| 1. | By changing the value of the shape parameter , we can adjust the approaching degree of the curves to their control polygon
通过改变局部形状参数的取值，可以调整曲线接近其控制多边形的程度。 |
| 2. | This paper present a sufficient and necessary condition of constructing quintic ph curves and analyze the geometric meaning of the control polygon
本文给出了构成五次ph曲线的充要条件，分析了其控制多边形的几何意义。 |
| 3. | On this basic , paper find the connection of rational b - spline basis and rational b zier basis , based on these relation , find the control polygons ’ relation
进一步还给出了有理b样条曲线和有理b zier曲线的相互转化关系 |
| 4. | Based on theory of spline surface offset , the first one directly finds the control polygon mesh of the offset surface from the original control mesh
第一种算法依据样条曲面等距原理，把对细分曲面的等距转化为其等距前后控制网格的对应关系。 |
| 5. | By changing the value of the shape parameter , we can adjust the approaching degree of the curves to their control polygon and manipulate the degree n bezier curves from both sides
通过改变形状参数的取值，可以调整生成曲线从n次b zier曲线的两侧逼近n次b zier曲线。 |
| 6. | Normalized b - basis , namely optimal normalized totally positive basis , plays an important role in cagd , for it possess positive properties such as variation diminishing , convex - hull , affine invariance , tangency to the control polygon at the endpoints and b - algorithm
规范b基即最优规范的全正基，因其具有凸包性、仿射不变性、最优保形性，端点插值性及b算法等重要性质，在cagd中起着重要的作用。 |
| 7. | In the forth chapter , we proposes an approach of constructing planar piecewise bezier curve of 3rd 4th and 6th degree with all edges tangent to a given control polygon and the curve segments are joined together with c1 c2 and c3 - continuity . the segmented bezier curves are all shape - preserving to their tangent polygon
第四章讨论与给定多边形相切的分段三次、四次、六次b zier曲线，所构造的曲线c ~ 1 、 c ~ 2 、 c ~ 3 -连续，并且对切线多边形是保形的。 |
| 8. | The main innovation of our method is that we only need construct polygonal mesh possessing simple symmetric properties on both sides of control polygon edges of interpolated curves , and do n ' t need modify the subdivision rules near the interpolation curves during the process of subdivision . thus the subdivision rules are simple . the process is convergent and the limit surface is c everywhere except a finite number of points
该方法的主要创新思想是，在被插值曲线的控制多边形两侧构造具有简单对称性质的多边形网格，而在细分过程中，则无须修改被插值曲线附近的细分规则，凶此细分算法是简单的，细分过程是收敛的，且最终的插值曲面除有限个点外是c ~ 2连续的。 |
| 9. | The parametric speed of the curve is firstly approximated by the bezier polynomial which takes the lengths of control polygon ' s edges of the direction curve of normal as bezier coordinates . then the corresponding geometric offset approximation algorithm is given . moreover , an offset approximation with high precision is obtained by degree elevation of the direction curve of normal
首先利用以法矢方向曲线的控制多边形边长为b zier纵标的b zier多项式来逼近曲线的参数速度，给出了相应的几何等距逼近算法，进一步结合法矢方向曲线的升阶获得了高精度逼近 |
| 10. | Hence designers can adjust the shape of curves by changing not only control points but also shape factor . our experiments show that h - bezier model approximate to the control polygon more closely than bezier model . so they are suitable to shape design and modeling in cad systems
而且h - b zier曲线还引入了一个称为形状因子的参数，形状设计者不仅可以像b zier曲线一样通过调节控制多边形来控制曲线形状，而且还可以调节形状因子来调整曲线对控制多边形的逼近程度 |
