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JanetTerra
Jul 28, 2006
Source Code for Plot3D
Tom Nally - 
steelweaver52
If you prefer, you may download the zipped file .
Return to Easy Functions for Plotting 3D Objects .
Source Code for Plot3D
'''''''''''''''''''''''''''''''''
' Plot3D.bas '
' Version 1.1 '
' by Tomas J. Nally '
' Steelweaver52@aol.com '
' Copyright September 2003 '
'''''''''''''''''''''''''''''''''
' Released as Open Source '
'''''''''''''''''''''''''''''''''
' Made with the following: '
' '
' Liberty BASIC '
' by Carl Gundel '
' http://www.libertybasic.com '
' '
' Liberty BASIC Workshop '
' by Alyce Watson '
' http://alycesrestaurant.com '
'''''''''''''''''''''''''''''''''
'''''''''''''''''''''''''''''''''''''''''''''''''''''''
'Version 1.1 Changes to ScreenX() and ScreenY(): '
' '
' The virtual X-axis vector and the virtual '
' Y-axis vector is divided by the length of '
' the Camera-to-Center vector. This change '
' enables the objects to look smaller as '
' the camera moves away from the viewing '
' center, or look larger as the camera moves '
' toward the viewing center. '
' '
' Additionally, the change noted above causes '
' the objects to appear very small. So, within '
' ScreenX() and ScreenY(), the scale is multiplied '
' by another number called SCM, for "Secondary '
' Scale Multiplier". This operations makes the '
' objects appear about as large as they appeared '
' in version 1.0 of ScreenX() and ScreenY(). '
'''''''''''''''''''''''''''''''''''''''''''''''''''''''
True = 1
False = 0
NumNodes = 42
NumLines = 47
CamX = 225
CamY = 225
CamZ = 325
CtrX = 0
CtrY = 0
CtrZ = 0
ScrCtrX = 200
ScrCtrY = 200
ScaleFactor = 1
Dim XX(100)
Dim YY(100)
Dim ZZ(100)
Dim SX(100)
Dim SY(100)
Dim inode(100)
Dim jnode(100)
'Node Data
'------X-----Y----Z----------
Data 25, 0, -25 'Node 1
Data 25, 0, 25 'Node 2
Data -25, 0, 25 'Node 3
Data -25, 0, -25 'Node 4
Data 25, 50, -25 'Node 5
Data 25, 50, 25 'Node 6
Data -25, 50, 25 'Node 7
Data -25, 50, -25 'Node 8
'''''''''''''''''''''''''''''
Data -40, 0, -25 'Node 9
Data -40, 0, 25 'Node 10
Data -90, 0, 25 'Node 11
Data -90, 0, -25 'Node 12
Data -50, 40, -15 'Node 13
Data -50, 40, 15 'Node 14
Data -80, 40, 15 'Node 15
Data -80, 40, -15 'Node 16
''''''''''''''''''''''''''''''
Data -105, 0, -05 'Node 17
Data -105, 0, 45 'Node 18
Data -155, 0, 45 'Node 19
Data -155, 0, -05 'Node 20
Data -105, 80, -05 'Node 21
Data -105, 80, 45 'Node 22
Data -155, 80, 45 'Node 23
Data -155, 80, -05 'Node 24
''''''' X - Axis '''''''''''''
Data 0, 0, 0 'Node 25
Data 50, 0, 0 'Node 26
Data 50, 0, -5 'Node 27
Data 60, 0, 5 'Node 28
Data 60, 0, -5 'Node 29
Data 50, 0, 5 'Node 30
''''''' Y - Axis ''''''''''''''
Data 0, 0, 0 'Node 31
Data 0, 70, 0 'Node 32
Data -5, 85, 0 'Node 33
Data 5, 85, 0 'Node 34
Data 0, 80, 0 'Node 35
Data 0, 75, 0 'Node 36
''''''' Z - Axis ''''''''''''''
Data 0, 0, 0 'Node 37
Data 0, 0, 50 'Node 38
Data -5, 0, 55 'Node 39
Data 5, 0, 55 'Node 40
Data -5, 0, 65 'Node 41
Data 5, 0, 65 'Node 42
'Line Data
'-----inode----jnode--------
Data 1, 2 'Line 1
Data 2, 3 'Line 2
Data 3, 4 'Line 3
Data 4, 1 'Line 4
Data 5, 6 'Line 5
Data 6, 7 'Line 6
Data 7, 8 'Line 7
Data 8, 5 'Line 8
Data 1, 5 'Line 9
Data 2, 6 'Line 10
Data 3, 7 'Line 11
Data 4, 8 'Line 12
'''''''''''''''''''''''''''''
Data 9, 10 'Line 13
Data 10, 11 'Line 14
Data 11, 12 'Line 15
Data 12, 9 'Line 16
Data 13, 14 'Line 17
Data 14, 15 'Line 18
Data 15, 16 'Line 19
Data 16, 13 'Line 20
Data 9, 13 'Line 21
Data 10, 14 'Line 22
Data 11, 15 'Line 23
Data 12, 16 'Line 24
'''''''''''''''''''''''''''''
Data 17, 18 'Line 25
Data 18, 19 'Line 26
Data 19, 20 'Line 27
Data 20, 17 'Line 28
Data 21, 22 'Line 29
Data 22, 23 'Line 30
Data 23, 24 'Line 31
Data 24, 21 'Line 32
Data 17, 21 'Line 33
Data 18, 22 'Line 34
Data 19, 23 'Line 35
Data 20, 24 'Line 36
''' X - Axis Lines ''''''''''
Data 25, 26 'Line 37
Data 27, 28 'Line 38
Data 29, 30 'Line 39
''' Y - Axis Lines ''''''''''
Data 31, 32 'Line 40
Data 33, 35 'Line 41
Data 34, 35 'Line 42
Data 35, 36 'Line 43
''' Z - Axis Lines ''''''''''
Data 37, 38 'Line 44
Data 39, 40 'Line 45
Data 40, 41 'Line 46
Data 41, 42 'Line 47
For i = 1 to NumNodes
Read QQ$, RR$, SS$
XX(i) = val(QQ$)
YY(i) = val(RR$)
ZZ(i) = val(SS$)
next i
For i = 1 to NumLines
Read QQ$, RR$
inode(i) = val(QQ$)
jnode(i) = val(RR$)
next i
[InitColors]
'It is suggested that default colors be used when possible.
'Activate the following color statements only if
'they are really necessary in the program.
'ForegroundColor$ = "Black"
'BackgroundColor$ = "Buttonface"
'TexteditorColor$ = "White"
'TextboxColor$ = "White"
'ComboboxColor$ = "White"
'ListboxColor$ = "White"
[WindowSetup]
NOMAINWIN
WindowWidth = 653 : WindowHeight = 485
UpperLeftX = INT((DisplayWidth-WindowWidth)/2)
UpperLeftY = INT((DisplayHeight-WindowHeight)/2)
[ControlSetup]
Menu #Plot3D, "&File" , _
"E&xit", [btnQuit.click]
Menu #Plot3D, "Help" , _
"Open Plot3D.txt with Notepad...", [Open.Plot3D.txt.With.Notepad], |, _
"About Plot 3D...", [File.About]
graphicbox #Plot3D.gbox1, 230, 5, 400, 400
statictext #Plot3D.stat01, "Cam:", 15, 45, 45, 20
statictext #Plot3D.stat02, "Ctr:", 15, 75, 45, 20
statictext #Plot3D.stat03, "ScrCtr:", 15, 105, 45, 20
statictext #Plot3D.stat04, "Scale:", 15, 135, 45, 20
statictext #Plot3D.stat05, "X ---------- Y --------- Z", 85, 15, 120, 20
button #Plot3D.btnRedraw, "RePlot Objects",[btnRedraw.click],UL, 60, 185, 150, 35
button #Plot3D.btnClear, "Clear Screen",[btnClear.click],UL, 60, 225, 150, 35
button #Plot3D.btnQuit, "Quit",[btnQuit.click],UL, 60, 370, 150, 35
button #Plot3D.btnReset, "Reset Original Values",[btnReset.click],UL, 60, 265, 150, 35
textbox #Plot3D.txtCamX, 60, 40, 50, 25
textbox #Plot3D.txtCamY, 115, 40, 50, 25
textbox #Plot3D.txtCamZ, 170, 40, 50, 25
textbox #Plot3D.txtCtrX, 60, 70, 50, 25
textbox #Plot3D.txtCtrY, 115, 70, 50, 25
textbox #Plot3D.txtCtrZ, 170, 70, 50, 25
textbox #Plot3D.txtScrCtrX, 60, 100, 50, 25
textbox #Plot3D.txtScrCtrY, 115, 100, 50, 25
textbox #Plot3D.txtScale, 60, 130, 50, 25
Open "Functions for Plotting 3D Objects" for Window as #Plot3D
print #Plot3D, "trapclose [btnQuit.click]"
print #Plot3D.gbox1, "down; fill White; flush"
print #Plot3D.gbox1, "setfocus; when mouseMove [MouseChange1]"
print #Plot3D, "font ms_sans_serif 10"
gosub [Initialize.All.Controls]
[loop]
Wait
[Initialize.All.Controls]
print #Plot3D.txtCamX, CamX
print #Plot3D.txtCamY, CamY
print #Plot3D.txtCamZ, CamZ
print #Plot3D.txtCtrX, CtrX
print #Plot3D.txtCtrY, CtrY
print #Plot3D.txtCtrZ, CtrZ
print #Plot3D.txtScrCtrX, ScrCtrX
print #Plot3D.txtScrCtrY, ScrCtrX
print #Plot3D.txtScale, ScaleFactor
For i = 1 to NumNodes
SX(i) = ScreenX(XX(i), YY(i), ZZ(i), CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, ScaleFactor)
SY(i) = ScreenY(XX(i), YY(i), ZZ(i), CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, ScaleFactor)
next i
print #Plot3D.gbox1, "cls"
For i = 1 to NumLines
print #Plot3D.gbox1, "line "; SX(inode(i)); " "; SY(inode(i)); " "; SX(jnode(i)); " "; SY(jnode(i))
next i
return
[MouseChange1]
'MouseX and MouseY contain mouse coordinates
Wait
[btnRedraw.click]
'Get the new values for the camera coordinates
print #Plot3D.txtCamX, "!contents? CamX$"
print #Plot3D.txtCamY, "!contents? CamY$"
print #Plot3D.txtCamZ, "!contents? CamZ$"
CamX = val(CamX$)
CamY = val(CamY$)
CamZ = val(CamZ$)
'Get the new values for the "Center"
print #Plot3D.txtCtrX, "!contents? CtrX$"
print #Plot3D.txtCtrY, "!contents? CtrY$"
print #Plot3D.txtCtrZ, "!contents? CtrZ$"
CtrX = val(CtrX$)
CtrY = val(CtrY$)
CtrZ = val(CtrZ$)
'Get the new values for the Screen Center
print #Plot3D.txtScrCtrX, "!contents? ScrCtrX$"
print #Plot3D.txtScrCtrY, "!contents? ScrCtrY$"
ScrCtrX = val(ScrCtrX$)
ScrCtrY = val(ScrCtrY$)
'Get the new values for the Scale Factor
print #Plot3D.txtScale, "!contents? ScaleFactor$"
ScaleFactor = val(ScaleFactor$)
For i = 1 to NumNodes
SX(i) = ScreenX(XX(i), YY(i), ZZ(i), CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, ScaleFactor)
SY(i) = ScreenY(XX(i), YY(i), ZZ(i), CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, ScaleFactor)
next i
print #Plot3D.gbox1, "cls"
For i = 1 to NumLines
print #Plot3D.gbox1, "line "; SX(inode(i)); " "; SY(inode(i)); " "; SX(jnode(i)); " "; SY(jnode(i))
next i
Wait
[btnClear.click]
print #Plot3D.gbox1, "cls"
Wait
[btnQuit.click]
close #Plot3D : END
Wait
[btnReset.click]
CamX = 225
CamY = 225
CamZ = 325
CtrX = 0
CtrY = 0
CtrZ = 0
ScrCtrX = 200
ScrCtrY = 200
ScaleFactor = 1
gosub [Initialize.All.Controls]
Wait
[Open.Plot3D.txt.With.Notepad]
RUN "NOTEPAD Plot3D.txt"
Wait
[File.About]
Notice "About Plot 3D Version 1.1 " + chr$(13) + _
"Copyright Tomas J. Nally " + chr$(13) + _
"September 2003 " + chr$(13) + _
"Steelweaver52@aol.com " + chr$(13) + _
" " + chr$(13) + _
"**Released as open source** " + chr$(13) + _
" " + chr$(13) + _
"Made with the following: " + chr$(13) + _
" " + chr$(13) + _
"Liberty BASIC by Carl Gundel " + chr$(13) + _
"http://www.libertybasic.com " + chr$(13) + _
" " + chr$(13) + _
"Liberty BASIC Workshop " + chr$(13) + _
"by Alyce Watson " + chr$(13) + _
"http://alycesrestaurant.com "
Wait
''''''''''''''''''''''''''''''''''
Function ScreenX(XX, YY, ZZ, CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, Scale)
'Note: This is version 1.1 of ScreenX()
'Establish the Vector Components of the Camera-to-Center Vector
Cam2CtrX = (CtrX - CamX)
Cam2CtrY = (CtrY - CamY)
Cam2CtrZ = (CtrZ - CamZ)
LenCam2Ctr = sqr(Cam2CtrX^2 + Cam2CtrY^2 + Cam2CtrZ^2)
'The vector equation for the virtual image plane can be written
'as follows:
'
'Cam2CtrX*(x - CtrX) + Cam2CtrY*(y - CtrY) + Cam2CtrZ*(z - CtrZ) = 0
'Imagine a unit vector pointing in the -Y direction. The
'components of this vector are 0i -1j + 0k. When we take
'the cross product of this vector with the Camera-to-Center
'vector, the result is the virtual x-axis vector imposed
'upon the virtual image plane. These are the vector
'components of the virtual x-axis vector.
virtualXi = (-1)*(Cam2CtrZ)
virtualXj = 0
virtualXk = Cam2CtrX
'Find the length of this vector, then divide components
'by this length.
LenVirtualX = sqr(virtualXi^2 + virtualXj^2 + virtualXk^2)
virtualXi = virtualXi / LenVirtualX
virtualXj = virtualXj / LenVirtualX
virtualXk = virtualXk / LenVirtualX
'In order to find the virtual y-axis on the image plane,
'we need to take the cross product of the virtual x-axis
'vector with the Camera-to-Center Vector. Given below is
'the result of that cross product.
virtualYi = (-1)*(virtualXk * Cam2CtrY)
virtualYj = (virtualXk * Cam2CtrX) - (virtualXi * Cam2CtrZ)
virtualYk = (virtualXi * Cam2CtrY)
'Find the length of this vector, then divide the
'components by this length
LenVirtualY = sqr(virtualYi^2 + virtualYj^2 + virtualYk^2)
virtualYi = virtualYi / LenVirtualY
virtualYj = virtualYj / LenVirtualY
virtualYk = virtualYk / LenVirtualY
'Divide the unit virtual X-axis vector and the
'virtual Y-axis vector by LenCam2Ctr. This transformation
'of these two vectors will allow the objects to get
'smaller as the camera moves away from the viewing
'center, or get larger as the camera moves toward
'the viewing center.
virtualXi = virtualXi / LenCam2Ctr
virtualXj = virtualXj / LenCam2Ctr
virtualXk = virtualXk / LenCam2Ctr
virtualYi = virtualYi / LenCam2Ctr
virtualYj = virtualYj / LenCam2Ctr
virtualYk = virtualYk / LenCam2Ctr
'Establish the vector components of the Camera-to-Node Vector
Cam2NodeX = (XX - CamX)
Cam2NodeY = (YY - CamY)
Cam2NodeZ = (ZZ - CamZ)
'The parametric equations for the Camera-to-Node Vector
'can be written as follows:
'
'x = CamX + Cam2NodeX*t
'y = CamY + Cam2NodeY*t
'z = CamZ + Cam2NodeZ*t
'
'Plug these three equations into the vector equation
'for the virtual image plane...
'
'Cam2CtrX*(x - CtrX) + Cam2CtrY*(y - CtrY) + Cam2CtrZ*(z - CtrZ) = 0
'
'...and then solve for t
numerator = Cam2CtrX^2 + Cam2CtrY^2 + Cam2CtrZ^2
denominator = (Cam2NodeX * Cam2CtrX) + (Cam2NodeY * Cam2CtrY) + (Cam2NodeZ * Cam2CtrZ)
t = (numerator / denominator)
'Having solved for t, determine the point in space
'(ipx, ipy, ipz) where 'the Camera-to-Node vector intersects
'the virtual image plane.
ipX = CamX + Cam2NodeX*t
ipY = CamY + Cam2NodeY*t
ipZ = CamZ + Cam2NodeZ*t
'Establish the vector components of the vector from the
'center to (ipx, ipy, ipz).
Ctr2ipX = (ipX - CtrX)
Ctr2ipY = (ipY - CtrY)
Ctr2ipZ = (ipZ - CtrZ)
'The projection of this vector along the virtual X-axis
'is the dot product of this vector with the unit vector
'along the virtual X-Axis"
PX = (Ctr2ipX*virtualXi) + (Ctr2ipY*virtualXj) + (Ctr2ipZ*virtualXk)
SCM = 500 'Note: SCM is an acronym for "Secondary Scale Multiplier".
' This value was found by experimentation when it was
' observed that the Scale factor by itself was
' too small without a multiplier.
ScreenX = ScrCtrX + (SCM*Scale * PX)
'The projection of this vector along the virtual Y-axis
'is the dot product of this vector with the unit vector
'along the virtual Y-Axis"
'PY = (Ctr2ipX*virtualYi) + (Ctr2ipY*virtualYj) + (Ctr2ipZ*virtualYk)
'ScreenY = ScrCtrY - (SCM*Scale * PY)
end function
'''''''''''''''''''''''''''''''''''
Function ScreenY(XX, YY, ZZ, CamX, CamY, CamZ, CtrX, CtrY, CtrZ, ScrCtrX, ScrCtrY, Scale)
'Note: This is version 1.1 of ScreenY()
'Establish the Vector Components of the Camera-to-Center Vector
Cam2CtrX = (CtrX - CamX)
Cam2CtrY = (CtrY - CamY)
Cam2CtrZ = (CtrZ - CamZ)
LenCam2Ctr = sqr(Cam2CtrX^2 + Cam2CtrY^2 + Cam2CtrZ^2)
'The vector equation for the virtual image plane can be written
'as follows:
'
'Cam2CtrX*(x - CtrX) + Cam2CtrY*(y - CtrY) + Cam2CtrZ*(z - CtrZ) = 0
'Imagine a unit vector pointing in the -Y direction. The
'components of this vector are 0i -1j + 0k. When we take
'the cross product of this vector with the Camera-to-Center
'vector, the result is the virtual x-axis vector imposed
'upon the virtual image plane. These are the vector
'components of the virtual x-axis vector.
virtualXi = (-1)*(Cam2CtrZ)
virtualXj = 0
virtualXk = Cam2CtrX
'Find the length of this vector, then divide components
'by this length.
LenVirtualX = sqr(virtualXi^2 + virtualXj^2 + virtualXk^2)
virtualXi = virtualXi / LenVirtualX
virtualXj = virtualXj / LenVirtualX
virtualXk = virtualXk / LenVirtualX
'In order to find the virtual y-axis on the image plane,
'we need to take the cross product of the virtual x-axis
'vector with the Camera-to-Center Vector. Given below is
'the result of that cross product.
virtualYi = (-1)*(virtualXk * Cam2CtrY)
virtualYj = (virtualXk * Cam2CtrX) - (virtualXi * Cam2CtrZ)
virtualYk = (virtualXi * Cam2CtrY)
'Find the length of this vector, then divide the
'components by this length
LenVirtualY = sqr(virtualYi^2 + virtualYj^2 + virtualYk^2)
virtualYi = virtualYi / LenVirtualY
virtualYj = virtualYj / LenVirtualY
virtualYk = virtualYk / LenVirtualY
'Divide the unit virtual X-axis vector and the
'virtual Y-axis vector by LenCam2Ctr. This transformation
'of these two vectors will allow the objects to get
'smaller as the camera moves away from the viewing
'center, or get larger as the camera moves toward
'the viewing center.
virtualXi = virtualXi / LenCam2Ctr
virtualXj = virtualXj / LenCam2Ctr
virtualXk = virtualXk / LenCam2Ctr
virtualYi = virtualYi / LenCam2Ctr
virtualYj = virtualYj / LenCam2Ctr
virtualYk = virtualYk / LenCam2Ctr
'Establish the vector components of the Camera-to-Node Vector
Cam2NodeX = (XX - CamX)
Cam2NodeY = (YY - CamY)
Cam2NodeZ = (ZZ - CamZ)
'The parametric equations for the Camera-to-Node Vector
'can be written as follows:
'
'x = CamX + Cam2NodeX*t
'y = CamY + Cam2NodeY*t
'z = CamZ + Cam2NodeZ*t
'
'Plug these three equations into the vector equation
'for the virtual image plane...
'
'Cam2CtrX*(x - CtrX) + Cam2CtrY*(y - CtrY) + Cam2CtrZ*(z - CtrZ) = 0
'
'...and then solve for t
numerator = Cam2CtrX^2 + Cam2CtrY^2 + Cam2CtrZ^2
denominator = (Cam2NodeX * Cam2CtrX) + (Cam2NodeY * Cam2CtrY) + (Cam2NodeZ * Cam2CtrZ)
t = (numerator / denominator)
'Having solved for t, determine the point in space
'(ipx, ipy, ipz) where 'the Camera-to-Node vector intersects
'the virtual image plane.
ipX = CamX + Cam2NodeX*t
ipY = CamY + Cam2NodeY*t
ipZ = CamZ + Cam2NodeZ*t
'Establish the vector components of the vector from the
'center to (ipx, ipy, ipz).
Ctr2ipX = (ipX - CtrX)
Ctr2ipY = (ipY - CtrY)
Ctr2ipZ = (ipZ - CtrZ)
'The projection of this vector along the virtual X-axis
'is the dot product of this vector with the unit vector
'along the virtual X-Axis"
'PX = (Ctr2ipX*virtualXi) + (Ctr2ipY*virtualXj) + (Ctr2ipZ*virtualXk)
SCM = 500 'Note: SCM is an acronym for "Secondary Scale Multiplier".
' This value was found by experimentation when it was
' observed that the Scale factor by itself was
' too small without a multiplier.
'ScreenX = ScrCtrX + (SCM*Scale * PX)
'The projection of this vector along the virtual Y-axis
'is the dot product of this vector with the unit vector
'along the virtual Y-Axis"
PY = (Ctr2ipX*virtualYi) + (Ctr2ipY*virtualYj) + (Ctr2ipZ*virtualYk)
ScreenY = ScrCtrY - (SCM*Scale * PY)
end function
'''''''''''''''''''''''''''''''''''
Return to Easy Functions for Plotting 3D Objects .
Tom Nally
Steelweaver52@aol.com
Note: This linked source code accompanies Easy Functions for Plotting 3D Objects , which originally appeared in the Liberty BASIC Newsletter, Issue #113 . It is reprinted here with the permission of the author. -
JanetTerra