1、服裝 CAD 原理與應用實驗報告目錄實驗報告一三點畫圓弧 實驗報告二兩點畫圓弧 實驗報告三Bezier曲線的繪制 02-07 08-12 13-17 18-22 實驗報告四 Hermite 曲線的繪制 實驗報告五B樣條曲線的繪制23-27 實驗報告一一、實驗題目使用 VB 軟件實現三點畫圓弧二、實驗目的1 了解服裝 CAD 中的常用曲線，靈活運用理論知識加以運 用，實現操作；2掌握三點畫圓弧的根本原理和繪制方法；3 運用 Visual Basic 6.0 軟件編寫程序實現通過三點的控 制成功繪制圓弧。三、實驗目的三個點 Ax1 ，y1 ，Bx2，y2Cx3 ，y3 的坐 標 根據中垂線相交于圓

2、心可以求出圓心x , y丨的坐標以及半徑 r 根據圓心以及三點的坐標， 判斷出所畫圓弧的起始角， 終止角和中間角的正切角度值， 進而求出這三個角的角度。 比較起始角，終止角和中間角這三點的角度大小，判斷出 所畫圓弧的方向。2源代碼Begin VB.Form Form1Caption = " 三點畫圓弧 "ClientHeight = 5835ClientLeft = 120ClientTop = 450ClientWidth = 8280LinkTopic = "Form1"ScaleHeight = 5835ScaleWidth = 8280Start

3、UpPosition = 3 '窗口缺省Begin VB.CommandButton Command3Caption = "退出 "Height = 615Left = 6000TabIndex = 3Top= 4800Width= 1455EndBegin VB.CommandButton Command2 Caption= "取消 "Height= 615Left = 3360TabIndex = 2Top= 4800Width= 1455EndBegin VB.CommandButton Command1Caption= "畫弧

4、"Height= 615Left = 720TabIndex = 1Top= 4800Width= 1455EndBegin VB.PictureBox Picture1Height = 4335Left = 360ScaleHeight = 4275ScaleWidth = 7515TabIndex = 0Top= 240Width= 7575EndEndAttribute VB_Name = "Form1"Attribute VB_GlobalNameSpace = FalseAttribute VB_Creatable = FalseAttribute VB

5、_PredeclaredId = TrueAttribute VB_Exposed = FalsePrivate pt() As mypointPrivate Sub Form_Load()ReDim pt(1)End Subx AsPrivate Sub Picture1_MouseDown(Button As Integer, Shift As Integer, Single, y As Single)Dim s As Integerpt(UBound(pt).x = xpt(UBound(pt).y = yPicture1.Circle (x, y), 15s = Val(UBound(

6、pt)Select Case sCase 1Picture1.Print "A"Case 2Picture1.Print "B"Case 3Picture1.Print "C"End SelectIf UBound(pt) > 1 Thenpt(UBound(pt)Picture1.Line (pt(UBound(pt) - 1).x, 1).y)-(pt(UBound(pt).x, pt(UBound(pt).y)End IfReDim Preserve pt(UBound(pt) + 1)End SubPrivate Sub

7、 Command1_Click()Dim A1, A2, B1, B2, C1, C2 As SingleDim X0, Y0, r, PI As DoubleDim t1, t2, t3 As DoubleDim t As DoubleA1 = pt(1).x A 2 + pt(1).y A 2 - pt(3).x A 2 - pt(3).y A 2A2 = pt( 2).x a 2 + pt(2).y a 2 - pt(3).x a 2 - pt(3).y a 2B1 = 2 * pt(3).x - 2 * pt(1).xB2 = 2 * pt(3).x - 2 * pt(2).xC1 =

8、 2 * pt(1).y - 2 * pt(3).yC2 = 2 * pt(2).y - 2 * pt(3).yX0 = (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

9、 pt(1).y - Y0 > 0 Thent1 = t1ElseIf pt(1).x - X0 < 0 And pt(1).y - Y0 > 0 Thent1 = t1 + PIElseIf pt(1).x - X0 < 0 And pt(1).y - Y0 < 0 Thent1 = t1 + PIElset1 = t1 + 2 * PIEnd IfEnd IfEnd Ift2 = Atn(pt(2).y - Y0) / (pt(2).x - X0)If pt(2).x - X0 > 0 And pt(2).y - Y0 > 0 Thent2 = t

10、2ElseIf pt(2).x - X0 < 0 And pt(2).y - Y0 > 0 Thent2 = t2 + PIElseIf pt(2).x - X0 < 0 And pt(2).y - Y0 < 0 Then t2 = t2 + PIElset2 = t2 + 2 * PIEnd IfEnd IfEnd IfIf t1 < t3 < t2 Thenx = X0 + r * Cos(t)y = Y0 + r * Sin(t)Picture1.PSet (x, y)Next tElseIf t2 < t1 < t3 Then t2 =

11、t2 + 2 * PIx = X0 + r * Cos(t) y = Y0 + r * Sin(t) Picture1.PSet (x, y)Next tElseIf t3 < t2 < t1 Then t2 = t2 + 2 * PIx = X0 + r * Cos(t)y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next tElseIf t1 < t2 < t3 Then t1 = t1 + 2 * PIx = X0 + r * Cos(t)y = Y0 + r * Sin(t) Picture1.PSet (x, y) Nex

12、t tElseIf t3 < t1 < t2 Then t1 = t1 + 2 * PIx = X0 + r * Cos(t)y = Y0 + r * Sin(t) Picture1.PSet (x, y) Next tElseIf t2 < t3 < t1 Thenx = X0 + r * Cos(t) y = Y0 + r * Sin(t)Picture1.PSet (x, y)Next tEnd IfEnd SubPrivate Sub Command2_Click()ReDim pt(1)End SubPrivate Sub Command3_Click()En

13、dEnd Sub四 實驗結果實驗報告實驗題目使用 VB 軟件實現兩點畫圓弧、 實驗目的1 了解服裝 CAD 中的常用曲線，靈活運用理論知識加以運 用，實現操作；2 掌握使用兩端點， 以及其中一端點切線畫圓弧的根本原理 和繪制方法；3 運用 Visual Basic 6.0 軟件編寫程序實現通過兩端點， 以及其中一端點切線成功繪制圓弧。、 實驗內容1、實驗原理一圓弧兩端點A , B和A端點切線的方向數L 根據向量的知識，由一圓弧兩端點A , B和A端點切線的方向數 L 求出圓心的坐標和半徑大小； 計算在圓心為原點的新坐標系下初始角和終止角的正切 值，進而求出對應的角度； 判斷 L 和半徑向量的乘

14、積，假設大于 0，那么為逆時針方向 畫圓弧，小于 0，那么為順時針方向畫圓弧； 根據圓的參數方程表達式，利用 VB繪制圓弧。2、源代碼Begin VB.Form Form1AutoRedraw = -1 'TrueCaption = " 兩點加切線畫圓弧 "ClientHeight = 6810ClientLeft = 120ClientTop = 450ClientWidth = 8340LinkTopic = "Form1"ScaleHeight = 6810ScaleWidth = 8340StartUpPosition = 3 '

15、窗口缺省Begin VB.CommandButton Command3Caption = "退出 "Height = 615Left = 6240TabIndex = 3Top= 6000Width= 1575EndBegin VB.CommandButton Command2Caption= "取消 "Height= 615Left = 3360TabIndex = 2Top= 6000Width= 1575EndBegin VB.CommandButton Command1Caption= "畫弧 "Height= 615Left

16、 = 480TabIndex = 1Top= 6000Width= 1575EndBegin VB.PictureBox Picture1AutoRedraw = -1 'TrueHeight = 5175Left = 360ScaleHeight = 5115ScaleWidth = 7515TabIndex = 0Top = 480Width = 7575EndEndAttribute VB_Name = "Form1"Attribute VB_GlobalNameSpace = FalseAttribute VB_Creatable = FalseAttrib

17、ute VB_PredeclaredId = TrueAttribute VB_Exposed = FalsePrivate pt() As mypointPrivate Sub Form_Load()ReDim pt(1)End Subx AsPrivate Sub Picture1_MouseDown(Button As Integer, Shift As Integer, Single, y As Single)Dim s As Integer pt(UBound(pt).x = x pt(UBound(pt).y = yPicture1.Circle (x, y), 1s = Val(

18、UBound(pt)Select Case sCase 1Picture1.Print "A"Case 2Picture1.Print "B"Case 3Picture1.Print "L" ' 曲線在 A 點處的切線矢量 Picture1.Line (pt(1).x, pt(1).y)-(pt(3).x, pt(3).y)End SelectReDim Preserve pt(UBound(pt) + 1)End SubPrivate Sub Command1_Click()Dim X0, Y0, r As DoubleDi

19、m a1, a2, b1, b2, c1, c2 As DoubleDim t, t1, t2, i, j, k, m, n As DoubleDim pi As Singlepi = 4 * Atn(1)a1 = 2 * pt(1).x - 2 * pt(2).xa2 = pt(3).x - pt(1).xb1 = 2 * pt(1).y - 2 * pt(2).yb2 = pt(3).y - pt(1).ycl = pt(1).x A 2 - pt (2) .x A 2 + pt(1).y A 2 - pt (2) .y A 2c2 = (pt(1).x - pt(3).x) * pt(1

20、).x + (pt(1).y - pt(3).y) * pt(1).yX0 = (b2 * c1 - b1 * c2) / (a1 * b2 - a2 * b1)Y0 = (a1 * c2 - a2 * c1) / (a1 * b2 - a2 * b1)r = Sqr(pt.x - XO) A 2 + (pt.y - YO) A 2)k = (pt(3).y - pt(1).y) * (pt(1).x - X0) - (pt(3).x - pt(1).x) (pt(1).y - YO)m = pt(1).x - XOn = pt(1).y - YOt1 = Atn(Abs(n / m)If m

21、 > O And n > O Thent1 = t1ElseIf m < O And n > O Thent1 = pi - t1ElseIf m < O And n < O Thent1 = pi + t1ElseIf m > O And n < O Thent1 = 2 * pi - t1End Ifi = pt(2).x - XOj = pt(2).y - YOt2 = Atn(Abs(j / i)If i > O And j > O Thent2 = t2ElseIf i < O And j > O Thent2

22、= pi - t2ElseIf i < O And j < O Thent2 = pi + t2ElseIf i > O And j < O Thent2 = 2 * pi - t2End IfIf k > O ThenIf t1 < t2 Thenx = XO + r * Cos(t) y = YO + r * Sin(t) Picture1.PSet (x, y)Next tElse: t2 = t2 + 2 * pix = XO + r * Cos(t) y = YO + r * Sin(t) Picture1.PSet (x, y)Next tEnd

23、 IfElseIf t1 > t2 Thenx = XO + r * Cos(t)y = YO + r * Si n(t)Picturel.PSet (x, y)Next tElse: t1 = t1 + 2 * pix = X0 + r * Cos(t) y = YO + r * Si n(t) Picturel.PSet (x, y)Next tEnd IfEnd IfEnd SubPrivate Sub Comma nd2_Click()ReDim pt(1)End SubPrivate Sub Comma nd3_Click() EndEnd Sub四、實驗結果實驗報告、實驗題目

24、運用VB軟件繪制Bezier曲線、實驗目的1、了解服裝CAD中的常用曲線，通過實際操作加以深入認識；2、了解Bezier曲線的特點，根據 Bezier曲線的根本原理， 推斷出繪制方法并進行操作；3、運用Visual Basic 6.0軟件編寫程序實現曲線的成功繪、實驗內容1、實驗原理設空間有n+1個點P0, P1 , P2 ,Pn,那么稱以下函數所決定的參數曲線為Bezier曲線：nQ(t)PBi(t)(O t 1)i 0式(1-1)中，B,n(t) cn(1 t)niti(i 0,1,n)在給定幾個點時，可在t 0 , 1區間取一系列值，相應的計 算一系列的x(t) , y(t) , z(t

25、)的值，由此可確定空間曲線上各 點的位置，連接后即得該空間曲線。2、源代碼Begin VB.Form BezierCaption= "Bezier 曲線 "ClientHeight= 7575ClientLeft= 60ClientTop= 450ClientWidth= 9255LinkTopic= "Form1"ScaleHeight = 7575ScaleWidth = 9255StartUpPosition = 3 '窗口缺省Begin VB.CommandButton Command2 Caption = "取 消 "

26、;Height = 495Left = 3840TabIndex = 3Top= 6600Width= 1455EndBegin VB.CommandButton Command3 Caption= "退 出 "Height= 495Left = 6720TabIndex = 2Top= 6600Width= 1455EndBegin VB.CommandButton Command1 Caption= "畫 弧 "Height= 495Left = 1080TabIndex = 1Top= 6600Width= 1455EndBegin VB.Pict

27、ureBox Picture1Height = 5655Left = 600ScaleHeight = 5595ScaleWidth = 7995TabIndex = 0Top= 480Width= 8055EndEndAttribute VB_Name = "Bezier"Attribute VB_GlobalNameSpace = FalseAttribute VB_Creatable = FalseAttribute VB_PredeclaredId = True Attribute VB_Exposed = FalsePrivate pt() As mypointP

28、rivate Sub Form_Load()ReDim pt(1)x AsEnd SubPrivate Sub Picture1_MouseDown(Button As Integer, Shift As Integer, Single, y As Single)Dim s As Integer pt(UBound(pt).x = x pt(UBound(pt).y = yPicture1.Circle (x, y), 15s = Val(UBound(pt)Select Case sCase 1 Picture1.Print "P0"Case 2 Picture1.Pri

29、nt "P1"Case 3 Picture1.Print "P2"Case 4Picture1.Print "P3"Case 5Picture1.Print "P4"Case 6Picture1.Print "P5"Case 7 Picture1.Print "P6"Case 8Picture1.Print "P7"Case 9Picture1.Print "P8"Case 10Picture1.Print "P9"

30、Case 11Picture1.Print "P10"End SelectIf UBound(pt) > 1 Thenpt(UBound(pt)Picture1.Line (pt(UBound(pt) - 1).x, 1).y)-(pt(UBound(pt).x, pt(UBound(pt).y)End IfReDim Preserve pt(UBound(pt) + 1)End SubPrivate Sub Command1_Click()Dim i%, t#Dim j, n As IntegerDim s, x, y As Singlen = UBound(pt)

31、 - 1 - 1For j = 1 To 1000x = 0y = 0For i = 0 To nt = j / 1000x = x + pt(i + 1).x * B(i, n, t)y = y + pt(i + 1).y * B(i, n, t)Next iPicture1.PSet (x, y)Next jEnd SubPrivate Function fact(n As Integer)Dim i As IntegerDim s As Longs = 1For i = 1 To ns = s * iNext ifact = sEnd FunctionPrivate Function B

32、(i%, n%, t#) As SingleB = (fact (n) * t A i * (1 - t) A (n - i) / (fact(i) * fact(n - i) End FunctionPrivate Sub Command2_Click()ReDim pt(1)'pt(1)為第一個點 P0End SubPrivate Sub Comma nd3_Click() EndEnd Sub四、實驗結果實驗報告四、 實驗題目運用 VB 軟件繪制三次 Hermite 曲線、 實驗目的1 、了解服裝 CAD 中的常用曲線，通過實際操作加以深入認 識；2 、了解 Hermite 曲線

33、的特點，根據 Hermite 曲線的根本 原理，推斷出繪制方法并進行操作；3 、運用 Visual Basic 6.0 軟件編寫程序實現 Hermite 曲線 的成功繪制。、 實驗內容1、實驗原理三次 Hermite 樣條曲線的一般表達式為：Q(t)=At 3 Bt2 Ct D 0 t 1( 2-1)上式中A、B、C、D四個系數矢量可以根據具體條件來確定。曲線端點 P0(t 0),P1(t 1 )和該曲線在兩個端點的切線矢量,P0'(t 0), P1'(t 1 ),那么可得下面結果：Q(0)=D=P 0Q(1) A B C D P1Q ' (0) C P0'Q&

34、#39;(1)=3A+2B+C=P 1'解上面 的方程組得：A=2( P0 P1) P0' P1'B 3(P1 P0) 2P0' P1'C P0'D P0將上面結果中的系數A、B、C、D代入式(2-1)中，并整理成下面的表達式：323232'32'Q(t)=(2t 3t 1)Po ( 2t 3t )P (t 2t t)F0 (t t )P上式即為三次 Hermite 曲線表達式。當給定P°(x,y,z), R(x,y,z), P°(x, y,z), R(x, y, z)時，可在t 0,1區間中取一系列值，相應的

35、計算 一系列的 x(t),y(t),z(t)的值，由此可確定空間曲線上各點的位置，連接后即得該空間曲線。2、源代碼Beg in VB.Form HermiteCaption= "三次 Hermite 曲線 "ClientHeight = 7575ClientLeft= 60ClientTop= 450ClientWidth = 9255LinkTopic= "Form1"ScaleHeight = 7575ScaleWidth = 9255StartUpPosition = 3 ' 窗口缺省Begin VB.PictureBox Picture1

36、Height = 5655Left = 600ScaleHeight = 5595ScaleWidth = 7995TabIndex = 3Top= 480Width = 8055EndBegin VB.CommandButton Command1Caption = "畫 弧"Height = 495Left = 1200TabIndex = 2Top= 6600Width= 1455EndBegin VB.CommandButton Command3 Caption= "退 出 "Height= 495Left = 6600TabIndex = 1To

37、p= 6600Width= 1455EndBegin VB.CommandButton Command2 Caption= "取 消 "Height= 495Left = 3960TabIndex = 0Top= 6600Width= 1455EndEndAttribute VB_Name = "Hermite"Attribute VB_GlobalNameSpace = FalseAttribute VB_Creatable = FalseAttribute VB_PredeclaredId = TrueAttribute VB_Exposed = F

38、alsePrivate pt() As mypointPrivate Sub Form_Load()ReDim pt(1)x AsEnd SubPrivate Sub Picture1_MouseDown(Button As Integer, Shift As Integer, Single, y As Single)Dim s As Integer pt(UBound(pt).x = x pt(UBound(pt).y = yPicture1.Circle (x, y), 1s = Val(UBound(pt)Select Case sCase 1 Picture1.Print "

39、P0"Case 2Picture1.Print "P1"Case 3Picture1.Print "P01" ' 曲線在 P0 點處的切線矢量Picture1.Line (pt(1).x, pt(1).y)-(pt(3).x, pt(3).y)Case 4Picture1.Print "P11" ' 曲線在 P1 點處的切線矢量Picture1.Line (pt(2).x, pt(2).y)-(pt(4).x, pt(4).y)End SelectReDim Preserve pt(UBound(pt) +

40、1)End SubPrivate Sub Command1_Click()Dim Ax, Bx, Cx, Dx, Ay, By, Cy, Dy As SingleDim P01x!, P11y!Dim j%, t As SingleP01x = 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 +

41、P11xAy = 2 * (pt(1).y - pt(2).y) + P01y + P11yBx = 3 * (pt(2).x - pt(1).x) - 2 * P01x - P11xBy = 3 * (pt(2).y - pt(1).y) - 2 * P01y - P11yCx = P01xCy = P01yDx = pt(1).xDy = pt(1).yFor j = 1 To 1000t = j / 1000x = Ax * t A 3 + Bx * t A 2 + Cx * t + Dxy = Ay * t a 3 + By * t a 2 + Cy * t + DyPicture1.

42、PSet (x, y)Next jEnd SubPrivate Sub Command2_Click()ReDim pt(1) 'pt(1) 為第一個點 P0 End SubPrivate Sub Command3_Click()EndEnd SubPrivate Sub Form_Activate()Picture1.Scale (0, 500)-(500, 0)End Sub四、 實驗結果實驗報告五實驗題目用VB繪制三次B樣條曲線實驗目的1、了解服裝CAD中的常用曲線。2、掌握B樣條曲線的根本原理和方法，了解 B樣條曲線的特點。、實驗內容1、實驗原理B樣條曲線的數學模型：設空間有n

43、+k+1 個點P°,R,RPki,Pk n，稱以下函數所決定的參數曲線為第i段B樣條曲線：kQi(t)P jFj,k(t)(O t 1,i j oO,1,2,n)其中：1 k jFj,k(t)-( 1)ck 1(tt! i ok jl)k(O t 1，j O,1,2,，k)為基函數。p ,Pi 1 ,P+k為Qi(t)的控制頂點，折線PP 1，P+k為Qi(t)的控制多邊形。k=3時，稱為三次B樣條曲線根據上式可得：132"(t3 3t2 3t 1)6F,3(t)2(3t3 6t24)6132F2,3(t)( 3t3 3t2 3t 1)613F3,3(t) -t36代入前面

44、的式中，第i段三次B樣條曲線表達式為：Qj(t)= Fo,3(t)RF1,3(t)R 1 F2,3(t)R 2F3,3(t)R 3根據給定四個點的，可在t 0 , 1區間取一系列值，相應的 計算一系列的x(t)，y(t)，z(t)的值，由此可確定空間曲線上 各點的位置，連接后即得該空間曲線。2、源代碼Begi n VB.Form Form1Caption="三次B樣條曲線"Clie ntHeight = 6240Clie ntLeft = 120Clie ntTop= 450Clie ntWidth = 9030Lin kTopic= "Form1"Sc

45、aleHeight = 6240ScaleWidth = 9030StartUpPosition = 3 '窗口缺省Beg in VB.Comma ndButt on Comma nd3Caption="退出"Height = 615Left = 6840Tabln dex= 3Top=54001575WidthEndBeg in VB.Comma ndButt on Comma nd2Cap ti on="取消"Height = 615Left = 3720TabIndex = 2Top= 5400Width= 1575EndBegin VB.CommandButton