transform point onto plane

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

transform point onto plane by Warner

2009

transforms a point (x, y, 0) on a plane to real world coords.
The plane is defined by (nx,ny,nz,d), or: ax + by + cz + d = 0
where (a,b,c)=(nx,ny,nz)

The code is not optimised, and I could not solve the 'roll' problem yet. At certain situations, the transformation turns 180 degrees upside down:
http://www.gamedev.net/community/forums/topic.asp?topic_id=399701

;input  = (X,Y) on plane
;output = Transformed point
Global resultx#, resulty#, resultz#
Function PointOntoPlane(x#, y#, z#, nx#, ny#, nz#, d#)

	a# = 0
	c# = ATan2(nx, ny)
	b# = ATan2(nz, Sqr(nx*nx+ny*ny))
		
	;apply yaw to point
	kx# = (Cos(-c) * z) - (Sin(-c) * x)
	ky# = y
	kz# = (Sin(-c) * z) + (Cos(-c) * x)
		
    ;apply pitch to point
	jx# = kx
	jy# = (Cos(-b) * ky) - (Sin(-b) * kz)
	jz# = (Sin(-b) * ky) + (Cos(-b) * kz)
			
    ;apply roll to point
	ix# = (Cos(-a) * jx) - (Sin(-a) * jy)
	iy# = (Sin(-a) * jx) + (Cos(-a) * jy)
	iz# = jz

    ;apply plane offset
	resultx# = ix# - nx*d
	resulty# = iy# - ny*d
	resultz# = iz# - nz*d

End Function
;Resources:
;http://www.geocities.com/siliconvalley/2151/math3d.html
;http://www.gamedev.net/community/forums/topic.asp?topic_id=399701

Comments

patmaba

2009

Hi, have you a small code to see your funtion in action, please ?

thanks

Warner

2009

Yes, the following rotates a plane, and transforms a number of points onto it.

;input  = (X,Y) on plane
;output = Transformed point
Global resultx#, resulty#, resultz#
Function PointOntoPlane(x#, y#, z#, nx#,ny#,nz#,d#)
	
	a# = 0
	c# = ATan2(nx, ny)
	b# = ATan2(nz, Sqr(nx*nx+ny*ny))
	
        ;apply pitch to point
	ix# = x
	iy# = (Cos(-b) * y) - (Sin(-b) * z)
	iz# = (Sin(-b) * y) + (Cos(-b) * z)

        ;apply roll to point
	jx# = (Cos(-a) * ix) - (Sin(-a) * iy)
	jy# = (Sin(-a) * ix) + (Cos(-a) * iy)
	jz# = iz

        ;apply plane offset
	resultx# = jx# - nx*d
	resulty# = jy# - ny*d
	resultz# = jz# - nz*d

End Function
;Resource: <a href="http://www.geocities.com/siliconvalley/2151/math3d.html" target="_blank">http://www.geocities.com/siliconvalley/2151/math3d.html</a>

;------------------------------------------------------------------------------------------------------------------------------------
;															EXAMPLE
;------------------------------------------------------------------------------------------------------------------------------------

	;setup 3D
	Graphics3D 800, 600, 0, 2
	SetBuffer BackBuffer()
	
	;create camera
	MoveEntity CreateCamera(), 0, 0, -5
	
	Dim sph(9)
	
	;create 10 spheres
	For i = 0 To 9
		sph(i) = CreateSphere()
		ScaleEntity sph(i), 0.1, 0.1, 0.1 ;make sphere smaller
		EntityColor sph(i), 255, 0, 0     ;make sphere red
	Next
	
	;basically, the plane is rotated around the y-axis
	;and the spheres are places accordingly
	Repeat
	
		;rotate plane
		
		angle = angle + 1  ;increase 'angle'
		nx# = Cos(angle)   ;calculate normal = vector pointing forward from plane
		ny# = 0
		nz# = Sin(angle)
		d# = 0             ;this is the distance of the plane from (0, 0, 0)
		
		;place spheres
		For i = 0 To 9
		
			x# = Cos(i * 36)	;calculate position of sphere in 2D space
			y# = Sin(i * 36)
		
			PointOntoPlane(x, y, 0, nx,ny,nz,d)   ;transform position from 2D space to 3D space
			PositionEntity sph(i), resultx, resulty, resultz  ;apply position
			
		Next
	
	
		RenderWorld
		Flip
	
	;esc=exit	
	Until KeyHit(1)
	
	End

Stevie G

2009

Why not use tformpoint instead?

BlitzSupport

2009

Why not use tformpoint instead?

Even if this works out the same, it's good to have the underlying algorithm -- it'd port to BlitzMax, for example.

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