You may want to check this article

http://web4.cs.ucl.ac.uk/staff/t.weyrich/projects/quadrics/pbg06.pdf

Basically, you need to find the bounding box in clip space (after applying the perspective projection). As you can see there are no trigonometric functions involved here.

Gino


On 1/11/2010 1:02 PM, Diogo de Andrade wrote:

Hi Benjamin,

 

I’ve looked at your explanation, and after you put it like that, I was all “doh!”… The problem is way simpler to solve in that form (extending the main line (center to red) so the projected point has the same characteristics of the purple points). After that it was pretty simple to get right…

 

Thanks a lot for the help!

 

Diogo

 

From: Benjamin Rouveyrol [mailto:pthiben77@yahoo.fr]
Sent: sexta-feira, 8 de Janeiro de 2010 16:36
To: Game Development Algorithms; drizzt.du@libero.it
Subject: [Algorithms] Re : Re : R: Sphere to rectangle

 

Hi Diogo,

You pretty much spotted the problem with http://www.spellcasterstudios.com/sphere_problem.jpg

What I wanted to do is to keep the old direction (ie center of the sphere towards the red dots), but change the vector's magnitude so that the point is on the line made by the camera position and the pink dot.
So you compute first an angle (alpha = asin(R/D) ) on the triangle made by light center, camera position and pink dot.
Then you apply Thales (tan(alpha) = x / D <=> x = D * tan(alpha) )  to get your final point outside the circle, and which is on the pink line. And yes, I computed the right/up vectors the same way you did (with a normalize for Right ;-) )

When I look at my source code, I see that the 2D bounding rectangle checks all the xy coordinates of all the points to get the left/right/top/bottom.
I can't remember why I did that, but I believe this was to solve the problem you're showing.

Ben

 


De : Diogo de Andrade <diogo.andrade@netvisao.pt>
À : Game Development Algorithms <gdalgorithms-list@lists.sourceforge.net>; drizzt.du@libero.it
Envoyé le : Ven 8 Janvier 2010, 10 h 51 min 22 s
Objet : Re: [Algorithms] Re : R: Sphere to rectangle

Hi Benjamin,

 

Your solution almost works for me…

 

It works when the camera is head on to the center of the sphere:

 

http://www.spellcasterstudios.com/sphere_rect_problem01.jpg

 

But when I turn left or right, I get:

 

http://www.spellcasterstudios.com/sphere_rect_problem02.jpg

http://www.spellcasterstudios.com/sphere_rect_problem03.jpg

 

This might be related to the projection part, I’ll look into it…

What do you mean by: “Up and right vectors based on the camera and light positions (and the camera Up).”? I’m just accounting for camera orientation to calculate the up and right vectors… Are you suggesting something like:

 

View=LightPos-CameraPos

Right=cross(CameraUp,View)

Up=cross(View,Right)

 

?

 

From the more practical standpoint, from what I understand, you’re applying a scale factor to the radius to account for distance… How did you came about this formula?

 

You didn’t happen to need something similar for spotlights/cones?

 

Thanks,

Diogo

 

 

From: Benjamin Rouveyrol [mailto:pthiben77@yahoo.fr]
Sent: sexta-feira, 8 de Janeiro de 2010 15:03
To: Game Development Algorithms; drizzt.du@libero.it
Subject: [Algorithms] Re : R: Sphere to rectangle

 

Hi,

The way I solved this (but a bit math heavy):
If R is the light Radius and D the distance between the camera and the light:
NewR = D * tan(asin(R/D))

Then you compute Up and right vectors based on the camera and light positions (and the camera Up).
You end up with 4 corners: LightCenter +|- Up * NewR  +|- Right * NewR


You can project them and this should give you your bounding rectangle. If someone has a simpler solution, I'd be most interested ^_^

Ben

 


De : Diogo de Andrade <diogo.andrade@netvisao.pt>
À : drizzt.du@libero.it; Game Development Algorithms <gdalgorithms-list@lists.sourceforge.net>
Envoyé le : Ven 8 Janvier 2010, 9 h 28 min 54 s
Objet : Re: [Algorithms] R: Sphere to rectangle

Hi!

That's basically what I'm trying to do with the "wrong" solution, although I don't tell it like that...
It was a good thought... I had to think about it for 2 mins before I understood that was exactly what I was trying to do...

Visually, you can see the problem at http://www.spellcasterstudios.com/sphere_problem.jpg

With your solution (and my initial one), I'd get the red points (and their projection, the yellow line), which is smaller than the correct solution (the purple points/projection), which has the correct size...

Thanks!

Diogo


-----Original Message-----
From: drizzt.du@libero.it [mailto:drizzt.du@libero.it]
Sent: sexta-feira, 8 de Janeiro de 2010 13:54
To: gdalgorithms-list@lists.sourceforge.net
Subject: [Algorithms] R: Sphere to rectangle

----Messaggio originale----
Da: diogo.andrade@netvisao.pt
Data: 08/01/2010 13.45

> Hi all…

> I’ve been wrestling with a problem for some days now, and I
> honestly can’t seem to figure an elegant solution…

> I want to find the rectangle that bounds a omni light source,
> so the problem is: given a sphere with center C=(x0,y0,z0) and radius
RADIUS, what is the bounding rectangle rect=(rx1,ry1,rx2,ry2) on screen?

Ok, I read this ML only for educational purpose, so...well, I'm sure I will
suggest the wrong solution :-D

Arent'you simply trying to do screen-aligned billboarding?
I mean...the bounding rectangle around a sphere of a given radius, on
screen...is not always the same rectangle simply billboarded?



------------------------------------------------------------------------------
This SF.Net email is sponsored by the Verizon Developer Community
Take advantage of Verizon's best-in-class app development support
A streamlined, 14 day to market process makes app distribution fast and easy
Join now and get one step closer to millions of Verizon customers
http://p.sf.net/sfu/verizon-dev2dev
_______________________________________________
GDAlgorithms-list mailing list
GDAlgorithms-list@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
Archives:
http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list


------------------------------------------------------------------------------
This SF.Net email is sponsored by the Verizon Developer Community
Take advantage of Verizon's best-in-class app development support
A streamlined, 14 day to market process makes app distribution fast and easy
Join now and get one step closer to millions of Verizon customers
http://p.sf.net/sfu/verizon-dev2dev
_______________________________________________
GDAlgorithms-list mailing list
GDAlgorithms-list@lists.sourceforge.net
https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list
Archives:
http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list

 

 

------------------------------------------------------------------------------ This SF.Net email is sponsored by the Verizon Developer Community Take advantage of Verizon's best-in-class app development support A streamlined, 14 day to market process makes app distribution fast and easy Join now and get one step closer to millions of Verizon customers http://p.sf.net/sfu/verizon-dev2dev
_______________________________________________ GDAlgorithms-list mailing list GDAlgorithms-list@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list