第三次作业 三次Bezier曲线的绘制

第三次作业三次Bezier曲线的绘制一．解题思路：

Bezier曲线是用N+1个顶点（控制点）所构成的N根折线来定义一根N阶曲线。本次作业中的三次Bezier曲线有4个顶点，设它们分别为P0，P1，P2，P3，那么对于曲线上各个点Pi（x,y）满足下列关系：

x=x0*1-u)*(1-u)*(1-u)+x1 *3*u*(1-u)*(1-u)+x2 *3*u*u*(1-u)+x3 *t*t*t

y=y0*(1-u)*(1-u)*(1-t)+y1*3*u*(1-u)*(1-u)+y2*3*u*u*(1-u) +y3 *u*u*u

所以只要确定控制点的坐标，该曲线可通过编程即可绘制出来。

本题取的初始控制点为：p0(-600,100)、p1(-300,400)、p2(300,600)、p3(600,100)。还可以通过输入不同的控制点画出不同的三次Bezier曲线。

程序中有绘制曲线，清空，清屏，退出四个按钮，其中点击绘制曲线按钮可根据控制点绘制出相应的曲线；点击清空按钮则可以将已绘制的曲线清除；点击清屏按钮可以将输入文本框中的数据清除，以方便输入新的数据；点击退出按钮则退出程序。

二．程序代码

Function f()

Picture1.FontSize = 9

Picture1.Scale (-900, 1000)-(900, -1000)

Picture1.Line (-800, 0)-(800, 0)

Picture1.Line (0, 800)-(0, -800)

For i = -7 To 7

Picture1.Line (100 * i, 0)-(100 * i, 20)

Picture1.CurrentX = i * 100 - 50: Picture1.CurrentY = -5: Picture1.Print i * 100 Next i

For i = -7 To -1

Picture1.Line (0, 100 * i)-(20, 100 * i)

Picture1.CurrentX = -100: Picture1.CurrentY = 100 * i + 20: Picture1.Print i * 100 Next i

For i = 1 To 7

Picture1.Line (0, 100 * i)-(20, 100 * i)

Picture1.CurrentX = -100: Picture1.CurrentY = 100 * i + 20: Picture1.Print i * 100 Next i

End Function

Private Sub Form_Load()

Picture1.AutoRedraw = True

Picture1.ScaleWidth = 900

Picture1.ScaleHeight = 900

f

Text1.Text = -600: Text2.Text = 100: Text3.Text = -300: Text4.Text = 400

Text5.Text = 300: Text6.Text = 600: Text7.Text = 600: Text8.Text = 100

End Sub

Private Sub command1_Click()

x0 = Text1.Text: y0 = Text2.Text

X1 = Text3.Text: Y1 = Text4.Text

X2 = Text5.Text: Y2 = Text6.Text

X3 = Text7.Text: Y3 = Text8.Text

Picture1.FontSize = 18

Picture1.CurrentX = 800: Picture1.CurrentY = -5: Picture1.Print "X"

Picture1.CurrentX = 10: Picture1.CurrentY = 810: Picture1.Print "Y"

For t = 0 To 1 Step 0.001

x = x0 * (1 - t) * (1 - t) * (1 - t) + X1 * 3 * t * (1 - t) * (1 - t) + X2 * 3 * t * t * (1 - t) + X3 * t * t * t

y = y0 * (1 - t) * (1 - t) * (1 - t) + Y1 * 3 * t * (1 - t) * (1 - t) + Y2 * 3 * t * t * (1 - t) + Y3 * t * t * t

Picture1.CurrentX = x0 + 10: Picture1.CurrentY = y0 + 10: Picture1.Print "p0" Picture1.CurrentX = X1 + 10: Picture1.CurrentY = Y1 + 10: Picture1.Print "p1" Picture1.CurrentX = X2 + 10: Picture1.CurrentY = Y2 + 10: Picture1.Print "p2" Picture1.CurrentX = X3 + 10: Picture1.CurrentY = Y3 + 10: Picture1.Print "p3" Picture1.DrawWidth = 1

Picture1.Line (x0, y0)-(X1, Y1), vbBlue

Picture1.Line (X1, Y1)-(X2, Y2), vbBlue Picture1.Line (X2, Y2)-(X3, Y3), vbBlue Picture1.DrawWidth = 2

Picture1.PSet (x, y), vbRed

Next t

End Sub

Private Sub Command2_Click()

Picture1.Cls

f

End Sub

Private Sub Command3_Click()

Text1.Text = ""

Text2.Text = ""

Text3.Text = ""

Text4.Text = ""

Text5.Text = ""

Text6.Text = ""

Text7.Text = ""

Text8.Text = ""

End Sub

Private Sub Command4_Click()

End

End Sub

三．运行结果截图