Hey everyone…

I’ve done a simple algorithm to get the cone area (for spot lights)…

It’s basically the same as the omni light, but I find the bounding rectangle of a sphere S=(C,R), where C=LightPos+LightDir*range and R=range*tan(light_fov).

After I do that, I calculate the projection of the position of light source, and do a min/max test to build the final bounding rectangle.

I’m sure there’s probably a much better way to do this, but this one actually works pretty well, considering how simple it is…

Again, thanks all for the help!

Diogo

Sent: segunda-feira, 11 de Janeiro de 2010 12:03
To: 'Game Development Algorithms'
Subject: Re: [Algorithms] Re : Re : R: Sphere to rectangle

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

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:

But when I turn left or right, I get:

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

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----
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?

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