可调控C^2连续四次参数曲线曲面研究

Study on a Class of Modifiable C^2-continuous Quartic Parametric Curves and Surfaces

在控制点中重新分布四次Bernstein基函数 ,采用矩阵形式和形状因子来生成可调控C2 连续四次参数曲线曲面 .当型值点给定时 ,改变形状因子 ,曲线就可以对控制多边形进行插值、逼近或二者的叠加 ,而不必求解线性方程组或者插入新的控制点 .B样条曲线是它的一个特例 .此类曲线曲面具有局部性 ,即移动单个控制点 ,只改变曲线曲面上该点附近的一小部分形状 ;可有理化 ,但要求形状因子在一定范围内取值 ,否则它的形状会剧烈变化 .此类曲线曲面在CAD/CAM建模和医学图像处理中具有明显的应用前景 .

Redistributing quartric Bernstein polynomials among the control points by using matrix form as a method for creating modifiable C 2 quartic parametric curves and surfaces with shape factors is proposed.When the control points are fixed,with varying the shape factors,the curve can interpolate or approximate to the control polygon,and even blend both,without solving the linear system of equation or inserting new control points.A particular case is just the cubic B spline curvve.The curves and surfaces have localization,i.e.moving an individual control point only changes a small part of the curve or surface around the point.The curve can be rationalized but requires that the shape factors are in a certain range,otherwise its shape would vary sharply.