CAD原理实验报告

CAD原理实验报告

服装CAD原理与应用

实验报告

目录

实验报告（一）三点画圆弧----------------------（02-07）

实验报告（二）两点画圆弧----------------------（08-12）

实验报告（三）Bezier曲线的绘制----------------（13-17）

实验报告（四）Hermite曲线的绘制---------------（18-22）

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实验报告（五）B样条曲线的绘制-----------------（23-27）

实验报告（一）

一、 实验题目

使用VB软件实现三点画圆弧

二、 实验目的

1．了解服装CAD中的常用曲线，灵活运用理论知识加以

运用，实现操作；

2．掌握三点画圆弧的基本原理和绘制方法；

3．运用Visual Basic 6.0软件编写程序实现通过三点的控制成功绘制圆弧。

三、 实验目的 1.实验原理

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已知三个点A（x1，y1），B（x2，y2）C（x3，y3）的坐标

①根据中垂线相交于圆心可以求出圆心（x，y）的坐标以及半径r

②根据圆心以及已知三点的坐标，判断出所画圆弧的起始角，终止角和中间角的正切角度值，进而求出这三个角的角度。

③比较起始角，终止角和中间角这三点的角度大小，判断出所画圆弧的方向。

2．源代码

VERSION 5.00

Begin VB.Form Form1

Caption = \"三点画圆弧\" ClientHeight = 5835 ClientLeft = 120 ClientTop = 450 ClientWidth = 8280 LinkTopic = \"Form1\" ScaleHeight = 5835 ScaleWidth = 8280

StartUpPosition = 3 '窗口缺省 Begin VB.CommandButton Command3 Caption = \"退出\" Height = 615 Left = 6000 TabIndex = 3 Top = 4800 Width = 1455 End

Begin VB.CommandButton Command2 Caption = \"取消\" Height = 615

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Left = 3360 TabIndex = 2 Top = 4800 Width = 1455 End

Begin VB.CommandButton Command1 Caption = \"画弧\" Height = 615 Left = 720 TabIndex = 1 Top = 4800 Width = 1455 End

Begin VB.PictureBox Picture1 Height = 4335 Left = 360 ScaleHeight = 4275 ScaleWidth = 7515 TabIndex = 0 Top = 240 Width = 7575 End End

Attribute VB_Name = \"Form1\"

Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False Private pt() As mypoint Private Sub Form_Load() ReDim pt(1) End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) Dim s As Integer

pt(UBound(pt)).x = x pt(UBound(pt)).y = y

Picture1.Circle (x, y), 15 s = Val(UBound(pt)) Select Case s Case 1

Picture1.Print \"A\" Case 2

Picture1.Print \"B\"

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Case 3

Picture1.Print \"C\" End Select

If UBound(pt) > 1 Then

Picture1.Line (pt(UBound(pt) - 1).x, pt(UBound(pt) - 1).y)-(pt(UBound(pt)).x, pt(UBound(pt)).y) End If

ReDim Preserve pt(UBound(pt) + 1) End Sub

Private Sub Command1_Click()

Dim A1, A2, B1, B2, C1, C2 As Single Dim X0, Y0, r, PI As Double Dim t1, t2, t3 As Double Dim t As Double

A1 = pt(1).x ^ 2 + pt(1).y ^ 2 - pt(3).x ^ 2 - pt(3).y ^ 2 A2 = pt(2).x ^ 2 + pt(2).y ^ 2 - pt(3).x ^ 2 - pt(3).y ^ 2 B1 = 2 * pt(3).x - 2 * pt(1).x B2 = 2 * pt(3).x - 2 * pt(2).x C1 = 2 * pt(1).y - 2 * pt(3).y C2 = 2 * pt(2).y - 2 * pt(3).y

X0 = (A1 * C2 - A2 * C1) / (B2 * C1 - B1 * C2) Y0 = (A1 * B2 - A2 * B1) / (B2 * C1 - B1 * C2)

r = Sqr((pt(1).x - X0) * (pt(1).x - X0) + (pt(1).y - Y0) * (pt(1).y - Y0))

PI = 4 * Atn(1)

t1 = Atn((pt(1).y - Y0) / (pt(1).x - X0))

If pt(1).x - X0 > 0 And pt(1).y - Y0 > 0 Then t1 = t1 Else

If pt(1).x - X0 < 0 And pt(1).y - Y0 > 0 Then t1 = t1 + PI Else

If pt(1).x - X0 < 0 And pt(1).y - Y0 < 0 Then t1 = t1 + PI Else

t1 = t1 + 2 * PI End If End If End If

t2 = Atn((pt(2).y - Y0) / (pt(2).x - X0))

If pt(2).x - X0 > 0 And pt(2).y - Y0 > 0 Then t2 = t2 Else

If pt(2).x - X0 < 0 And pt(2).y - Y0 > 0 Then

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t2 = t2 + PI Else

If pt(2).x - X0 < 0 And pt(2).y - Y0 < 0 Then t2 = t2 + PI Else

t2 = t2 + 2 * PI End If End If End If

If t1 < t3 < t2 Then

For t = t1 To t2 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

ElseIf t2 < t1 < t3 Then t2 = t2 + 2 * PI

For t = t1 To t2 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

ElseIf t3 < t2 < t1 Then t2 = t2 + 2 * PI

For t = t1 To t2 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

ElseIf t1 < t2 < t3 Then t1 = t1 + 2 * PI

For t = t2 To t1 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

ElseIf t3 < t1 < t2 Then t1 = t1 + 2 * PI

For t = t2 To t1 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

ElseIf t2 < t3 < t1 Then

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For t = t2 To t1 Step 0.001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t End If End Sub

Private Sub Command2_Click() Picture1.Cls ReDim pt(1) End Sub

Private Sub Command3_Click() End End Sub

四 实验结果

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实验报告（二）

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一、 实验题目

使用VB软件实现两点画圆弧

二、 实验目的

1．了解服装CAD中的常用曲线，灵活运用理论知识加以

运用，实现操作；

2．掌握使用两端点，以及其中一端点切线画圆弧的基本原理和绘制方法；

3．运用Visual Basic 6.0软件编写程序实现通过两端点，以及其中一端点切线成功绘制圆弧。

三、 实验内容 1、实验原理

已知一圆弧两端点A，B和A端点切线的方向数L ①根据向量的知识，由已知一圆弧两端点A，B和A端点切线的方向数L求出圆心的坐标和半径大小； ②计算在圆心为原点的新坐标系下初始角和终止角的正切值，进而求出对应的角度；

③判断L和半径向量的乘积，若大于0，则为逆时针方向画圆弧，小于0，则为顺时针方向画圆弧； ④根据圆的参数方程表达式，利用VB绘制圆弧。

2、源代码

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VERSION 5.00

Begin VB.Form Form1

AutoRedraw = -1 'True

Caption = \"两点加切线画圆弧\" ClientHeight = 6810 ClientLeft = 120 ClientTop = 450 ClientWidth = 8340 LinkTopic = \"Form1\" ScaleHeight = 6810 ScaleWidth = 8340

StartUpPosition = 3 '窗口缺省 Begin VB.CommandButton Command3 Caption = \"退出\" Height = 615 Left = 6240 TabIndex = 3 Top = 6000 Width = 1575 End

Begin VB.CommandButton Command2 Caption = \"取消\" Height = 615 Left = 3360 TabIndex = 2 Top = 6000 Width = 1575 End

Begin VB.CommandButton Command1 Caption = \"画弧\" Height = 615 Left = 480 TabIndex = 1 Top = 6000 Width = 1575 End

Begin VB.PictureBox Picture1 AutoRedraw = -1 'True Height = 5175 Left = 360 ScaleHeight = 5115 ScaleWidth = 7515 TabIndex = 0 Top = 480

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Width = 7575 End End

Attribute VB_Name = \"Form1\"

Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False Private pt() As mypoint Private Sub Form_Load() ReDim pt(1) End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) Dim s As Integer

pt(UBound(pt)).x = x pt(UBound(pt)).y = y

Picture1.Circle (x, y), 1 s = Val(UBound(pt)) Select Case s Case 1

Picture1.Print \"A\" Case 2

Picture1.Print \"B\" Case 3

Picture1.Print \"L\" '曲线在A点处的切线矢量

Picture1.Line (pt(1).x, pt(1).y)-(pt(3).x, pt(3).y) End Select

ReDim Preserve pt(UBound(pt) + 1) End Sub

Private Sub Command1_Click() Dim X0, Y0, r As Double

Dim a1, a2, b1, b2, c1, c2 As Double Dim t, t1, t2, i, j, k, m, n As Double Dim pi As Single pi = 4 * Atn(1)

a1 = 2 * pt(1).x - 2 * pt(2).x a2 = pt(3).x - pt(1).x

b1 = 2 * pt(1).y - 2 * pt(2).y b2 = pt(3).y - pt(1).y

c1 = pt(1).x ^ 2 - pt(2).x ^ 2 + pt(1).y ^ 2 - pt(2).y ^ 2

c2 = (pt(1).x - pt(3).x) * pt(1).x + (pt(1).y - pt(3).y) * pt(1).y X0 = (b2 * c1 - b1 * c2) / (a1 * b2 - a2 * b1) Y0 = (a1 * c2 - a2 * c1) / (a1 * b2 - a2 * b1)

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r = Sqr((pt(1).x - X0) ^ 2 + (pt(1).y - Y0) ^ 2)

k = (pt(3).y - pt(1).y) * (pt(1).x - X0) - (pt(3).x - pt(1).x) * (pt(1).y - Y0)

m = pt(1).x - X0 n = pt(1).y - Y0

t1 = Atn(Abs(n / m)) If m > 0 And n > 0 Then t1 = t1

ElseIf m < 0 And n > 0 Then t1 = pi - t1

ElseIf m < 0 And n < 0 Then t1 = pi + t1

ElseIf m > 0 And n < 0 Then t1 = 2 * pi - t1 End If

i = pt(2).x - X0 j = pt(2).y - Y0

t2 = Atn(Abs(j / i)) If i > 0 And j > 0 Then t2 = t2

ElseIf i < 0 And j > 0 Then t2 = pi - t2

ElseIf i < 0 And j < 0 Then t2 = pi + t2

ElseIf i > 0 And j < 0 Then t2 = 2 * pi - t2 End If

If k > 0 Then

If t1 < t2 Then

For t = t1 To t2 Step 0.0001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

Else: t2 = t2 + 2 * pi

For t = t1 To t2 Step 0.0001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t End If Else

If t1 > t2 Then

For t = t2 To t1 Step 0.0001

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x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t

Else: t1 = t1 + 2 * pi

For t = t2 To t1 Step 0.0001 x = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next t End If End If End Sub

Private Sub Command2_Click() Picture1.Cls ReDim pt(1) End Sub

Private Sub Command3_Click() End End Sub

四、 实验结果

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实验报告（三）

一、 实验题目

运用VB软件绘制Bezier曲线

二、 实验目的

1、了解服装CAD中的常用曲线，通过实际操作加以深入认识；

2、了解Bezier曲线的特点，根据Bezier曲线的基本原理，推断出绘制方法并进行操作；

3、运用Visual Basic 6.0软件编写程序实现曲线的成功绘制。

三、 实验内容 1、实验原理

设空间有n+1个点P0，P1，P2，……，Pn，则称下列函数所决定的参数曲线为Bezier曲线：

Q(t)PBii,n(t)(0t1)i0i式(1-1)中，Bi,n(t)Cn(1t)niti(i0,1,L,n)n

在给定几个点时，可在t[0，1]区间取一系列值，相应的计算一系列的x(t)，y(t)，z(t)的值，由此可确定空间曲线上各点的位置，连接后即得该空间曲线。

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2、源代码

VERSION 5.00

Begin VB.Form Bezier

Caption = \"Bezier曲线\" ClientHeight = 7575 ClientLeft = 60 ClientTop = 450 ClientWidth = 9255 LinkTopic = \"Form1\" ScaleHeight = 7575 ScaleWidth = 9255

StartUpPosition = 3 '窗口缺省 Begin VB.CommandButton Command2 Caption = \"取 消\" Height = 495 Left = 3840 TabIndex = 3 Top = 6600 Width = 1455 End

Begin VB.CommandButton Command3 Caption = \"退 出\" Height = 495 Left = 6720 TabIndex = 2 Top = 6600 Width = 1455 End

Begin VB.CommandButton Command1 Caption = \"画 弧\" Height = 495 Left = 1080 TabIndex = 1 Top = 6600 Width = 1455 End

Begin VB.PictureBox Picture1 Height = 5655 Left = 600

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ScaleHeight = 5595 ScaleWidth = 7995 TabIndex = 0 Top = 480 Width = 8055 End End

Attribute VB_Name = \"Bezier\"

Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False Private pt() As mypoint

Private Sub Form_Load() ReDim pt(1) End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) Dim s As Integer

pt(UBound(pt)).x = x pt(UBound(pt)).y = y

Picture1.Circle (x, y), 15 s = Val(UBound(pt)) Select Case s Case 1

Picture1.Print \"P0\" Case 2

Picture1.Print \"P1\" Case 3

Picture1.Print \"P2\" Case 4

Picture1.Print \"P3\" Case 5

Picture1.Print \"P4\" Case 6

Picture1.Print \"P5\" Case 7

Picture1.Print \"P6\" Case 8

Picture1.Print \"P7\" Case 9

Picture1.Print \"P8\"

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Case 10

Picture1.Print \"P9\" Case 11

Picture1.Print \"P10\" End Select

If UBound(pt) > 1 Then

Picture1.Line (pt(UBound(pt) - 1).x, pt(UBound(pt) - 1).y)-(pt(UBound(pt)).x, pt(UBound(pt)).y) End If

ReDim Preserve pt(UBound(pt) + 1) End Sub

Private Sub Command1_Click() Dim i%, t#

Dim j, n As Integer Dim s, x, y As Single n = UBound(pt) - 1 - 1 For j = 1 To 1000 x = 0 y = 0

For i = 0 To n t = j / 1000

x = x + pt(i + 1).x * B(i, n, t) y = y + pt(i + 1).y * B(i, n, t) Next i

Picture1.PSet (x, y) Next j End Sub

Private Function fact(n As Integer) Dim i As Integer Dim s As Long s = 1

For i = 1 To n s = s * i Next i fact = s End Function

Private Function B(i%, n%, t#) As Single

B = (fact(n) * t ^ i * (1 - t) ^ (n - i)) / (fact(i) * fact(n - i)) End Function

Private Sub Command2_Click() Picture1.Cls

ReDim pt(1) 'pt(1)为第一个点P0

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End Sub

Private Sub Command3_Click() End End Sub

四、 实验结果

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实验报告（四）

一、 实验题目

运用VB软件绘制三次Hermite曲线

二、 实验目的

1、了解服装CAD中的常用曲线，通过实际操作加以深入认识；

2、了解Hermite曲线的特点，根据Hermite曲线的基本原理，推断出绘制方法并进行操作；

3、运用Visual Basic 6.0软件编写程序实现Hermite曲线的成功绘制。

三、 实验内容 1、实验原理

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三次Hermite样条曲线的一般表达式为：Q(t)=At3Bt2CtD　　　0t1　　（2-1）上式中A、B、C、D四个系数矢量可以根据具体已知条件来确定。已知曲线端点P0(t0),P1(t1)和该曲线在两个端点的切线矢量,P0'(t0),P1'(t1),则可得下面结果：Q(0)=D=P0Q(1)ABCDP1Q'(0)CP0'Q'(1)=3A+2B+C=P1'解上面的方程组得：''A=2(P0P1)P0P1''B3(P1P0)2P0P1CP0'DP0将上面结果中的系数A、B、C、D代入式(2-1)中，并整理成下面的表达式：32'32'Q(t)=(2t33t21)P0(2t33t2)P1(t2tt)P0(tt)P1　上式即为三次Hermite曲线表达式。''当给定P0(x,y,z),P区间中取一系列值，相应的计算1(x,y,z),P0(x,y,z),P1(x,y,z)时，可在t[0,1]一系列的x(t),y(t),z(t)的值，由此可确定空间曲线上各点的位置，连接后即得该空间曲线。2、源代码

VERSION 5.00

Begin VB.Form Hermite

Caption = \"三次Hermite曲线\" ClientHeight = 7575 ClientLeft = 60 ClientTop = 450 ClientWidth = 9255 LinkTopic = \"Form1\" ScaleHeight = 7575 ScaleWidth = 9255

StartUpPosition = 3 '窗口缺省 Begin VB.PictureBox Picture1 Height = 5655 Left = 600 ScaleHeight = 5595 ScaleWidth = 7995 TabIndex = 3 Top = 480 Width = 8055 End

Begin VB.CommandButton Command1 Caption = \"画 弧\" Height = 495 Left = 1200

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TabIndex = 2 Top = 6600 Width = 1455 End

Begin VB.CommandButton Command3 Caption = \"退 出\" Height = 495 Left = 6600 TabIndex = 1 Top = 6600 Width = 1455 End

Begin VB.CommandButton Command2 Caption = \"取 消\" Height = 495 Left = 3960 TabIndex = 0 Top = 6600 Width = 1455 End End

Attribute VB_Name = \"Hermite\"

Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False Private pt() As mypoint

Private Sub Form_Load() ReDim pt(1) End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) Dim s As Integer

pt(UBound(pt)).x = x pt(UBound(pt)).y = y

Picture1.Circle (x, y), 1 s = Val(UBound(pt)) Select Case s Case 1

Picture1.Print \"P0\" Case 2

Picture1.Print \"P1\"

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Case 3

Picture1.Print \"P01\" '曲线在P0点处的切线矢量 Picture1.Line (pt(1).x, pt(1).y)-(pt(3).x, pt(3).y) Case 4

Picture1.Print \"P11\" '曲线在P1点处的切线矢量 Picture1.Line (pt(2).x, pt(2).y)-(pt(4).x, pt(4).y) End Select

ReDim Preserve pt(UBound(pt) + 1) End Sub

Private Sub Command1_Click()

Dim Ax, Bx, Cx, Dx, Ay, By, Cy, Dy As Single Dim P01x!, P11y! Dim j%, t As Single

P01x = 2 * (pt(3).x - pt(1).x) P01y = 2 * (pt(3).y - pt(1).y)

P11x = 2 * (pt(2).x - pt(UBound(pt) - 1).x) P11y = 2 * (pt(2).y - pt(UBound(pt) - 1).y) Ax = 2 * (pt(1).x - pt(2).x) + P01x + P11x Ay = 2 * (pt(1).y - pt(2).y) + P01y + P11y

Bx = 3 * (pt(2).x - pt(1).x) - 2 * P01x - P11x By = 3 * (pt(2).y - pt(1).y) - 2 * P01y - P11y Cx = P01x Cy = P01y Dx = pt(1).x Dy = pt(1).y

For j = 1 To 1000 t = j / 1000

x = Ax * t ^ 3 + Bx * t ^ 2 + Cx * t + Dx y = Ay * t ^ 3 + By * t ^ 2 + Cy * t + Dy Picture1.PSet (x, y) Next j End Sub

Private Sub Command2_Click() Picture1.Cls

ReDim pt(1) 'pt(1)为第一个点P0 End Sub

Private Sub Command3_Click() End End Sub

Private Sub Form_Activate()

Picture1.Scale (0, 500)-(500, 0)

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End Sub

四、 实验结果 23

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实验报告（五）

一、 实验题目

用VB绘制三次B样条曲线

二、 实验目的

1、了解服装CAD中的常用曲线。

2、掌握B样条曲线的基本原理和方法，了解B样条曲线的特点。

3、运用Visual Basic 6.0软件编写程序实现三次B样条曲线的成功绘制

三、 实验内容 1、实验原理

B样条曲线的数学模型： 设空间有n+k+1个点P0,P1,L,Pk,Pk1,L,Pkn，称下列函数所决

定的参数曲线为第i段B样条曲线：

Qi(t)PijFj,k(t)(0t1,i0,1,2,L,n)j0k1kj 其中：Fj,k(t)(1)lCkl1(tkjl)k(0t1，j0,1,2,L,k)为基函数。t!l0Pi,Pi1,L,Pi+k为Qi(t)的控制顶点，折线PPii1,LPi+k为Qi(t)的控制多边形。k=3时，称为三次B样条曲线

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根据上式可得：

1F0,3(t)(t33t23t1)61F1,3(t)(3t36t24)6

1F2,3(t)(3t33t23t1)61F3,3(t)t36代入前面的式中，第i段三次B样条曲线表达式为：

Qi(t)=F0,3(t)PiF1,3(t)Pi1F2,3(t)Pi2F3,3(t)Pi3

根据给定四个点的，可在t[0，1]区间取一系列值，相应的计算一系列的x(t)，y(t)，z(t)的值，由此可确定空间曲线上各点的位置，连接后即得该空间曲线。

2、源代码

VERSION 5.00

Begin VB.Form Form1

Caption = \"三次B样条曲线\" ClientHeight = 6240 ClientLeft = 120 ClientTop = 450 ClientWidth = 9030 LinkTopic = \"Form1\" ScaleHeight = 6240 ScaleWidth = 9030

StartUpPosition = 3 '窗口缺省 Begin VB.CommandButton Command3 Caption = \"退出\" Height = 615 Left = 6840 TabIndex = 3 Top = 5400 Width = 1575 End

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Begin VB.CommandButton Command2 Caption = \"取消\" Height = 615 Left = 3720 TabIndex = 2 Top = 5400 Width = 1575 End

Begin VB.CommandButton Command1 Caption = \"画弧\" Height = 615 Left = 600 TabIndex = 1 Top = 5400 Width = 1455 End

Begin VB.PictureBox Picture1 Height = 4575 Left = 360 ScaleHeight = 4515 ScaleWidth = 8235 TabIndex = 0 Top = 360 Width = 8295 End End

Attribute VB_Name = \"Form1\"

Attribute VB_GlobalNameSpace = False Attribute VB_Creatable = False Attribute VB_PredeclaredId = True Attribute VB_Exposed = False Private pt() As mypoint Private Sub Form_Load() ReDim pt(1) End Sub

Private Sub Picture1_MouseDown(Button As Integer, Shift As Integer, x As Single, y As Single) Dim s As Integer

pt(UBound(pt)).x = x pt(UBound(pt)).y = y

Picture1.Circle (x, y), 15 s = Val(UBound(pt)) Select Case s Case 1

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Picture1.Print \"P0\" Case 2

Picture1.Print \"P1\" Case 3

Picture1.Print \"P2\" Case 4

Picture1.Print \"P3\" End Select

If UBound(pt) > 1 Then

Picture1.Line (pt(UBound(pt) - 1).x, pt(UBound(pt) - 1).y)-(pt(UBound(pt)).x, pt(UBound(pt)).y) End If

ReDim Preserve pt(UBound(pt) + 1) End Sub

Private Sub Command1_Click()

Dim f0, f1, f2, f3 As Double Dim x, y, i, n, j As Integer Dim t As Single n = UBound(pt) - 3 For j = 1 To 1000 t = j / 1000

f0 = 1 / 6 * (-t ^ 3 + 3 * t ^ 2 - 3 * t + 1) f1 = 1 / 6 * (3 * t ^ 3 - 6 * t ^ 2 + 4)

f2 = 1 / 6 * (-3 * t ^ 3 + 3 * t ^ 2 + 3 * t + 1) f3 = 1 / 6 * t ^ 3

x = f0 * pt(1).x + f1 * pt(2).x + f2 * pt(3).x + f3 * pt(4).x y = f0 * pt(1).y + f1 * pt(2).y + f2 * pt(3).y + f3 * pt(4).y Picture1.PSet (x, y) Next j End Sub

Private Sub Command2_Click() Picture1.Cls ReDim pt(1) End Sub

Private Sub Command3_Click() End End Sub

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四、 实验结果

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