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Sets up some basic Math for transforming objects or an environement in 3D Structures,ideas,Matix an

Sets up some basic Math for transforming objects or an environement in 3D Structures,ideas,Matix and Vertex Math.

API Declarations


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Rate Sets up some basic Math for transforming objects or an environement in 3D Structures,ideas,Matix an

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'****************************************************************************************************************************
	'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
'****************************************************************************************************************************