CAD 和电脑解方程比赛二次曲线

1、信息科学与技术学院,CAD Development,张利,Li Zhang,辽宁大学计算机系,School of Information , Liaoning,University,曲线与曲面,本讲总体纲要,曲线曲面,曲线表示,曲线基本性质,曲线的画法,曲线表示方法,二维曲线表示方法,三维曲线表示方法,二维曲线表示方法,显式表示,y,f,x,x,D,隐式表示,f,x,y,0 ,x,y,T,D,参数表示,C,t,x,t,y,t,T,t,D,过程描述,如多边形曲线、细分曲线,二维直线段表示,显式表示,隐式表示,参数表示,过程描述,0,1,2,x,1,2,y,P,0,P,1,y,x,x,1,2,x,

2、y,0,x,y,T,1,2,1,2,C,t,P,0,t,P,1,P,0,t,1,t,1,T,t,0,1,以,P,0,和,P,1,为端点的直线段,参数表示,x,t,1,t,0,1,y,t,1,t,0,1,二维圆表示,显式表示,隐式表示,参数表示,x,2,y,2,1,x,y,T,1,1,1,1,C,t,( cos,t, sin,t,T,t,0,2,0,1,x,1,y,sin,cos,t,y,t,x,2,0,t,三维曲线表示方法,显式表示,隐式表示,参数表示,x,g,z,x,f,y,b,a,x,0,0,z,y,x,g,z,y,x,f,x,y,z,T,D,t,z,z,t,y,y,t,x,x,b,a,t

3、,其它,优点,隐式表示,判断点在曲线上,参数表示,表示能力,有更大的自由度来控制曲线、曲面的形状,变换、设计、显示,易于用矢量和矩阵表示几何分量,简洁,参数规格化,t,0, 1,曲线基本性质,切向量,弧长,主法向量,曲率,连续性,切向量,二维,三维,t,y,t,x,t,C,t,y,t,x,t,C,t,z,t,y,t,x,t,C,t,z,t,y,t,x,t,C,弧长,弧长公式,t,n,i,i,i,n,n,dt,t,t,n,L,t,s,0,2,1,2,1,d,d,lim,lim,C,P,P,P,0,P,n,P,i,1,P,i,二维曲线画法,和计算机比赛解方程,0,1,2,x,1,2,y,P,0,P

4、,1,y,x,x,1,2,以,P,0,和,P,1,为端点的直线段,参数表示,x,t,1,t,0,1,y,t,1,t,0,1,程序运行效果,程序代码,画坐标轴,Private Sub draw_Click(,Picture1.Scale (-5, 4)-(5, -5,Picture1.DrawWidth = 3,设置绘线宽度,Picture1.Line (-5, 0)-(5, 0),画,X,轴,Picture1.Line (0, 5)-(0, -5),画,y,轴,For i = -5 To 5,Picture1.Line (i, 0.3)-(i, 0,Picture1.Print i,Next

5、i,For i = -5 To 5,Picture1.Line (0, i)-(0.3, i,Picture1.Print i,Next i,End Sub,程序效果图,画线，求第一个点的坐标,Private Sub Command1_Click(,Dim a, b, c As Double,Dim x, y As Double,Dim x1, y1, x2, y2 As Double,Dim sig1, sig2 As String,Call draw_Click,a = Val(Text3.Text,b = Val(Text6.Text,c = Val(Text9.Text,sig1 =

6、Text5.Text,sig2 = Text8.Text,x1 = -10,If sig1 = + Then,y1 = a * x1 * x1 + b * x1,Else,y1 = a * x1 * x1,b * x1,End If,If sig2 = + Then,y1 = y1 + c,Else,y1 = y1,c,End If,画线，求第二个点的坐标,For i = 1 To 100,x2 = x1 + 0.2,If sig1 = + Then,y2 = a * x2 * x2 + b * x2,Else,y2 = a * x2 * x2,b * x2,End If,If sig2 = + Then,y2 = y2 + c,Else,y2 = y2,