by Marc Ceulemans (1 Submission)
Category: Math/Dates
Compatability: Visual Basic 3.0
Difficulty: Unknown Difficulty
Originally Published: Sun 4th September 2011
Date Added: Mon 8th February 2021
Rating: 
(1 Votes)
Sets up some basic Math for transforming objects or an environement in 3D Structures,ideas,Matix and Vertex Math.
API Declarations
Teaser for the inquisitive people out there
I'm still learning and share what a have so far. Warts and all...
VBcoders
'****************************************************************************************************************************
'Conversion from Degrees to Radials used in Math.Cos and Math.Sin
Public Const rad As Double = Math.PI/180
'****************************************************************************************************************************
'Camera structure
'Movement: Concider stepping when changing dx,dy,dz as a variance of speed?
' remember INVERT : walk forward = -z etc. as the world moves against the grain on your static monitor display!!!
'Rotation: Convert angles 0 to 360 to radial equivalens , degrees * rad (the const!)
' remember INVERT : Left = right , up = down etc.
'Scale: 2 = twice at large !!! Use fractions
Public Structure Camera
' Location 'd' for displasement
Friend dx As Double
Friend dy As Double
Friend dz As Double
' Angles 'a' for angle
Friend ax As Double
Friend ay As Double
Friend az As Double
' Zoom or Scale 's' for Scale
Friend sx As Double
Friend sy As Double
Friend sz As Double
'friend lives as integer
'friend health as integer
'AliveDead as boolean
'Props...
End Structure
Public Cam As Camera = New Camera ' Camera: Cam = ready for you!
' The Structure Camera is a good place to start creating a Player ? Add some Lives,Health,AliveDead...Props...
' Just keep there behaviour in sinc : movement,rotation ...Ore replace Cam by your extended Player Srtuctur?
'****************************************************************************************************************************
Public matX(4,4) as double 'Rotation on the x-axis
Public matY(4,4) as double 'Rotation on the y-axis
Public matZ(4,4) as double 'Rotation on the z-axis
Public matMove(4,4) as double 'Movement in dx,dy and dz : invers of the Camera-movement !!!
Public matScale(4,4) as double 'Scaling sx,sy and sz invers of the Camera-rotations !!!
Public matMaster(4,4) as double 'Master transformation matrix
'****************************************************************************************************************************
'Initialize all transforms and cocatinate th Master Transformation Matrix :-)
Public Sub CreatMasterTransformer()
SetMatX() 'Set x-rotation
SetMatY() 'Set y-rotation
SetMatZ() 'Set z-rotation
SetMatMove() 'Set Movement
SetMatScale() 'Set Scaling
Concat() 'Master Transformation matrix is ready
End Sub
'****************************************************************************************************************************
'Set x-rotation
Public Sub SetMatX()
for c = 0 to 3
for r = 0 to 3
matX(c,r) = 0
Next r
Next c
matX(0,0) = 1 '1 0 0 0
matX(1,1) = Math.cos(Cam.ax) : matX(2,1) = Math.sin(Cam.ax) '0 cos sin 0
matX(1,2) = -Math.sin(Cam.ax) : matX(2,2) = Math.cos(Cam.ax) '0 -sin cos 0
matX(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // Set y-rotation
Public Sub SetMatY()
' Initialize matrix to identiy matrix
for c = 0 to 3
for r = 0 to 3
MatY(c,r) = 0
Next r
Next c
MatY(0,0) = Math.cos(Cam.ay) : matY(2,0) = Math.sin(Cam.ay) 'cos 0 sin 0
MatY(1,1) = 1 '0 1 0 0
MatY(0,2) = -Math.sin(Cam.ay) : matY(2,2) = Math.cos(Cam.ay) '-sin 0 cos 0
MatY(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // Set z-rotation
Public Sub SetMatZ()
' Initialize matrix to identiy matrix
for c = 0 to 3
for r = 0 to 3
MatZ(c,r) = 0
Next r
Next c
MatZ(0,0) = Math.cos(Cam.az) : matZ(1,0) = Math.sin(Cam.az) 'cos sin 0 0
MatZ(1,1) = -Math.sin(Cam.az) : matZ(2,2) = Math.cos(Cam.az) '-sin cos 0 0
MatZ(2,2) = 1 '0 0 1 0
MatZ(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // Set Movement
Public Sub SetMatMove()
' Initialize matrix to identiy matrix
for c = 0 to 3
for r = 0 to 3
MatMove(c,r) = 0
Next r
Next c
MatMove(0,0) = 1 : MatMove(3,0) = Cam.dx '1 0 0 dx
MatMove(1,1) = 1 : MatMove(3,1) = Cam.dy '0 1 0 dy
MatMove(2,2) = 1 : MatMove(3,2) = Cam.dz '0 0 1 dz
MatMove(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // Set Scaling
Public Sub SetMatScale()
' Initialize matrix to identiy matrix
for c = 0 to 3
for r = 0 to 3
MatScale(c,r) = 0
Next r
Next c
MatScale(0,0) = Cam.sx 'sx 0 0 0
MatScale(1,1) = Cam.sy '0 xy 0 0
MatScale(2,2) = Cam.sz '0 0 sz 0
MatScale(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // set MatMaster to Identiy matrix conditions
Public Sub SetmatMasterID()
' Initialize matrix to identiy matrix
for c = 0 to 3
for r = 0 to 3
matMaster(c,r) = 0
Next r
Next c
MatScale(0,0) = 1 '1 0 0 0
MatScale(1,1) = 1 '0 1 0 0
MatScale(2,2) = 1 '0 0 1 0
MatScale(3,3) = 1 '0 0 0 1
End Sub
'****************************************************************************************************************************
' // Concatinate Master Transformation matrix
' The camera moves then looks left/right than up/dow and eventualy tilts if need me
' Separate movements, rotations and scaleing ca n be done by leaving all other transforms set to ZERO!
' Example:
' ax = 0 , ay = 0 , az = 0 ,dx = 0 , dy = 10 , sx = 2 sy = 0 sz = 0
' These settings would result in movin 10 units up and making the object rezise in the y direction by a factor of 2
'****************************************************************************************************************************
Public Sub Concat()
Dim temp1(4,4) As Double
' // Initialize temp1 to identiy matrix
for c = 0 to 3
for r = 0 to 3
temp1(c,r) = 0
Next r
Next c
temp1(0,0) = 1 '1 0 0 0
temp1(1,1) = 1 '0 1 0 0
temp1(2,2) = 1 '0 0 1 0
temp1(3,3) = 1 '0 0 0 1
Dim temp2(4,4) As Double
' // Initialize temp2 to identiy matrix
for c = 0 to 3
for r = 0 to 3
temp2(c,r) = 0
Next r
Next c
temp2(0,0) = 1 '1 0 0 0
temp2(1,1) = 1 '0 1 0 0
temp2(2,2) = 1 '0 0 1 0
temp2(3,3) = 1 '0 0 0 1
' // temp1() = MatMove() + MatY()
For i = 0 to 3
For j = 0 to 3
For k = 0 to 3
temp1(i,j) += MatMove(i,k) * MatY(k,j)
Next k
Next j
Next i
' // temp2() = temp1() + MatX()
For i = 0 to 3
For j = 0 to 3
For k = 0 to 3
temp2(i,j) += temp1(i,k) * MatX(k,j)
Next k
Next j
Next i
' // Prep matMaster() to Identity matrix
SetmatMasterID()
' // matMaster() = Temp2() + MatZ()
For i = 0 to 3
For j = 0 to 3
For k = 0 to 3
matMaster(i,j) += temp2(i,k) * MatX(k,j)
Next k
Next j
Next i
' *** DONE !!! Ready to transfor shapes,objects or the whole environement ***
End Sub
'****************************************************************************************************************************
'What does the world consit of?
Public Structure Vertex3D
Friend x As Double
Friend y As Double
Friend z As Double
Friend w As Double 'Must have for transforms = 1 always ?
'Friend c As vbColor ore something like it...
End Structure
'****************************************************************************************************************************
'The world is solid Geometry and never changes accept when editing?
Public World(Sizeofworld) As vertex3D
'The Scene holds the transformed Geometry ...
Public Scene(Sizeofworld) As Vertex3D
'****************************************************************************************************************************
Public Sub Transform()
'Use the number of vertecies in the world to set up the Vertex Counter !
'Transform the world...
For i = 0 to Sizeofworld
Scene(i).x = World(i).x * matMaster(0,0)+World(i).y * matMaster(1,0)+World(i).z * matMaster(2,0) + World(i).w * matMaster(3,0)
Scene(i).y = World(i).x * matMaster(0,1)+World(i).y * matMaster(1,1)+World(i).z * matMaster(2,1) + World(i).w * matMaster(3,1)
Scene(i).z = World(i).x * matMaster(0,2)+World(i).y * matMaster(1,2)+World(i).z * matMaster(2,2) + World(i).w * matMaster(3,2)
Scene(i).w = World(i).x * matMaster(0,3)+World(i).y * matMaster(1,3)+World(i).z * matMaster(2,2) + World(i).w * matMaster(3,2)
Next i
End Sub
'****************************************************************************************************************************
' // Not Done yet !!! Som vector manipultion please...
'****************************************************************************************************************************
'Vector Addition
Public Function AddVector(ByVal v1 As Vertex3D,ByVal v2 As Vertex3d) As Vertex3D
Dim result As Vertex3d
result.x = v1.x + v2.x
result.y = v1.y + v2.y
result.z = v1.z + v2.z
result.w = 1
Return result
End Function
'****************************************************************************************************************************
'Vector Subtraction
Public Function SubVector(ByVal v1 As Vertex3D,ByVal v2 As Vertex3d) As Vertex3D
Dim result As Vertex3d
result.x = v1.x - v2.x
result.y = v1.y - v2.y
result.z = v1.z - v2.z
result.w = 1
Return result
End Function
'****************************************************************************************************************************
' // Vector multiplication
Public Function SubVector(ByVal v1 As Vertex3D,ByVal v2 As Vertex3d) As Vertex3D
Dim result As Vertex3d
result.x = v1.x * v2.x
result.y = v1.y * v2.y
result.z = v1.z * v2.z
result.w = 1
Return result
End Function
'****************************************************************************************************************************
' // Vector Length ?
Public Function SubVector(ByVal v1 As Vertex3D,ByVal v2 As Vertex3d) As double
Dim result As Double
result =math.sqrt(math.pow((v1.x - v2.x , 2)) + math.pow((v1.y - v2.y , 2))math.pow((v1.z - v2.z , 2)))
Return result
End Function
'****************************************************************************************************************************
'Getting the Normal vector : perpendicular to the plane ?
'Needed for light calulations
'Useful to dedermin if somthing is visible or not ?
'
' (Normal.z * Normam.y * Normal.z) > 0 VISIBLE
'
' (Normal.z * Normam.y * Normal.z) <= 0 INVISIBLE Visible, facing away...
'
'Normal vertecies can be precomputed as part of the world but must than also be transformed with it!
'Normal vertecies could be computed after transform on fewer vertecies after deciding what can be visible
'BSP : Lots of reading to do on that subject, reduced dramaticly the need for CPU overhead
'What's behind you needs no computing at all !!! etc.
Public Function NormalVector(ByVal v1 As Vertex3D,ByVal v2 As Vertex3d) As Vertex3D
Dim Normal As Vertex3d
Normal.x = (v1.y * v2.z) - (v1.z * v2.y)
Normal.y = (v1.z * v2.x) - (v1.x * v2.z)
Normal.z = (v1.x * v2.y) - (v1.y * v2.x)
Normal.w = 1
Return result
End Function
'****************************************************************************************************************************
'CACH THE DREADED : "DIVISION_BY_ZERO" Error !
'****************************************************************************************************************************
' // Unit vector math : pass length of corresponding Normal vector !!!!!
Public sub UnitVector(ByRef v As Vertex3D,ByVal Length As Double)
Length = math.abs(Length) 'A positive number is usefull...
If lenght > 0.001 Then 'DIVISION_BY_ZERO Error Cought !!!
v.x = v.x / Length
v.y = v.y / Length
v.z = v.z / Length
End if
End Sub
'****************************************************************************************************************************
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