By changing the value of the shape parameter , we can adjust the approaching degree of the curves to their control polygon 通過改變局部形狀參數的取值,可以調整曲線接近其控制多邊形的程度。
This paper present a sufficient and necessary condition of constructing quintic ph curves and analyze the geometric meaning of the control polygon 本文給出了構成五次ph曲線的充要條件,分析了其控制多邊形的幾何意義。
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 進一步還給出了有理b樣條曲線和有理b zier曲線的相互轉化關系
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 第一種算法依據樣條曲面等距原理,把對細分曲面的等距轉化為其等距前后控制網格的對應關系。
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 通過改變形狀參數的取值,可以調整生成曲線從n次b zier曲線的兩側逼近n次b zier曲線。
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 規(guī)范b基即最優(yōu)規(guī)范的全正基,因其具有凸包性、仿射不變性、最優(yōu)保形性,端點插值性及b算法等重要性質,在cagd中起著重要的作用。
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 第四章討論與給定多邊形相切的分段三次、四次、六次b zier曲線,所構造的曲線c ~ 1 、 c ~ 2 、 c ~ 3 -連續(xù),并且對切線多邊形是保形的。
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 該方法的主要創(chuàng)新思想是,在被插值曲線的控制多邊形兩側構造具有簡單對稱性質的多邊形網格,而在細分過程中,則無須修改被插值曲線附近的細分規(guī)則,兇此細分算法是簡單的,細分過程是收斂的,且最終的插值曲面除有限個點外是c ~ 2連續(xù)的。
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線的控制多邊形邊長為b zier縱標的b zier多項式來逼近曲線的參數速度,給出了相應的幾何等距逼近算法,進一步結合法矢方向曲線的升階獲得了高精度逼近
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曲線還引入了一個稱為形狀因子的參數,形狀設計者不僅可以像b zier曲線一樣通過調節(jié)控制多邊形來控制曲線形狀,而且還可以調節(jié)形狀因子來調整曲線對控制多邊形的逼近程度