S (x)二 Mii1(X厂 X)3 + M (X X-)3i6hi/ M 7、x x / M,、x xt-i + (y h 2)i+ (y i-h 2)16hi-i6 i hi 6 i hiiii = 1,2,3,., nlxi1iM+ 2M +i+1i+1yiyi1i+1i+1yiyi1i+1这是一个含有n+1个未知数的、n-1个方程的线性方程组。要完全确定M的值还需要补充两 个条件。Dim X(1000) As Si ngle, Y(1000) As Si ngleDim u1(0 To 80000) As Sin gle, v1(0 To 80000) As Sin gleDim num As LongDim t As In tegerPrivate Declare Sub Sleep Lib kernel32 (ByVai dwMilliseconds As Long)Dim de As In tegerDim Tolnit As Boolea nDim Dow nX As Sin gle, Dow nY As Si ngleSub Drawposi( In dex As In teger)Me.Picturel.ForeColor = 0Me.Picturel.Line (0, Y(Index)-(1024, Y(Index)Me.Picturel.Line (X(Index), 0)-(X(Index), 770)End SubFun ction hypot(ByVal X As Sin gle, ByVal Y As Sin gle)hypot = Sqr(X A 2 + Y A 2)End Fun cti onSub MovePic(lndex As Integer)Dim i As In tegerX(I ndex) = Picture2(I ndex).Left + 4Y(I ndex) = Picture2(I ndex).Top + 4IblX.Capti on = X: + CStr(CI nt(X(I ndex)IblY.Caption = Y: + CStr(CI nt(Y(I ndex) lblX.RefreshlblY.RefreshMe.Picture1.ClsMe.Picture1.ForeColor = QBColor(10)For i = 0 To t - 1Me.Picture1.Curre ntX = X(i) + 4Me.Picture1.Curre ntY = Y(i) + 4 Me.Picture1.Pri nt iNext iEnd SubPrivate Sub Comma nd1_Click()Dim i As LongPicture1.Scale (0, 0)-(640, 550)DrawWidth = 3Picture1.ClsIf Check1.Value Then Command2_ClickX(0) = 1Y(0) = 1X(t - 1) = 638Y(t - 1) = 548Picture1.ForeColor = QBColor(10)For i = 0 To t - 1Picture1.Line (X(i) - 1, Y(i) - 1)-(X(i) + 1, Y(i) + 1), QBColor(10), BPicture1.Pri nt iNext iPicture1.ForeColor = QBColor(12)DrawWidth = 1tspLi ne t - 1,2, 0, 0, 0, 0Picture 1.P Set (u1(0), v1(0)For i = 1 To num - 1Picturel.Line -(u1(i), v1(i)For de = 1 To 12000: Next de Sleep 1Next iPicture1.ForeColor = QBColor(10)For i = 0 To t - 1Picture1.Line (X(i) - 1, Y(i) - 1)-(X(i) + 1, Y(i) + 1), QBColor(10), BPicture1.Pri nt iNext iEnd SubPrivate Sub Comma nd2_Click()Dim i As In tegerRan domize TimerToI nit = Not ToI nitIf ToI nit The nMe.Comma nd1.E nabled = FalseMe.Comma nd2.Captio n =结束初始化Me.ClsFor i = 1 To t - 1Load Me.Picture2(i)Next iFor i = 0 To t - 1Picture2(i).Left = X(i) - 4Picture2(i).Top = Y(i) - 4Picture2(i).Visible = TrueNext iPicture1.ClsMe.Picture1.ForeColor = QBColor(10)For i = 0 To t - 1Picture1.Line (X(i) - 1, Y(i) - 1)-(X(i) + 1, Y(i) + 1), QBColor(10), B Picture1.Pri nt iNext iElseMe.Comma nd1.E nabled = TrueMe.Comma nd2.Captio n =开始初始化For i = 1 To t - 1Un load Me.Picture2(i)Next iMe.Picture2(0).Visible = FalseEnd IfExit SubFor i = 0 To tX(i) = Rn d(1) * 500 + Rn d(1) * 50 + 12Y(i) = Rn d(1) * 400 + Rn d(1) * 100 + 12X(i) = i * 20 + Rn d(1) * 10 + 12Y(i) = i * 10 + Rn d(1) * 300 + 22 - Rn d(1) * 200Next iEnd SubSub tspLine(ByVal n As Integer, ByVal ch As Integer, ByVal tx1 As Single, ByVal tx2 AsSingle, ByVal ty1 As Single, ByVal ty2 As Single)Dim a(1000) As Single, b(1000) As Single, c(1000) As Single, dX(1000) As Single, dY(1000) As Sin gleDim qx(1000) As Single, qy(1000) As SingleDim tt As Single, bx3 As Single, bx4 As Single, by3 As Single, by4 As SingleDim cx As Sin gle, cy As Sin gle, t(1000) As Sin gle, px(1000) As Sin gle, py(1000) As Si ngleDim u(3000) As Si ngle, v(3000) As Sin gle, i As In tegernum = 0For i = 1 To nt(i) = hypot(X(i) - X(i - 1), Y(i) - Y(i - 1)Next iSelect Case chCase 0 抛物条件u(0) = (X(1) - X(0) / t(1): u(1) = (X(2) - X(1) / t(2)u(2) = (u(1) - u(0) / (t(2) + t(1)tx1 = u(0) - u(2) * t(1)u(0) = (Y(1) - Y(0) / t(1): u(1) = (Y(2) - Y(1) / t(2)u(2) = (u(1) - u(0) / (t(2) + t(1)ty1 = u(0) - u(2) * t(1)u(0) = (X( n) - X(n - 1) / t(n): u(1) = (X(n - 1) - X(n - 2) / t(n - 1)u(2) = (u(0) - u(1) / (t( n) + t(n - 1)tx2 = u(0) + u(2) * t(n)u(0) = (Y( n) - Y(n - 1) / t(n): u(1) = (Y(n - 1) - Y(n - 2) / t(n - 1)u(2) = (u(0) - u(1) / (t( n) + t(n - 1)ty2 = u(0) + u(2) * t(n)Case 1 夹持条件a(0) = 1: c(0) = 0: dX(O) = txl: dY(O) = ty1a(n) = 1: b(n) = 0: dX(n) = tx2: dY( n) = ty2Case 2 自由条件a(0) = 2: c(0) = 1dX(0) = 3 * (X(1) - X(0) / t(1): dY(0) = 3 * (Y(1) - Y(0) / t(1)a(n) = 2: b(n) = 1dX( n) = 3 * (X( n) - X(n - 1) / t(n): dY( n) = 3 * (Y(n) - Y(n - 1) / t(n)Case 3 循环条件a(0) = 2: c(0) = 1dX(0) = 3 * (X(1) - X(0) / t(1) - (t(1) * (X(2) - X(1) / t(2) - X(1) + X(0) / (t(1) + t(2) dY(0) = 3 * (Y(1) - Y(0) / t(1) - (t(1) * (Y(2) - Y(1) / t(2) - Y(1) + Y(0) / (t(1) + t(2) a(n) = 2: b(n) = 1dX( n) = 3 * (X(n) - X(n - 1) / t(n)dX( n) = dX( n) + (X( n) - X(n - 1) - t(n) * (X(n - 1) - X(n - 2) / t(n - 1) / (t( n) + t(n - 1) dY( n) = 3 * (Y( n) - Y(n - 1) / t(n)dY( n) = dY( n) + (Y( n) - Y(n - 1) - t(n) * (Y(n - 1) - Y(n - 2) / t(n - 1) / (t( n) + t(n - 1) End Select计算方程组系数阵和常数阵For i = 1 To n - 1a(i) = 2 * (t(i) + t(i