3D coordinate systems

This code has been declared by its author to be Public Domain code.

3D coordinate systems by MusicianKool

2010

I made this library as doing the math in Blitz3D is slow, so here it is for you. The source and examples are included.

http://www.mediafire.com/?w2v7phqmmyclzq0

; Here is the Source code in Blitz3D.
; It's slower but does the same thing as the lib.

;#Region    ;Spherical Vector

Global SphericalBank = CreateBank(4*5)

Function Spherical(x#,y#,z#,Vector#)
	RD# = Vector#
	zen# = ATan2(Sqr(x#*x#+y#*y#),z#)
	azi# = ATan2(y#,x#)
	PokeFloat (SphericalBank,0,Sin(Zen#))
	PokeFloat (SphericalBank,4,Cos(Zen#))
	PokeFloat (SphericalBank,8,Sin(Azi#))
	PokeFloat (SphericalBank,12,Cos(Azi#))
	PokeFloat (SphericalBank,16,RD#)
End Function

Function Spherical_X#()
	Return (PeekFloat(SphericalBank,16)*PeekFloat(SphericalBank,0)*PeekFloat(SphericalBank,12))
End Function

Function Spherical_Y#()
	Return (PeekFloat(SphericalBank,16)*PeekFloat(SphericalBank,0)*PeekFloat(SphericalBank,8))
End Function

Function Spherical_Z#()
	Return (PeekFloat(SphericalBank,16)*PeekFloat(SphericalBank,4))
End Function

;#End Region

;#Region	;Cartesian Vector
Global CartesianBank = CreateBank(3*4)
Function Cartesian#(Pitch#,Yaw#,Roll#,X_vector#,Y_vector#,Z_vector#)
	sx# = Sin(Pitch#)
	cx# = Cos(Pitch#)
	sy# = Sin(Yaw#)
	cy# = Cos(Yaw#)
	sz# = Sin(Roll#)
	cz# = Cos(Roll#)

	;// rotation around x
	xy# = cx#*Y_vector# - sx#*Z_vector#
	xz# = sx#*Y_vector# + cx#*Z_vector#
	;// rotation around y
	yz# = cy#*xz# - sy#*X_vector#
	yx# = sy#*xz# + cy#*X_vector#
	;// rotation around z
	zx# = cz#*yx# - sz#*xy#
	zy# = sz#*yx# + cz#*xy#

	PokeFloat (CartesianBank,0,zx#)
	PokeFloat (CartesianBank,4,zy#)
	PokeFloat (CartesianBank,8,yz#)
End Function
Function Cartesian_X#():		Return PeekFloat(CartesianBank,0):	End Function
Function Cartesian_Y#():		Return PeekFloat(CartesianBank,4):	End Function
Function Cartesian_Z#():		Return PeekFloat(CartesianBank,8):	End Function
;#End Region

Global ProjectionBank = CreateBank(3*4)
Function Project_3dto2d(gx,gy,gz,x,y,z,dst = 1000,dst2 = 100)
	PokeFloat(ProjectionBank, gx + dst * x / (z + dst2) , 0)
	PokeFloat(ProjectionBank, gy + dst * y / (z + dst2) , 4)
	PokeFloat(ProjectionBank, gz + dst * z / (x + dst2) , 8)
End Function
Function Projected_X#()
	Return PeekFloat(ProjectionBank,0)
End Function
Function Projected_Y#()
	Return PeekFloat(ProjectionBank,4)
End Function
Function Projected_Z#()
	Return PeekFloat(ProjectionBank,8)
End Function

Comments

MusicianKool

2010

Here is a fun little example:

Graphics 800,600,32,2
SetBuffer BackBuffer()
Global Image = LoadImage("C:\Program Files\Blitz3D\help\commands\3d_examples\media\b3dlogo.jpg")
;
; With the CoordinateSystems Lib you can add an additional Coordinate System to your entities.
; There are many things that you can do with this as it's like a mini 3D engine.
; 

Type Point
	Field X#
	Field Y#
	Field Z#
	Field ARGB
End Type

Local P.Point

Global IB = ImageBuffer(Image)
LockBuffer IB
For x = 0 To ImageWidth(Image)-1
	For y = 0 To ImageHeight(Image)-1
		P.Point = New Point
		P\X = x - ImageWidth(Image)/2
		P\Y = y - ImageHeight(Image)/2
		P\Z = Rand(-20,20)
		P\argb = ReadPixelFast(x,y,IB)
	Next
Next
UnlockBuffer IB
Local N#
While Not KeyHit(1)
	Cls
	pitch# = pitch# + .1
	yaw# = yaw# + .1
	roll# = roll# + .1
	N = N + 1
	ms = MilliSecs()
	LockBuffer BackBuffer()
	For P.point = Each Point
		; Get the 3D coordinates for each point
		Cartesian(pitch,yaw,roll,P\X,P\Y,P\Z)

		; Project the 3D coordinates to 2D
		Project_3Dto2D(GraphicsWidth()/2,GraphicsHeight()/2,GraphicsHeight()/2,Cartesian_X(),Cartesian_Y(),Cartesian_Z(),1000,1000)
		WritePixelFast(Projected_X(),Projected_Y(),P\ARGB,BackBuffer())
	Next
	UnlockBuffer BackBuffer()
	Locate 0,0
	Print "Render Time: "+(MilliSecs()-ms)
	Flip
Wend

Ian Thompson

2010

Nice example of optimisation, thank you!

_PJ_

2010

I get an error whenever I try to run it:

---------------------------
Runtime Error
---------------------------
Offset out of range
---------------------------
OK
---------------------------

	PokeFloat(ProjectionBank, gx + dst * x / (z + dst2) , 0)

From function:
Function Project_3dto2d(gx,gy,gz,x,y,z,dst = 1000,dst2 = 100)

puki

2010

This looks exciting.

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