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2019年03月23日 |
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3-D Function plotting Three dimensional (3-D) computer graphics are graphics render that using a 3-D representation of geometric data that is stored in computer for the purposes of performing graphic calculations and rendering 2D images.3-D computer graphics algorithms rely on many of the same algorithms as 2D computer vector graphics of wire-frame model and 2D computer raster graphics in the final rendered display. In computer graphics software, the distinction between 2D and 3-D is occasionally blurred. 2D applications may use 3-D techniques to achieve effects such as lighting, and primarily 3-D may use 2D rendering techniques. A 3-D model is a mathematical representation of any 3-D object. A 3-D model can be rendered visually as a 2D image by means of a 3-D rendering process, or used in non-graphical computer simulations and calculations. In this article, we will focus on the 3-D function graphic plotting not concerned with the mathematical elements such as 3-D transformation, if readers are interest the mathematical material, please refer “Visual graphics programming( Rod Stephens) “ or writer’s another publication “Projection and transformation matrix(www.chday169.url.tw)”.
(a) Coordinate system in world and eye system.
To represent a point in 3-D space, we need a 3-D mutually perpendicular axes coordinate system (rectangular coordinate system). The 3-D coordinate can be derived from 2d coordinate system (xy plane) by adding another augment z through the origin as z axis, resulting two additional planes (yz and xz plane). Two orientations are possible when elect to z axis. If the z axis points toward the view’s eye, the associate system is referred to as right-hand system. Similarly, a coordinate system with the z axis pointing away from the viewer is called the left-hand system. Which system you choose is no matter, but you’ll coincidence with your projection system. If your data is created by a non-rectangular coordinate system, you may convert this data to the rectangular coordinate system first.
(b) Data creating and structure Type(VB 6)
The 3-D graphic algorithm discussing here can be applied by any mathematical functions (z function(z=f(x,y), parametric function(x=f(u,v),y=g(u,v),z=h(u,v) ,implicit function( f(x,y,z)=c) or surface generating of profile rotation, extrusion, transformation ,tube function, etc., or scatter data. For convention, the point data Type can be declared as:
VB 6.0 Public PointApi ‘same as ‘Point’ of VB.Net X as Long Y as Long End Type Public Type PtXy ‘same as ‘PointF’ of VB.Net x As Single y As Single End Type
Public Type PtXyz ‘same as ‘Public Structure’ of VB.Net x As Single ‘same as ‘Dim x as single’ of VB.Net y As Single z As Single End Type ‘same as ‘End Structure’
Public Type Point3-D Coord(0 to 3) As Single Trans(0 to 3) As Single PrjBotm(0 to 2) As single ‘bottom view projection PrjBack(0 to 2) As single ‘back view projection PrjSide(0 to 2) as single ‘side view projection End Type
(c)Transformation matrix (VB 6 and VB.NeT)
As a matter of convention, we will use the rectangular coordinate to represent the position of a point or a point vector. We can use the generalized 4*4 transformation matrix for a point in 3-D homogeneous coordinate system. In 3-D computer graphics, the transformation matrix may include such as translation, shearing, scaling, rotation and reflection, etc. You can find the detail transformation operation processers in many textbook or link www.chday169.url.tw to get more information, so we don’t intend to discuss here. Hereafter, we list some useful snippet codes of function or sub to get transformation matrix coefficients.
Public Sub CreateTransFormationMatrix(ByVal ViewTypeIn As Integer) Select Case ViewTypeIn Case 1 CalTransformationMatrixA() Case 2 CalTransformationMatrixB()
End Select
End Sub
'Calculate the transformation matrix. ' ******************************************************** Private Sub CalTransformationMatrixA() 'get glAx,glAy,glAz,----------------- 'MsgBox ("eyexin=" & EyeXIn) Dim T1(3, 3) As Single Dim T2(3, 3) As Single Dim r1 As Single Dim r2 As Single Dim ctheta As Single Dim stheta As Single Dim cphi As Single Dim sphi As Single
' Rotate around the Z axis so the '繞z軸旋轉,觀測者眼睛在Y-Z 平面 ' eye lies in the Y-Z plane. r1 = System.Math.Sqrt(EyeX * EyeX + EyeY * EyeY) stheta = EyeX / r1 's(theta) ctheta = EyeY / r1 'cos(theta) MakeIdentity(T1) T1(0, 0) = ctheta T1(0, 1) = stheta T1(1, 0) = -stheta T1(1, 1) = ctheta
' Rotate around the X axis so the '繞x軸旋轉,觀測者眼睛在Z軸上 ' eye lies the Z axis. r2 = System.Math.Sqrt(EyeX * EyeX + EyeY * EyeY + EyeZ * EyeZ) sphi = -r1 / r2 'sin(phi) cphi = -EyeZ / r2 'cos(phi) MakeIdentity(T2) T2(1, 1) = cphi T2(1, 2) = sphi T2(2, 1) = -sphi T2(2, 2) = cphi ' here. We just ignore the Z coordinate when drawing.)
' Combine the transformations. MatrixMatrixMult(T, T1, T2) glAx = T(0, 0) glAy = T(1, 0) glAz = T(2, 0) glBx = T(0, 1) glBy = T(1, 1) glBz = T(2, 1) glCx = T(0, 2) glCy = T(1, 2) glCz = T(2, 2)
End Sub ' ******************************************************** ' Calculate the transformation matrix. ' ******************************************************** Private Sub CalTransformationMatrixB() 'get glAx,glAy,glAz,----------------- 'MsgBox("into CalTransformationMatrixB" & " m3Perspective= " & m3Perspective & "; focusx= " & FocusX) Dim T(0 To 3, 0 To 3) As Single m3PProject(T, m3Perspective, eyeR, eyePhi, eyetheta, FocusX, FocusY, FocusZ, 0, 1, 0) FactorMaker(T)
End Sub
Public Sub IsomPrjMaker() Dim i As Integer, j As Integer, tIso(0 To 3, 0 To 3) As Single Dim Phi As Single, Theta As Single Phi = 45 * Ra Theta = 35.26439 * Ra Erase tIso() For i = 0 To 3 For j = 0 To 3 tIso(i, j) = 0 Next j Next i tIso(0, 0) = Cos(Phi) tIso(0, 1) = Sin(Phi) * Sin(Theta) tIso(0, 2) = -Sin(Phi) * Cos(Theta)
tIso(1, 0) = 0# tIso(1, 1) = Cos(Theta) tIso(1, 2) = Sin(Theta)
tIso(2, 0) = Sin(Phi) tIso(2, 1) = -Cos(Phi) * Sin(Theta) tIso(2, 2) = Cos(Phi) * Cos(Theta)
tIso(3, 3) = 1# glAxIso = tIso(0, 0) glAyIso = tIso(1, 0) glAzIso = tIso(2, 0) glBxIso = tIso(0, 1) glByIso = tIso(1, 1) glBzIso = tIso(2, 1) glCxIso = tIso(0, 2) glCyIso = tIso(1, 2) glCzIso = tIso(2, 2) End Sub
Public Sub DimetricPrjMaker() Dim i As Integer, j As Integer, tDim(0 To 3, 0 To 3) As Single Dim Phi As Single, Theta As Single Phi = 22.208 * Ra Theta = 20.705 * Ra Erase tDim() For i = 0 To 3 For j = 0 To 3 tDim(i, j) = 0 Next j Next i tDim(0, 0) = Cos(Phi) tDim(0, 1) = Sin(Phi) * Sin(Theta) tDim(0, 2) = -Sin(Phi) * Cos(Theta) tDim(1, 0) = 0# tDim(1, 1) = Cos(Theta) tDim(1, 2) = Sin(Theta) tDim(2, 0) = Sin(Phi) tDim(2, 1) = -Cos(Phi) * Sin(Theta) tDim(2, 2) = Cos(Phi) * Cos(Theta) tDim(3, 3) = 1# glAxDim = tDim(0, 0) glAyDim = tDim(1, 0) glAzDim = tDim(2, 0) glBxDim = tDim(0, 1) glByDim = tDim(1, 1) glBzDim = tDim(2, 1) glCxDim = tDim(0, 2) glCyDim = tDim(1, 2) glCzDim = tDim(2, 2) End Sub
Public Function CabinetPrjMaker(Alph As Single)
Dim Sx As Single, Sy As Single, Sz As Single Sx = 1 Sy = 1 Sz = 0.5 Alph = Alph * Ra glAxCab = Sx glAyCab = 0 glAzCab = Sz * Cos(Alph) glBxCab = 0 glByCab = Sy glBzCab = Sz * Sin(Alph) glCxCab = 0 glCyCab = 0 glCzCab = 1 End Function
Public Function CavalierPrjMaker(Alph As Single) Dim Sx As Single, Sy As Single, Sz As Single Sx = 0.5 Sy = 0.5 Sz = 1 Alph = Alph * Ra glAxCav = Sx glAyCav = 0 '-Sy * Cos(Beta) glAzCav = Sz * Cos(Alph) glBxCav = 0 glByCav = Sy 'Sy * Sin(Beta) glBzCav = Sz * Sin(Alph) glCxCav = 0 glCyCav = 0 glCzCav = 1
End Function Public Function EqualAnglePrjMaker(z As Single) glAxEang = 1 / (1 + z) glAyEang = 0 glAzEang = 0 glBxEang = 1 / (1 + z) glByEang = 0 glBzEang = 0 End Function
Public Function EqualAreaPrjMaker(z As Single) glAxEang = 1 / Sqr(1 + z) glAyEang = 0 glAzEang = 0 glBxEang = 1 / Sqr(1 + z) glByEang = 0 glBzEang = 0 End Function
To get the projection point(xp,yp) of projection of 3-D point(x,y,z), you can apply the formulas as following:
(a) Trimetric projection xp=glAx*x+glAy*y+glAz*z yp=glBx*x+glBy*y+glBz*z zp=glCx*x+glCy*y+glCz*z
(b) Isometric projection xp=glAxIso*x+glAyIso*y+glAzIso*z yp=glBxIso*x+glByIso*y+glBzIso*z
(c) Cabinet projection xp=glAxCab*x+glAyCab*y+glAzCab*z yp=glBxCab*x+glByCab*y+glBzCab*z
The data of projection point(xp,yp) can be used to draw on VB 6PictureBox with ScaleMode = Vbuser , for Win32 Api or VB.net ,you need to convert the floating data type to Api or VB Net long data Type.
(d)Conversion between user scale and pixel scale
The size of left and top Form of PictureBox of VB 6.0 can be set as negative, so the function z=x^2+y^2, (-5>= x>=5, -5>= y>=5), the z values vary from -50 to 50), if (xp,yp) values are negative after transformation, we can draw the graph by setting the canvas scale as canvas.Scale(-50,50)-(50,-50), while in Api or VB.Net you can use the following sub or function to convert the function values to coincide with the graphic devices.
Public Function ptConvertToUser(ByVal canvas As PictureBox, ByVal xLeft As Single, ByVal xRight As Single, ByVal yTop As Single, ByVal yBottom As Single, _ ByVal xPix As Integer, ByVal yPix As Integer) As PointF ‘for VB,Net ptConvertToUser.X = CSng(xRight - xLeft) / CSng(canvas.ClientSize.Width) * xPix + xLeft ptConvertToUser.Y = CSng(yBottom - yTop) / CSng(canvas.ClientSize.Height) * yPix + yTop End Function
Public Function ptConvertToPix(ByVal canvas As PictureBox, ByVal xLeft As Double, ByVal xRight As Double, ByVal yTop As Double, ByVal yBottom As Double, _ ByVal xUser As Single, ByVal yUser As Single) As PointF ptConvertToPix.X = xUser * CSng(canvas.ClientSize.Width) / (xRight - xLeft) - xLeft * CSng(canvas.ClientSize.Width) / (xRight - xLeft) ptConvertToPix.Y = yUser * CSng(canvas.ClientSize.Height) / (yBottom - yTop) - yTop * CSng(canvas.ClientSize.Height) / (yBottom - yTop) End Function
Public Function ptConvertToUser(ByVal canvas As PictureBox, ByVal xLeft As Single, ByVal xRight As Single, ByVal yTop As Single, ByVal yBottom As Single, _ ByVal ptPix As Point) As PointF ptConvertToUser.X = CSng(xRight - xLeft) / CSng(canvas.ClientSize.Width) * ptPix.X + xLeft ptConvertToUser.Y = CSng(yBottom - yTop) / CSng(canvas.ClientSize.Height) * ptPix.Y + yTop End Function
Public Function ptConvertToPix(ByVal canvas As PictureBox, ByVal xLeft As Double, ByVal xRight As Double, ByVal yTop As Double, ByVal yBottom As Double,ByVal PtUser As PointF) As Point ptConvertToPix.X = PtUser.X * CSng(canvas.ClientSize.Width) / (xRight - xLeft) - xLeft * CSng(canvas.ClientSize.Width) / (xRight - xLeft) ptConvertToPix.Y = PtUser.Y * CSng(canvas.ClientSize.Height) / (yBottom - yTop) - yTop * CSng(canvas.ClientSize.Height) / (yBottom - yTop) End Function
Please note here, “ByVal xPix As Integer, ByVal yPix As Integer” should change to ByVal xPix As Long, ByVal yPix As long” ,”Point” change to “pointAPI”, “PointF” tO “PtXy” for VB 6.
(e)Drawing of 3-D graph(VB 6.0)
Private Sub Function3-DValues() ' Initialize the data points. Dim i As Integer, j As Integer Dim xU As Single, yV As Single, zW As Single, ans As Variant Erase T, Points ReDim T(0 To 3, 0 To 3) As Single ReDim Preserve Points(0 To NdoXU, 0 To NdoYV) zBotmBase = 99999 xBotmBase = 99999 yBotmBase = 99999 zTopBase = -99999 xTopBase = -99999 yTopBase = -99999 Select Case functionType Case "contour3-D" dxU = (V1Domn2 - V1Domn1) / NdoXU dyV = (V2Domn2 - V2Domn1) / NdoYV For i = 0 To NdoXU xU = V1Domn1 + i * dxU For j = 0 To NdoYV yV = V2Domn1 + j * dyV Points(i, j).Coord(0) = xU ' Sin(x) Points(i, j).Coord(1) = yV ' Cos(y) Points(i, j).Coord(2) = FunctionZValFromXY(glVbScriptA, ZEq, CDbl(xU), CDbl(yV)) 'ans Points(i, j).Coord(3) = 1# If i = 0 And (j = 0 Or j = NdoYV) Then If Points(i, j).Coord(0) > xTopBase Then xTopBase = Points(i, j).Coord(0) If Points(i, j).Coord(1) > yTopBase Then yTopBase = Points(i, j).Coord(1) If Points(i, j).Coord(2) > zTopBase Then zTopBase = Points(i, j).Coord(2) If Points(i, j).Coord(0) < xBotmBase Then xBotmBase = Points(i, j).Coord(0) If Points(i, j).Coord(1) < yBotmBase Then yBotmBase = Points(i, j).Coord(1) If Points(i, j).Coord(2) < zBotmBase Then zBotmBase = Points(i, j).Coord(2) Next j Next i Case "parameter3-D" . . . End Select ‘modify the values of function Dim TptXY As Single, tptZ As Single TptXY = DMAX1(Abs(xTopBase), Abs(xBotmBase), Abs(yTopBase), Abs(yBotmBase)) tptZ = DMAX1(Abs(zTopBase), Abs(zBotmBase)) If TptXY >= 0.001 Then ratioXY = 10# / TptXY If tptZ >= 0.001 Then ratioZ = 10# / tptZ For i = 0 To NdoXU For j = 0 To NdoYV With Points(i, j) .Coord(0) = .Coord(0) * ratioXY .Coord(1) = .Coord(1) * ratioXY .Coord(2) = .Coord(2) * ratioZ End With Next j Next i xTopBase = xTopBase * ratioXY yTopBase = yTopBase * ratioXY zTopBase = zTopBase * ratioZ xBotmBase = xBotmBase * ratioXY yBotmBase = yBotmBase * ratioXY zBotmBase = zBotmBase * ratioZ zBotmBase = zBotmBase - 2.5 yBotmBase = yBotmBase - 2.5 xBotmBase = xBotmBase - 2.5 zTopBase = zTopBase + 2.5 yTopBase = yTopBase + 2.5 xTopBase = xTopBase + 2.5
pt3-DCen.Coord(0) = (xTopBase + xBotmBase) / 2 pt3-DCen.Coord(1) = (yTopBase + yBotmBase) / 2 pt3-DCen.Coord(2) = (zTopBase + zBotmBase) / 2 End Sub
Private Sub Function3-DPrj() Dim i As Integer, j As Integer Dim x As Single, y As Single, ans As Variant, Z As Single Dim stEq As String 'case 3-D view lcXPrjMin = 99999 lcXPrjMax = -99999 lcYPrjMin = 99999 lcYPrjMax = -99999 lcZPrjMin = 99999 lcZPrjMax = -99999 For i = 0 To NdoXU For j = 0 To NdoYV Points(i, j).Trans(0) = glAx * Points(i, j).Coord(0) + glAy * Points(i, j).Coord(1) + glAz * Points(i, j).Coord(2) Points(i, j).Trans(1) = glBx * Points(i, j).Coord(0) + glBy * Points(i, j).Coord(1) + glBz * Points(i, j).Coord(2) Points(i, j).Trans(2) = glCx * Points(i, j).Coord(0) + glCy * Points(i, j).Coord(1) + glCz * Points(i, j).Coord(2) If i = 0 And (j = 0 Or j = NdoYV) Then FrmDocument.List1.AddItem (i & " ; " & j & " ; " & Points(i, j).Coord(0) & " ; " & Points(i, j).Coord(1) & "; " & Points(i, j).Coord(2)) If i = 0 And (j = 0 Or j = NdoYV) Then FrmDocument.List1.AddItem (i & " ; " & j & " ; " & Points(i, j).Trans(0) & " ; " & Points(i, j).Trans(1) & "; " & Points(i, j).Trans(2)) If Points(i, j).Trans(0) >= lcXPrjMax Then lcXPrjMax = Points(i, j).Trans(0) If Points(i, j).Trans(1) >= lcYPrjMax Then lcYPrjMax = Points(i, j).Trans(1) If Points(i, j).Trans(2) >= lcZPrjMax Then lcZPrjMax = Points(i, j).Trans(2) If Points(i, j).Trans(0) < lcXPrjMin Then lcXPrjMin = Points(i, j).Trans(0) If Points(i, j).Trans(1) < lcYPrjMin Then lcYPrjMin = Points(i, j).Trans(1) If Points(i, j).Trans(2) < lcYPrjMin Then lcZPrjMin = Points(i, j).Trans(2) Next j Next i xPrjMin3-DV = lcXPrjMin yPrjMin3-DV = lcYPrjMin zPrjMin3-DV = lcZPrjMin xPrjMax3-DV = lcXPrjMax yPrjMax3-DV = lcYPrjMax zPrjMax3-DV = lcZPrjMax '------------------------------------------ pt3-DCen.Trans(0) = glAx * pt3-DCen.Coord(0) + glAy * pt3-DCen.Coord(1) + glAz * pt3-DCen.Coord(2) pt3-DCen.Trans(1) = glBx * pt3-DCen.Coord(0) + glBy * pt3-DCen.Coord(1) + glBz * pt3-DCen.Coord(2) ' case Botm ‘ ‘ ‘
' case back ‘ ‘ ‘ ' case Side ‘ ‘ ‘
canvas_Xmin = DMIN1(CDbl(xPrjMin3-DV), CDbl(xPrjMinBotm), CDbl(xPrjMinSide), CDbl(xPrjMinBack)) canvas_Xmax = DMAX1(CDbl(xPrjMax3-DV), CDbl(xPrjMaxBotm), CDbl(xPrjMaxSide), CDbl(xPrjMaxBack)) canvas_Ymin = DMIN1(CDbl(yPrjMin3-DV), CDbl(yPrjMinBotm), CDbl(yPrjMinSide), CDbl(yPrjMinBack)) canvas_Ymax = DMAX1(CDbl(yPrjMax3-DV), CDbl(yPrjMaxBotm), CDbl(yPrjMaxSide), CDbl(yPrjMaxBack)) End Sub
Sub SurfaceDraw(DrwTypeIn As String, Optional LineColor As Long = -1) ReDim Preserve T(0 To 3, 0 To 3) Picture1.Cls Picture2.Cls isDrawing = True ' Calculate the transformation matrix. CreateTransFormationMatrix ViewType
' Split the equation from listbox Equation_Split 'Calculate the value of function Function3-DValues 'Calculte the projection value of 3-D points Function3-DPrj canvas_Xmin = xPrjMin3-DV - 15 canvas_Xmax = xPrjMax3-DV + 15 canvas_Ymin = yPrjMin3-DV - 15 canvas_Ymax = yPrjMax3-DV + 15
xLeft = Round(canvas_Xmin + 0.5, 0) xRight = Round(canvas_Xmax + 0.5, 0) yTop = Round(canvas_Ymax + 0.5, 0) yBottom = Round(canvas_Xmin + 0.5, 0) Picture1.Scale (xLeft, yTop)-(xRight, yBottom) '(canvas_Xmin, canvas_Ymax)-(canvas_Xmax, canvas_Ymin) Picture2.Scale (xLeft, yTop)-(xRight, yBottom) '(canvas_Xmin, canvas_Ymax)-(canvas_Xmax, canvas_Ymin) 'Plot the x,y,z axels\ . . . '-------------------------------------------------- Dim i As Integer, j As Integer Dim ptTpt As Point2D, ptsPrj() As PointAPI, ptTptApi As PointAPI, ptsPrjB() As PointAPI Dim LineColors(0 To 3) As Long Select Case LCase(DrawType) Case "mesh" If LineColor = -1 Then LineColors(0) = vbBlue LineColors(1) = vbCyan LineColors(2) = vbGreen LineColors(3) = vbMagenta End If
If LineColor = -1 Then Picture1.ForeColor = LineColors(0) Picture2.ForeColor = LineColors(0) Else Picture1.ForeColor = LineColor Picture2.ForeColor = LineColor End If Case "face" Picture1.DrawStyle = vbSolid Picture1.FillStyle = vbFSSolid Picture2.DrawStyle = vbSolid Picture2.FillStyle = vbFSSolid 'setting of color(顏色設定) Dim tptV0 As Single, tptV1 As Single, tptV2 As Single Dim tpt1(0 To 2) As Single Dim rgb_R As Byte, rgb_G As Byte, rgb_B As Byte tpt1(0) = (xTopBase - xBotmBase) tpt1(1) = (yTopBase - yBotmBase) tpt1(2) = (zTopBase - zBotmBase) For i = 0 To 2 If Abs(tpt1(i)) < 0.01 And tpt1(i) <= 0.01 Then tpt1(i) = -0.01 If Abs(tpt1(i)) < 0.01 And tpt1(i) > 0.01 Then tpt1(i) = 0.01 If Abs(tpt1(i)) < 0.01 And tpt1(i) = 0# Then tpt1(i) = 0.01 Next i
For i = 0 To NdoXU For j = 0 To NdoYV With Points(i, j) Select Case LCase(fillColorType) Case "rgb", "pattern" tptV0 = .Coord(0) * PI / tpt1(0) tptV1 = .Coord(1) * PI / tpt1(1) tptV2 = .Coord(2) * PI / tpt1(2) rgb_R = CInt((Sin(tptV0) + 1) * 255 * 0.5) rgb_G = CInt((Cos(tptV1) + 1) * 255 * 0.5) rgb_B = CInt((Cos(tptV2) + 1) * 255 * 0.5) If rgb_R >= 255 Then rgb_R = 255 If rgb_G >= 255 Then rgb_G = 255 If rgb_B >= 255 Then rgb_B = 255 If rgb_R < 0 Then rgb_R = 0 If rgb_G < 0 Then rgb_G = 0 If rgb_B < 0 Then rgb_B = 0 .ptRGBcol = RGB(rgb_R, rgb_G, rgb_B) Case "transparent" .ptRGBcol = colorBack Case "color" .ptRGBcol = FillColor End Select End With Next j Next i Dim PtsAPI() As PointAPI, ptsAPIB() As PointAPI Dim ptsRect(0 To 3) As PointAPI, ptsRectB(0 To 3) As PointAPI
' Select Case LCase(TypeStr) 'Case "side" . . . ' Case "back" . . . ‘Case "bottom", "botm" . . . 'Case "3-D", "3-Dview" Erase PtsAPI, ptsAPIB ReDim Preserve PtsAPI(0 To NdoXU, 0 To NdoYV), ptsAPIB(0 To NdoXU, 0 To NdoYV) For i = 0 To NdoXU For j = 0 To NdoYV ptTpt.x = Points(i, j).Trans(0) ptTpt.y = Points(i, j).Trans(1) PtsAPI(i, j) = PtConvertToPix(Picture1, ptTpt) ptsAPIB(i, j) = PtConvertToPix(Picture2, ptTpt) Next j Next i For i = 0 To NdoXU - 1 For j = 0 To NdoYV - 1 ptsRect(0) = PtsAPI(i, j) ptsRect(1) = PtsAPI(i, j + 1) ptsRect(2) = PtsAPI(i + 1, j + 1) ptsRect(3) = PtsAPI(i + 1, j) ptsRectB(0) = ptsAPIB(i, j) ptsRectB(1) = ptsAPIB(i, j + 1) ptsRectB(2) = ptsAPIB(i + 1, j + 1) ptsRectB(3) = ptsAPIB(i + 1, j) Picture1.FillColor = Points(i, j).ptRGBcol Picture2.FillColor = Points(i, j).ptRGBcol If LCase(fillColorType) = "pattern" Then Dim mRgn As Long, mRgnB As Long mRgn = CreatePolygonRgn(ptsRect(0), 4, 1) mRgnB = CreatePolygonRgn(ptsRectB(0), 4, 1) Call FillRgn(Picture1.hdc, mRgn, glPatternBrush) Call FillRgn(Picture2.hdc, mRgnB, glPatternBrush) Picture1.ForeColor = vbMagenta Picture2.ForeColor = vbMagenta 'DrawMesh Picture2, "3-D" Else Polygon Picture1.hdc, ptsRect(0), 4 Polygon Picture2.hdc, ptsRectB(0), 4 End If Next j Next i If LCase(fillColorType) = "pattern" Then Picture1.ForeColor = vbMagenta Picture2.ForeColor = vbMagenta DrawMesh Picture1, "3-D", vbMagenta DrawMesh Picture2, "3-D", vbMagenta End If End Select End Sub
For more information, please link “chday169.url.tw” http://vlog.xuite.net/play/MmhYbWNzLTgzOTQ1MTIuZmx2 ContourPlot_0001 @ 隨意窩 Xuite 影音
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