Spline multiresolution and wavelet-like decompositions

Splines are useful tools to represent, modify and analyze curves and they play an important role in various practical applications. We present a multiresolution approach to spline curves with arbitrary knots that provides good feature detection and localization properties for non-equally distributed geometric data. In addition, we show how equidistributed data and knot sequences can be efficiently handled using signal processing techniques.     

指数曲线贮仓的设计剖析

贮仓是许多工业过程中的常用设备，起拱是贮仓使用时常出现的故障，如何解决起拱问题是贮仓设计的关键，除常采取增大仓壁倾角、设置破拱装置等方法外，设计成曲线贮仓也是行之有效的措施之一。分析了指数曲线贮仓的工作原理和特点，建立了仓壁指数曲线方程，阐述了设计步骤与注意事项，并举例说明。     

Self-intersections of rational Bézier curves

Rational Bézier curves provide a curve fitting tool and are widely used in Computer Aided Geometric Design, Computer Aided Design and Geometric Modeling. The injectivity (one-to-one property) of rational Bézier curve as a mapping function is equivalent to the curve without self-intersections. We present a geometric condition on the control polygon which is equivalent to the injectivity of rational Bézier curve with this control polygon for all possible choices of weights. The proof is based on the degree elevation and toric degeneration of rational Bézier curve.     

Total curvature variation fairing for medial axis regularization

We present a new fairing method for planar curves, which is particularly well suited for the regularization of the medial axis of a planar domain. It is based on the concept of total variation regularization. The original boundary (given as a closed B-spline curve or several such curves for multiply connected domains) is approximated by another curve that possesses a smaller number of curvature extrema. Consequently, the modified curve leads to a smaller number of branches of the medial axis. In order to compute the medial axis, we use the state-of-the-art algorithm from [1] which is based on arc spline approximation and a domain decomposition approach. We improve this algorithm by using a different decomposition strategy that allows to reduce the number of base cases from 13 to only 5. Moreover, the algorithm reduces the number of conic arcs in the output by approx. 50%.     

基于GP2Y0A02距离测量的仿真与辅助设计

为了实现非接触距离测量,利用多个仿真与设计软件设计了采用GP2Y0A02模块的距离光学测试系统。在PROTEUS中测量GP2Y0A02电压值,并在Matlab中采用多元线性回归建立GP2Y0A02电压与距离的拟合曲线,最后在开发的测量程序中利用拟合曲线求解得到距离量。测试结果表明,对于非线性位置测量采用适当数据处理方法能得到满意的测量精度。     

Markov随机场与Gaussian曲线在MR图像分割中的应用

针对扫描的人脑组织MR图像边缘分辨率低、模糊性大的特点,本文提出了一种基于模糊Markov随机场和Gaussian曲线相结合的MR图像最佳阈值分割方法。该方法通过对图像的像素邻域属性的统计将模糊论引入其中,建立模糊Markov随机场,并利用Gaussian曲线对二维直方图最佳一维投影进行拟合,确定出图像中各脑组织的二维阈值点,在二维直方图上实现对脑组织的分割。通过实验表明,本算法能够有效提高脑组织的分辨率,对噪声的鲁棒性、结果区域的连通性相对于一维Otsu和二维Otsu算法都有了很大的提高。     

基于GPU-CUDA的共轭斜量法实现及性能对比

偏微分方程数值解法(包括有限差分法、有限元法)以及大量的数学物理方程数值解法最终都会演变成求解大型线性方程组。因此,探讨快速、稳定、精确的大型线性方程组解法一直是数值计算领域不断深入研究的课题且具有特别重要的意义。在迭代法中,共轭斜量法(又称共轭梯度法)被公认为最好的方法之一。但是,该方法最大缺点是仅适用于线性方程组系数矩阵为对称正定矩阵的情况,而且常规的CPU算法实现非常耗时。为此,通过将线性方程组系数矩阵作转换成对称矩阵后实施基于GPU-CUDA的快速共轭斜量法来解决一般性大型线性方程组的求解问题。试验结果表明:在求解效率方面,基于GPU-CUDA的共轭斜量法运行效率高,当线性方程组阶数超过3000时,其加速比将超过14;在解的精确性与求解过程的稳定性方面,与高斯列主元消去法相当。基于GPU-CUDA的快速共轭斜量法是求解一般性大型线性方程组快速而非常有效的方法。     

Bezier曲线到AH-Bezier曲线的升阶算法

关于曲线升阶,已有的结论往往限于同类曲线之间。为了突破这一限制,考虑不同类曲线间的升阶,关注代数多项式空间中的Bezier曲线到代数双曲多项式空间中的AH-Bezier曲线的升阶。研究从基函数入手,利用Bezier和AH-Bezier共有的求导降阶的特点,结合矩阵分块的思想,先给出AH-Bezier基到Bernstein基的转换矩阵,进而推出控制顶点的升阶公式,最后给出升阶算法。结果表明,任意n次Bezier曲线可以通过该算法升到n＋3阶（等同于n＋2次）的AH-Bezier曲线。算法实现了Bezier到AH-B＆#233;zier曲线模型的精确转换。     

基于视觉原理的曲线重构算法研究

曲线和曲面的重构是逆向工程中的重要问题,特别是按照计算机图形学中点线面的发展规律,曲线重构更是其中很重要的一步,为后面的曲面重构奠定了研究基础。论文研究和实现了一种曲线重构算法,该算法将人类的视觉具有的接近性和连续性融入到了曲线重构算法中。实验结果表明了该算法的有效性。