1. 3-d equation
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Could someone please give me an equation or an algorithm to display a =
set of 3-d points on a x-y coordinate system? I will give a registered =
copy of a program I'm making with it to who gives me the one I'll use.
Thank you=20
Jesse
jk2000
DalNet on mirc in #double
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<DIV><FONT color=3D#000000 size=3D2>Could someone please give me an =
equation or an=20
algorithm to display a set of 3-d points on a x-y coordinate system? I =
will give=20
a registered copy of a program I'm making with it to who gives me the =
one I'll=20
use.</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>Thank you </FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>Jesse</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>jk2000</FONT></DIV>
<DIV><FONT color=3D#000000 size=3D2>DalNet on mirc in=20
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2. Re: 3-d equation
jesse kint writes:
> could someone please give me an equation or an algorithm to
> display a set of 3-d points on a x-y coordinate system?
euphoria\demo\dos32\wire.ex takes a bunch of lines in 3-D
(specified by their end-points) and maps them to the
2-D screen. It involves a bunch of fancy trigonometry
(sin's and cos's) that I got out of a book on computer graphics.
I sort of understood it when I wrote it, but please don't ask
me any questions about it now. 
You can change the data from a block "E" to something else.
Regards,
Rob Craig
Rapid Deployment Software
http://members.aol.com/FilesEu/
3. Re: 3-d equation
- Posted by lithex <lithex at INTERGATE.BC.CA>
Aug 27, 1998
-
Last edited Aug 28, 1998
Hi Jesse
Here's a pretty simple function that will project a point located in
the 3d space behind the screen onto the screen. The sequence "eye"
holds the coordinates of the viewer's viewpoint. The sequence "thing"
holds the coordinates of the point to be projected on the screen.
Bye
Martin
>>Euphoria code starts
constant X=1
constant Y=2
constant Z=3
sequence thing, eye
eye = {100,100,-100}
thing={50,50,100}
function perspective (sequence thing, sequence eye)
sequence t, i
atom r
r=thing[Z]/(thing[Z]-eye[Z])
t=thing[X..Y] i=eye[X..Y]
return (t+r*(i-t))
end function
?perspective(thing, eye)
?perspective(thing+10, eye)
?perspective(thing+20, eye)
?perspective(thing+{0,0,100}, eye)
>>Euphoria code ends
> Could someone please give me an equation or an algorithm to display a =
> set of 3-d points on a x-y coordinate system? I will give a registered =
> copy of a program I'm making with it to who gives me the one I'll use.
> Thank you=20
> Jesse
4. Re: 3-d equation
At 17:13 26/08/98 -0400, you wrote:
>Could someone please give me an equation or an algorithm to >display a
>set of 3-d points on a x-y coordinate system?
function transform(sequence point,sequence angles, integer d)
atom a,b,c
sequence sine,cosine
sine=sin(angles) cosine=cos(angles)
a=point[1]*cosine[1]+point[2]*sine[1]
b=point[2]*cosine[1]-point[1]*sine[1]
c=point[3]*cosine[2]-a*sine[2]
a=d-(a*cosine[2]+point[3]*sine[2])
return floor({((b*cosine[3]+c*sine[3])*d)/a,
((c*cosine[3]-b*sine[3])*d)/a})
end function
This function will return a set of 2D co-ords from
a 3D point and 3 rotation angles.
the parameters are :
point : {x,y,z}
angles : {alpha, beta, gamma} in radians
d : Distance between view point and
projection plane
The output will have to be scaled to fit your screen.
i.e.
constant scale={3,2} -- insert appropriate values here
sequence p2d,p3d,ang
p3d={28,9,18}
ang={1.3,0.4,5.6}
p2d=transform(p3d,ang,80)*scale
The d parameter affects the severity of the
perspective applied to the transformation, play
around with it until you find a value you like.
If you are transforming a lot of points at the same
rotation angles (highly likely), you will want to
remove the cos() and sin() calls from inside the
function to avoid them being re-calculated for each
point.
Hope this helps.
Graeme.
----------------------------------------------------
5. Re: 3-d equation
Apologies if this has already been answered, I've been away for the weekend.
> Could someone please give me an equation or an algorithm to display a set of
3-
> d points on a x-y coordinate system?
I think that what you are after is this :
You have {x,y,z} and want to plot it on screen. Assuming that increasing Z
represents a greater distance away from you, an accurate perpestive plot is
achieved by dividing both x and y by z.
{x/z,y/z} or {x,y}/z
In euphoria code :
function plot3d( coord3d xyz)
coord2d xy
xy = xyz[1..2]/xyz[3]
return xy
end function
You now have a problem. If z is 0 you get a divide by zero error. This can be
avoided by checking or objects that are behind you (z<=0) before plotting. All
of this and much more is implemented in my 3d toolkit (FREEWARE), which should
make its first alpha release this week. There are just a couple of fatal bugs
to fix. It implements full three-dimensional clipping (behind, too far away or
off-screen) and single buffering.
> I will give a registered copy of a
> program I'm making with it to who gives me the one I'll use.
What might that be ?
God Bless
Daniel
