处满足GC^2连续,用能量极小化方法确定扩展部分的曲线形状,通过对曲线重新参数化使两部分曲线满足C^2连续,进而确定新增加点的节点值,新B样条曲线的控制点由一个显式递推公式计算,原B样条曲线和扩展后的部分合在一起形成一条新的B样条曲线,新的B样条曲线满足原B样条曲线和扩展的点,文章还讨论了运用该方法进行B样条曲面扩展,且以实例对新方法与其它方法进行了比较,结果表明新方法的光顺性得到了明显改善,曲率变化更平坦,且有较小的旋转数指标。 相似文献
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为了对任意NUBS曲线进行精确的分解和重构,提出了半正交B样条小波分解和重构的新算法,同时给出了处理非均匀B样条曲线的非整数阶分辨率的小波分解和重构算法,并实现了任意非均匀B样条曲线的多分辨率表示,对于任意非均匀B样条或NUBS曲线,无论它有多少个控制点,均可以对它进行半正交分解和重构,而不受控制点数必须等于2+3的限制,从这个意义上讲,该方法不仅可以实现连续分辨率水平(continuous-resolutionlevel)的非均匀B样条曲线造型,还可以对非均匀B样条和NURBS曲线进行精确的分解和重构,这对于B样条曲线曲面的多分辨率造型与显示具有重大应用价值。 相似文献
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Hyungjun Park Author Vitae 《Computer aided design》2003,35(14):1261-1268
This paper proposes a new approach for lofted B-spline surface interpolation to serial contours, where the number of points varies from contour to contour. The approach first finds a common knot vector consisting of fewer knots that contain enough degrees of freedom to guarantee the existence of a B-spline curve interpolating each contour. Then, it computes from the contours a set of compatible B-spline curves defined on the knot vector by adopting B-spline curve interpolation based on linearly constrained energy minimization. Finally, it generates a B-spline surface interpolating the curves via B-spline surface lofting. As the energy functional is quadratic, the energy minimization problem leads to that of solving a linear system. The proposed approach is efficient in computation and can realize more efficient data reduction than previous approaches while providing visually pleasing B-spline surfaces. Moreover, the approach works well on measured data with noise. Some experimental results demonstrate its usefulness and quality. 相似文献
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B-样条曲线反算中的尖点构造 总被引:3,自引:0,他引:3
本文讨论了B-样条曲线反算中的尖点构造方法,成功地推导出构造公式。使得B-样条反算曲线可以作为表达基本图形的统一数学模型,对B-样条曲线的理论研究和图形处理程序的应用开发有积极的意义。 相似文献
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通过对B样条的de Boor-Cox定义式分析,给出了一种基于向量扩展的B样条基函数快速求值算法。该算法能够将k次B样条非零值计算效率提高2k+1倍。该算法用于数控实时插补中的B样条曲线求值求导运算时,可获得比de Boor算法更高的计算效率。 相似文献
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基于二次B样条曲线拟合的新算法 总被引:1,自引:1,他引:0
针对由四点拟合成一条三次B样条曲线过程中计算量大的缺点,提出了一种简单的二次B样条曲线拟合算法。即用两条二次B样条曲线近似一条三次B样条曲线,以期达到计算量小,光滑度也达到要求,提高B样条曲线的绘制速度。 相似文献
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D.-S. KimAuthor Vitae J. RyuAuthor VitaeH.C. LeeAuthor Vitae H. ShinAuthor Vitae 《Computer aided design》2002,34(4):337-345
The evaluation of points and the computations of inflection points or cusps on a curve are often necessary in CAGD applications. When a curve is represented in a B-spline form, such computations can be made easier once it is transformed into a set of piecewise polynomial curves in power form. The usual practice of the transformation of a B-spline curve into a set of piecewise polynomial curves in power form is done either by a knot refinement followed by basis conversions, or by applying a Taylor expansion on each knot span of a B-spline curve.Presented in this paper is a new algorithm to convert a B-spline curve into a set of piecewise polynomial curves in power form. Experiment shows that the proposed algorithm significantly outperforms the conventional approach when one or more control points of a B-spline curve are continuously moving. 相似文献
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Hyungjun Park 《Computer aided design》2011,(3):258-264
By expanding the idea of B-spline curve fitting using dominant points (Park and Lee 2007 [13]), we propose a new approach to B-spline surface fitting to rectangular grid points, which is based on adaptive knot placement using dominant columns along u- and v-directions. The approach basically takes approximate B-spline surface lofting which performs adaptive multiple B-spline curve fitting along and across rows of the grid points to construct a resulting B-spline surface. In multiple B-spline curve fitting, rows of points are fitted by compatible B-spline curves with a common knot vector whose knots are computed by averaging the parameter values of dominant columns selected from the points. We address how to select dominant columns which play a key role in realizing adaptive knot placement and thereby yielding better surface fitting. Some examples demonstrate the usefulness and quality of the proposed approach. 相似文献
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为解决均匀参数采样在许多情况下得到质量不高的采样点,进而生成不理想的B样条拟合曲线,提出空间曲线基于内在几何量的均匀采样方法,以获得给定总数且具有代表性的采样点.首先定义基于弧长、曲率和挠率加权组合的特征函数,通过调整组合参数更好匹配不同的曲线形状;然后提出空间曲线基于内在几何量的自适应采样方法,迭代生成满足给定距离阈值的采样点.采用最大绝对误差和均方根误差作为评价指标,与均匀弧长采样方法和基于弧长和曲率平均的均匀采样方法进行对比,并通过实例进行验证.结果表明,文中方法在采样质量和B样条拟合结果上获得明显改善. 相似文献
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LIN Hongwei WANG Guojin DONG Chenshi Department of Mathematics Zhejiang University Hangzhou China State Key Laboratory of CAD&CG Zhejiang University Hangzhou China 《中国科学F辑(英文版)》2004,47(3):315-331
In this paper, based on the idea of profit and loss modification, we presentthe iterative non-uniform B-spline curve and surface to settle a key problem in computeraided geometric design and reverse engineering, that is, constructing the curve (surface)fitting (interpolating) a given ordered point set without solving a linear system. We startwith a piece of initial non-uniform B-spline curve (surface) which takes the given point setas its control point set. Then by adjusting its control points gradually with iterative formula,we can get a group of non-uniform B-spline curves (surfaces) with gradually higherprecision. In this paper, using modern matrix theory, we strictly prove that the limit curve(surface) of the iteration interpolates the given point set. The non-uniform B-spline curves(surfaces) generated with the iteration have many advantages, such as satisfying theNURBS standard, having explicit expression, gaining locality, and convexity preserving,etc 相似文献