| 1. | New method for auto - generating curve contour character
一种新的曲线字库自动生成方法 |
| 2. | In the second chapter , a class of polynomial blending functions of degree n + 1 is presented . based on the functions , we present polynomial curves with some shape parameters . the generated curves are similar with the degree n bezier curves
第二章给出一类n + 1次多项式调配函数，并由此构造了带形状参数的多项式曲线，生成曲线具有与n次b zier曲线类似的几何性质。 |
| 3. | There are two mainly method for surface rebuild , one is based on three angular bezier surface , the other is b - spline or nurbs surface . the property of b - spline and nurbs curve is introduced and how to generate curve and surface with interpolation is studied
对基于三角bezier曲面和b样条或nurbs曲面的曲面重构进行了论述，介绍了b样条和nurbs曲线曲面特点并对用插值法生成曲线曲面进行了研究。 |
| 4. | In chapter 4 , we research a way how to generate curve by discrete points . the way uses several low - order bezier curve to substitute one high - order bezier curve in order to avoid computing high - order negative matrix . the curve produced by this way has good smoothness
第四章对由离散点构建曲线进行了研究，绕过高阶矩阵求逆，把由k个低阶的bezier曲线拼合产生的复合曲线来代替单一的高阶bezier曲线，并保证曲线之间的光滑过渡。 |
| 5. | Another algorithm is based on pixels : sample many points along the curve , round them to the nearest integer and set each pixel the computed point falls in . although this algorithm uses integer arithmetic , it provides the smooth curve possible at the expense of computation time as many points have to be computed to ensure that no gaps are created along the curve . furthermore these two algorithms we mentioned above is appropriate for low degree parametric curves , for high degree parametric curves , we usually approach them by using low degree rational parametric curves , the generating curve ' s fairness property is not very good
我们知道当节点矢量的两端节点均为k重节点且无内节点时， b样条基函数退化为bemstein多项式，因此该生成算法还可推广到b能ier曲线中，具有广泛的应用价值、同样地，在cad和cagd中，有理b样条曲线，特别是非均匀有理b样条曲线( nurbs )已经成为曲线曲面设计中最广为流行的技术，然而对这些曲线目前也尚无很好的曲线生成算法，因此有理b样条曲线的生成算法无疑有着更重要的意义 |
| 6. | It is proved that the step length got by subsection is more than or equal to that of not subsection . so the points calculated are less than or equal to those of not subsection . thus the problem of uneven densities in generating curves is radically solved , and the algorithm is speeded up
将所需绘制的曲线按照曲线的次数分段，每段给出不同的步长，可以证明分段后每段的步长都大于或等于分段前的步长，所以实际上所计算的点数小于或等于不分段绘制时的点数，这样就从根本上解决了曲线绘制过程中，绘制点疏密不均的现象，提高了运行速度。 |
| 7. | Starting from the generativ e procedure of conjugate curves the generator 2 and generated curve 1 ar e re garded as two bunches of spatial point sets and the 1 is being considered a s a macroscopic expression in s1 coordinate space of points , satisfying the co n dition of conjugation during the course of relative movement , on 2
从共轭曲线的创成过程出发，将母曲线2和创成曲线1看作两簇空间点集，认为1是由相对运动过程中2上满足共轭条件的点在s1坐标空间中的宏观表现。 |
