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上次修改此網站的日期： 2018年12月02日

第十五章  VB 6.0電算機及2D函數圖繪製

程式設計簡介

15.1 前言

   一般簡易之電算機，多可以做加、減、乘及除、開平方及反數(1/x)的功能，先進一點的電算機，則會再提供三角函數、反三角函數、對數等計算功能。下圖為Windows所提供之 標準型及工程型電算機(小算盤)。要在Windows offices程式中使用一般小算盤時，可在Windows螢幕下方，點按[開始]→所有程式→附屬所有程式→小算盤。 開啟一般小算盤後，可在檢視(Y)下拉對話方塊中選取工程型小算盤，使用完畢後只要按小算盤上的「關閉」鈕即可。

本章所要介紹之電算機屬科學用或工程用類型，舉凡一般科學上或工程上用得到之函數多包括在內。另外在測量工程用到之度、分、秒量測單位也一併介紹。下圖為作者所設計設計之科學電算機畫面。

15.2科學電算機功能及程式設計介紹

    本章要介紹之科學電算機功能多，計算能力強，因其有計算方程式及函數值的功能，因此需使用到前面介紹過的VBscript控制項。為方便初學者熟悉函數及圖形繪製，另外又設計簡易之二維函數圖製作，唯對二維內隱型(Implicit function)及三維函數圖繪製有興趣之讀者，可參考編者另外一本即將出版之函數圖(二維及三維、tube plot等)繪圖程式書籍。

15.2.1指令按鈕及功能鍵介紹

為方便介紹，特將電算機之功能鍵及按鈕標題，依出現先後位置抄錄如下。

下表為對照於上表之指令按鈕名稱。

下表為三角函數及反三角函數等資料輸入及輸出類型說明

如需使用到函數繪圖功能，則點按開啟圖框功能鍵，就能開啟及使用到函數繪圖功能，開啟圖框後整個畫面如下圖所示。

15.2.2程式設計

    電算機程式設計內容繁雜，如要一一說明並不容易，在此我們將其分為兩部份來說明：

(a) 加、減、乘、除四則運算：

   以計算 5+7=12為例，必須使用到指令按鈕(1)數字5 [Cmdnum(5)]，(2)運算子+[ CmdOper(0)]，(3)數字7 [Cmdnum(7)]及(4)等號= [Cmdequal]四個指令按鈕，因此其程序設計可考慮如下。

數字(0~9)按鈕可設計成cmdnum(Index)陣列，分別以指數Index(0~9)代表數字。運算子為CmdOper(Index)指數Index(0~5)分別代表運算子(＋、－、×、/及\)。等號則配合計算式中是否有左括弧，而分為”=”之Cmdequal，含右括弧”=)”之CmdRBEqual，含雙引號及右括弧” "=)”之CmdDBrEqual三種。因此”3+5”須採用”=”；”3*(2+9”須採用”)=”；”SinS(“56d43m48s須採用"”=)”配合，否則會出現語法錯誤(invalid expression)訊息。

(1).數字指令程序

Private Sub cmdnum_Click(Index As Integer)

If txtInput.Text = "0" Then txtInput.Text = ""

txtInput.Text = txtInput.Text & Index

End Sub

(2).運算子指令程序

Private Sub cmdoper_Click(Index As Integer)

On Error Resume Next

If Mid(txtShow.Text, Len(txtShow.Text), 1) <> ")" Then txtShow.Text = txtShow.Text + txtInput.Text

txtInput.Text = "0"   '開始時txtInput顯示為0

txtShow.Text = txtShow.Text + cmdoper(Index).Caption 

End Sub

(3).等號指令程序

Private Sub cmdequal_Click()  '按等號得答案

Dim starrey() As String, Xtpt As Double, Ytpt As Double

Dim StTpt As String

On Error Resume Next

Dim expression As String

Dim com As Control

StTpt = Trim$(txtShow.Text)

starrey = Split(StTpt, "(", -1, vbTextCompare) '輸入資料分離

Select Case glIndex

Case 42, 43   ' Atan2()及Atn2D

starrey = Split(starrey(1), ",", -1, vbTextCompare)

Ytpt = Val(starrey(0))

Xtpt = Mid(starrey(1), 1, Len(starrey(1)) - 1)

'MsgBox ("ytpt=" & Ytpt)

'MsgBox ("xtpt=" & Xtpt)

 If glIndex = 42 Then txtInput.Text = Round(Atan2(Ytpt, Xtpt), 10) 'Atan2(y,x)

 If glIndex = 43 Then txtInput.Text = Round(Atn2D(Ytpt, Xtpt), 10) 'Atn2D(y,x)

GoTo 60

Case 47  'Modxy()

starrey = Split(starrey(1), ",", -1, vbTextCompare)

Ytpt = Val(starrey(0))

Xtpt = Mid(starrey(1), 1, Len(starrey(1)) - 1)

txtInput.Text = Round((Ytpt Mod Xtpt), 10)

GoTo 60

.

.

.

.

Case Else

50 If IsOper(Mid(txtShow.Text, Len(txtShow.Text), 1)) = True And CmdLeftBrk.Enabled = True Then txtShow.Text = txtShow.Text + txtInput.Text

55 expression = EditedEqu(txtShow.Text)

If IsValid(expression, False, False, False) = False Then MsgBox ("Invalid expression"): Exit Sub

 Call Init(expression)

txtInput.Text = Round(StrGetVal(0, 0, 0, 0), 10)

End Select

60 cmdequal.Enabled = True

CmdClsAll.Enabled = True

txtInput.Enabled = True

txtShow.Enabled = True

AnsResult = Round(Val(txtInput.Text), 10)

glIndex = -100

End Sub

上述數求最小公倍數及最大公約數，原規劃只求兩數的最小公倍數及最大公約數，讀者可以將其改為較多數之求法。

(b) 函數計算：

    三角函數、反三角函數、對數、雙曲線函數(SinH,CosH)等，因語法(systax)需要，必須使用到對稱之左右小括弧，如Sin()，Asin()，AsinH()，Exp()等，如函數指令標題(Caption)名稱為”Sin(“或”Asin(“，或”AsinH(“或”Exp(“，則等號指令標題須以”)=”配合。另函數SinS()，CosS()，TanS()等，因函數之引數(Argument)為文字度分秒(dms)，故函數指令標題如為”SinS("”，”CosS("”，”TanS("”，故等號需以”")”配合。

(1).函數指令程序

Private Sub cmdfunc_Click(Index As Integer)

glIndex = Index

If Index >= 12 And Index <= 17 Then

txtShow.Text = txtShow.Text + cmdfunc(Index).Caption + "("""

Else

txtShow.Text = txtShow.Text + cmdfunc(Index).Caption + "("

End If

End Sub

(2).右括弧等號指令程序

Private Sub CmdRBEqual_Click()

txtShow.Text = txtShow.Text + txtInput.Text + ")"

Call cmdequal_Click

txtShow.Text = txtShow.Text & "= " & Round(AnsResult, 10)

End Sub

(3).引號右括弧等號指令程序

Private Sub CmdDRBEqual_Click()

txtShow.Text = txtShow.Text + txtInput.Text + """)"

Call cmdequal_Click

txtShow.Text = txtShow.Text & "= " & Round(AnsResult, 10)

End Sub

15.3二維函數圖繪製介紹

    二維函數指的是兩個變數，一個主變數及一個附屬變數的函數。二維函數可簡單概分為(1)外顯型函數(Explicit functions)，(2)內隱型函數(Implicit functions)兩大類。一般其類型為y=f(x)，如y=x+tan(x)；或為x=f(y)類型，如y=x*sin(x)；或參數類型x=x(t)，y=y(t)，如x=3sin(t)；或如y=3*cos(t)者；或為極座標形式的類型，如以r(t)=e-4cos(4t)+sin(t/4)表示者。主變數與副變數如為一對一關係者，多屬外顯型函數；另函數只能以類似f(x,y)=0表示者，如x+(y-4)-4=0，主變數與副變數非為一對一的，而為多值型就是所謂內隱型函數。外顯型函數因兩變數間為一對一關係，且不必像三維函數圖必須考慮隱藏線及背面去除問題，故其函數圖繪製非常簡單；而內隱型函數一般多必須先假定一個變數已知，然後求另一變數值，其解答可能有許多組，因此作業程序比較複雜。外顯型三維函數可以說是二維函數外顯型的延伸或推廣，因此適用在二維函數圖繪製的演算法，多可適用在三維函數作業中。一般y=f(x)或x=f(y)類型，多可以參數型式表示，如x=t以表示，則y=f(t)，如y=t表示，則x=f(t)。

15.4外顯型函數圖繪製

外顯型函數因兩變數間為一對一關係，函數圖繪製非常簡單。下面我們就介紹y=f(x)， x=f(y) 及x=x(t)，y=y(t) 與r=r(t)類型類型的外顯型函數圖繪製。

15.3.1 y=f(x)類型函數圖繪製

y=f(x)二維類型函維圖繪製，因為其兩變數純為一對一，故製圖作業既簡單又單純，在此不特別介紹其詳細演算程序，讀者只要閱讀下面的程序碼便能瞭解一切。

Sub Form_Load()

glNumberOfTriangles = 0

glXbeg = -10   ‘變數x起點值

glXend = 10    ‘變數x終點值

gldX = 0.25    ‘變數x每次計算增量

glYbeg = -10    ‘變數y起點值

glYend = 10     ‘變數y終點值

gldY = 0.25     ‘變數y每次計算增量

gltbeg = -10     ‘變數t起點值

gltend = 10     ‘變數t終點值

gldt = 0.25     ‘變數t每次計算增量

glnumX = (glXend - glXbeg) / gldX

glnumY = (glYend - glYbeg) / gldY

glnumt = (gltend - gltbeg) / gldt

PicCanvas.ScaleMode = 0

PicCanvas.AutoRedraw = True

PicCanvas.Scale (glXbeg, glYend)-(glXend, glYbeg)

Randomize

End Sub

Private Sub PlotNormalX()

Dim I As Integer

Dim Pts() As Point2D

ReDim Pts(1 To glnumX)

glColoruse = RGB(Rnd * 250, Rnd * 250, Rnd * 250)  '線條顏色

For I = 1 To glnumX 

Pts(I).x = glXbeg + (I - 1) * gldX

Pts(I).y = glFx(Pts(I).x)  '定義的外顯型函數y=f(x)

If I = 1 Then

PicCanvas.PSet (Pts(I).x, Pts(I).y)

Else

PicCanvas.Line -(Pts(I).x, Pts(I).y), glColoruse

End If

Next I

End Sub

15.4.2 x=f(y)類型函數圖繪製

    此類似函數圖製作與上節所介紹的y=f(x)極為相似，差別只在兩變數位置互換而已。

Sub PlotNormalY()

Dim I As Integer

Dim Pts() As Point2D

ReDim Pts(1 To glnumY)

glColoruse = RGB(Rnd * 250, Rnd * 250, Rnd * 250)  '線條顏色

For I = 1 To glnumY

Pts(I).y = glYbeg + (I - 1) * gldY

Pts(I).x = glFy(Pts(I).y) '定義的外顯型函數x=f(y)

If I = 1 Then

PicCanvas.PSet (Pts(I).x, Pts(I).y)

Else

PicCanvas.Line -(Pts(I).x, Pts(I).y), glColoruse

End If

Next I

End Sub

15.4.3 x=x(t)，y=y(t)類型

    參數型函數x=x(t)，y=y(t)圖型的繪製、與y=f(x)及x=f(y)類型相差不大，給定主變數t後，x及y值便能求得。

Sub PlotParametric()

Dim t As Single, I As Integer

Dim Pts() As Point2D

ReDim Pts(1 To glnumt)

glColoruse = RGB(Rnd * 250, Rnd * 250, Rnd * 250)  '線條顏色

For I = 1 To glnumt

t = gltbeg + (I - 1) * gldt

Pts(I).x = glFt_x(t)   '定義的參數函數x=f(t)

Pts(I).y = glFt_y(t)   '定義的參數函數y=f(t)

If I = 1 Then

PicCanvas.PSet (Pts(I).x, Pts(I).y)

Else

PicCanvas.Line -(Pts(I).x, Pts(I).y), glColoruse

End If

Next I

End Sub

15.4.4 r=r(t)類型

極座標型函數為極為特殊型態的二維函數，其數學表示法非常簡便，如中心在(0,0)的半徑為2單位的圓形，其數學公式為ρ(θ)=2。而中心在(1,2)的半徑為2單位的圓形，則公式為

ρ(θ)=

或

ρ(θ)=

兩者都代表相同的圓。一般矩形(x,y)座標轉換為極座標(ρ,θ)時其關係為：

ρ=

θ=tan

極座標(ρ,θ)轉換為矩形(x,y)座標時則關係為：

x=ρcos(θ)

y=ρsin(θ)

=ρ

    有關極座標的函數圖繪製VB程序碼，披露如下供讀者參考：

Private Sub PlotPolar(color As Long, tStart As Single, tEnd As Single)

Dim x As Single, y As Single

Dim i As Integer, steps As Integer, t As Single, rl As Single

Dim dt As Single

Dim xmin_t As Single, xmax_t As Single, ymin_t As Single, ymax_t As Single

On Error GoTo errhandler

steps = 640

dt = (tEnd - tStart) / steps

xmin_t = 999999#

xmax_t = -999999#

ymin_t = 999999#

ymax_t = -999999#

For i = 1 To steps 'Do While t <= tEnd  '

t = tStart + (i - 1) * dt

rl = glFrt(CDbl(t))

x = rl * Cos(t)

y = rl * Sin(t)

If x > xmax_t Then xmax_t = x

If x < xmin_t Then xmin_t = x

If y > ymax_t Then ymax_t = y

If y < ymin_t Then ymin_t = y

       If (i = 1 Or ltest > 2 * gldt) Then

       PicCanvas.PSet (x, y)

       Else

       PicCanvas.Line -(x, y), color

       End If

  Next i

Txtxmin_t.Text = xmin_t

Txtxmax_t.Text = xmax_t

Txtymin_t.Text = ymin_t

Txtymax_t.Text = ymax_t

Exit Sub

errhandler:

Error = True

Resume Next

End Sub

下面為繪圖程式函數圖繪製程式中幾個重要程序如座標軸(矩形及極座標)、刻度及單位標示、等之程序碼供讀者參考。

Private Sub CmdPolar_Click()’畫極座標類型函數圖

Dim stIn As String, St1 As String, St2 As String, expXY As String

Dim tBeg As Double, tEnd As Double

Dim STresult() As String

If txtEQInput.Text = "" Then

MsgBox ("尚未選取或輸入方程式及變數範圍,請重來")

Exit Sub

End If

stIn = txtEQInput.Text

STresult = Split(stIn, "=", -1, vbTextCompare)

If UBound(STresult) <> 1 Then

MsgBox ("資料有問題???,請重來")

Exit Sub

End If

expXY = STresult(1)

tBeg = Val(txttBeg.Text)

tEnd = Val(txttEnd.Text)

PicGraph.DrawWidth = Val(txtDrawwidth)

Call drawPolar(expXY, colorPlot, tBeg, tEnd)

txtShow = stIn

txtEQInput.Text = ""

End Sub

Private Sub CmdClosePic_Click() ‘關閉圖框

Frame1.Visible = False

PicGraph.Visible = False

txtInput.Visible = False

Label1.Visible = False

CmdPolar.Visible = False

CmdParameter.Visible = False

PicHruler.Visible = False

PicVruler.Visible = False

OptPolar(0).Visible = False

OptPolar(1).Visible = False

OptPolar(1).value = False

FrmEngCal.Width = 4800

txtShow.Width = FrmEngCal.Width - 200

txtInput.Width = FrmEngCal.Width - 200

Label3.Visible = False

List1.Visible = False

CmdPolar.Enabled = False

CmdParameter.Enabled = False

CmdClosePic.Enabled = False

CmdOpenPic.Enabled = True

txtInput.Text = ""

txtShow.Text = ""

CmdClosePic.Visible = False

End Sub

Private Sub CmdOpenPic_Click() ’開啟圖框

.

.

.

.

rue

End Sub

Private Sub Form_Load() ’載入表單(資料初始化)

glXmax = 10

glXmin = -10

glYmax = 10

glYmin = -10

PicGraph.AutoRedraw = True

gl主格間距x = 2#

gl副格間距x = 0.5

gl主格間距y = 2#

gl副格間距y = 0.5

gl軸線顏色 = vbRed

gl刻度顏色 = vbMagenta

gl遮蓋顏色 = vbBlue

gl主格線色 = &H808080

gl副格線色 = &HC0C0C0

gl軸線線型 = 0

gl軸線寬 = 1

gl座標類型 = 0

gl主格線型 = 0

gl顯主格線嗎 = True

gl顯副格線嗎 = True

glx弳度 = False

gly弳度 = False

Call createCoordinates

'Private Sub form_load()

Call Init("")

'Option1(0) = True

'FctINput = 1#

'Option2(0) = True

'FctOutPut = 1#

PicGraph.Scale (-10, 10)-(10, -10)

PicGraph.AutoRedraw = True

Frame1.Visible = False

PicGraph.Visible = False

txtEQInput.Visible = False

Label1.Visible = False

Label3.Visible = False

List1.Visible = False

CmdPolar.Visible = False

CmdParameter.Visible = False

PicHruler.Visible = False

PicVruler.Visible = False

OptPolar(0).Visible = False

OptPolar(1).Visible = False

CmdClosePic.Visible = False

FrmEngCal.Width = 4800

txtShow.Width = FrmEngCal.Width - 200

txtEQInput.Width = FrmEngCal.Width - 200

txtEQInput.Text = ""

Randomize

   colorPlot = RGB(Rnd * 250, Rnd * 250, Rnd * 250)

   PicGraph.DrawWidth = 2

End Sub

Private Sub 座標及格線()

.

.

.

.

200      End Sub

Private Sub 畫副格線(Nsec副x As Integer, Nsec副y As Integer)

Dim i As Integer, Xi As Double, Yi As Double

Select Case gl座標類型 '0為矩形;1為極座標

Case 0   '矩形座標

Select Case glx弳度

Case False

For i = 1 To Nsec副x * 4

      Xi = 0 + (i - 1) * gl副格間距x

           PicGraph.Line (Xi, -200)-(Xi, 200), gl副格線色

Next i

For i = 1 To Nsec副x * 4

      Xi = 0 - (i - 1) * gl副格間距x

           PicGraph.Line (Xi, -200)-(Xi, 200), gl副格線色

Next i

Case True

For i = 1 To Nsec副x * 4

      Xi = 0 + (i - 1) * gl副格間距x * pi / 2

           PicGraph.Line (Xi, -200)-(Xi, 200), gl副格線色

Next i

For i = 1 To Nsec副x * 4

      Xi = 0 - (i - 1) * gl副格間距x * pi / 2

           PicGraph.Line (Xi, -200)-(Xi, 200), gl副格線色

Next i

End Select

Select Case gly弳度

Case False

.

.

.

.

End Select

Case 1 '1為極座標

Dim x1 As Double, y1 As Double, x2 As Double, y2 As Double, Radi As Double, AngI As Double, Nang As Integer

Select Case glx弳度

Case False

      For Radi = gl副格間距x To 200 Step gl副格間距x

      PicGraph.Circle (0, 0), Radi, gl副格線色

       Next Radi

Case True

     For Radi = gl副格間距x * pi / 2 To 200 Step gl副格間距x * pi / 2

      PicGraph.Circle (0, 0), Radi, gl副格線色

       Next Radi

End Select

   End Select

End Sub

Private Sub 畫主格線(Nsec主x As Integer, Nsec主y As Integer)

Dim i As Integer, Xi As Double, Yi As Double

Select Case gl座標類型 '0為矩形;1為極座標

Case 0   '矩形座標

Select Case glx弳度

Case False

For i = 1 To Nsec主x * 4

      Xi = 0 + (i - 1) * gl主格間距x

           PicGraph.Line (Xi, -200)-(Xi, 200), gl主格線色

Next i

For i = 1 To Nsec主x * 4

      Xi = 0 - (i - 1) * gl主格間距x

           PicGraph.Line (Xi, -200)-(Xi, 200), gl主格線色

Next i

Case True

‘

‘

‘

End Select

Select Case gly弳度

Case False

For i = 1 To Nsec主y * 4 + 1

      Yi = 0 + (i - 1) * gl主格間距y

      PicGraph.Line (-200, Yi)-(200, Yi), gl主格線色

Next i

For i = 1 To Nsec主y * 4 + 1

      Yi = 0 - (i - 1) * gl主格間距y

      PicGraph.Line (-200, Yi)-(200, Yi), gl主格線色

Next i

Case True

.

.

.

.

End Select

Case 1 '1為極座標

Dim x1 As Double, y1 As Double, x2 As Double, y2 As Double, Radi As Double, AngI As Double, Nang As Integer

Select Case glx弳度

Case False

      'For Radi = gl主格間距 To glXmax * 16.1 Step gl主格間距

      For Radi = gl主格間距x To 200 Step gl主格間距x

      PicGraph.Circle (0, 0), Radi, gl主格線色

       Next Radi

Case True

    .

.

.

End Select

     Dim Angtpt As Integer, Ndo As Integer

     Ndo = 360 / gl角度間距 + 1

     For i = 1 To Ndo

     Angtpt = i * gl角度間距

     If Angtpt > 360# Then Exit For

     x1 = Cos(Angtpt * Ra)

     y1 = Sin(Angtpt * Ra)

     If Angtpt Mod 90 = 0 Then GoTo 100

     x2 = 200 * Cos(Angtpt * Ra)

     y2 = 200 * Sin(Angtpt * Ra)

     PicGraph.Line (x1, y1)-(x2, y2), gl主格線色

100    Next i

   End Select

End Sub

Private Sub 水平尺()

Dim i As Integer, Xi As Double, Nsec主x As Integer, Nsec副x As Integer

Nsec主x = Abs(glXmax - glXmin) / gl主格間距x + 1

Nsec副x = Abs(glXmax - glXmin) / gl副格間距x + 1

PicHruler.Scale (glXmin * 1.1, 1#)-(glXmax * 1.1, -1#)

'picHruler.Line (glxmin, -0.95)-(8.1 * glXmax, -0.95), vbRed

PicHruler.Line (-100, -0.95)-(100, -0.95), vbRed

Select Case glx弳度

Case False

For i = 1 To Nsec副x * 4 + 1  '主格線

   Xi = 0 + (i - 1) * gl副格間距x

   PicHruler.Line (Xi, -0.95)-(Xi, 0.001), gl副格線色

Next i

For i = 1 To Nsec副x * 4 + 1   '副格線

   Xi = 0 - (i - 1) * gl副格間距x

   PicHruler.Line (Xi, -0.95)-(Xi, 0.001), gl副格線色

Next i

For i = 1 To Nsec主x * 4 + 1  '主格線

   Xi = 0 + (i - 1) * gl主格間距x

   PicHruler.Line (Xi, -0.95)-(Xi, 0.02), gl主格線色

   PicHruler.PSet (Xi, 0.75), PicHruler.BackColor

   PicHruler.Print Xi

Next i

For i = 1 To Nsec主x * 4 + 1   '主格線

   Xi = 0 - (i - 1) * gl主格間距x

   PicHruler.Line (Xi, -0.95)-(Xi, 0.02), gl主格線色

   PicHruler.PSet (Xi, 0.75), PicHruler.BackColor

      PicHruler.Print Xi

Next i

Case True

For i = 1 To Nsec副x * 4 + 1  '主格線

   Xi = 0 + (i - 1) * gl副格間距x * 0.5 * pi

   PicHruler.Line (Xi, -0.95)-(Xi, 0.001), gl副格線色

Next i

For i = 1 To Nsec副x * 4 + 1   '副格線

   Xi = 0 - (i - 1) * gl副格間距x * 0.5 * pi

   PicHruler.Line (Xi, -0.95)-(Xi, 0.001), gl副格線色

Next i

For i = 1 To Nsec主x * 4 + 1  '主格線

   Xi = 0 + (i - 1) * gl主格間距x * pi / 2

   PicHruler.Line (Xi, -0.95)-(Xi, 0.02), gl主格線色

   PicHruler.PSet (Xi, 0.75), PicHruler.BackColor

    PicHruler.Print Round(Xi / pi, 3) & "π"

Next i

For i = 1 To Nsec主x * 4 + 1   '主格線

   Xi = 0 - (i - 1) * gl主格間距x * pi / 2

   PicHruler.Line (Xi, -0.95)-(Xi, 0.02), gl主格線色

   PicHruler.PSet (Xi, 0.75), PicHruler.BackColor

      PicHruler.Print Round(Xi / pi, 3) & "π"

Next i

End Select

End Sub

Private Sub 垂直尺()

.

.

.

.

End Sub

Private Sub Combo1_Click()

Select Case Combo1.Text

Case "極座標類"

List1.Clear

List1.AddItem "r(t)=1.5"

List1.AddItem "r(t)=5*cos(2t)"

List1.AddItem "r(t)=5/cos(t)"

List1.AddItem "r(t)=5/sin(t)"

.

.

.

List1.AddItem "r(t)=13/(4*cos(t)+6*sin(t))"

List1.AddItem "r(t)=2.5*(exp(cos(t))-2*cos(4*t)+sin(t/4)^3)"

List1.AddItem "r(t)=((2 * Cos(t) + 4 * Sin(t))+sqr((2 * Cos(t) + 4 * Sin(t))^2-4))/2"

List1.AddItem "r(t)=2*((2 * Cos(t) + 4 * Sin(t))-sqr((2 * Cos(t) + 4 * Sin(t))^2-4))/2"

CmdPolar.Enabled = True

CmdParameter.Enabled = False

Case "參數類"

List1.Clear

List1.AddItem "x=t,y=sin(t)"

List1.AddItem "x=t,y=cos(t)"

List1.AddItem "x=t,y=tan(t)"

.

.

.

List1.AddItem "x=2+2*cosd(30)*cos(t)-3*sind(30)*sin(t),y=2+2*sind(30)*cos(t)+3*cosd(30)*sin(t)"

List1.AddItem "x=(2+cos(2.5*t))*cos(t),y=(2+cos(2.5*t))*sin(t)"

List1.AddItem "x=2+2*cosd(30)/cos(t)-3*sind(30)*tan(t),y=2-2*sind(30)*tan(t)+3*cosd(30)/cos(t)"

.

.

.

CmdParameter.Enabled = True

CmdPolar.Enabled = False

End Select

End Sub

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