Re: [Algorithms] Re : Re : R: Sphere to rectangle

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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:pth...@ya...]
> *Sent:* sexta-feira, 8 de Janeiro de 2010 16:36
> *To:* Game Development Algorithms; dri...@li...
> *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 <dio...@ne...>
> *À :* Game Development Algorithms 
> <gda...@li...>; dri...@li...
> *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:pth...@ya...]
> *Sent:* sexta-feira, 8 de Janeiro de 2010 15:03
> *To:* Game Development Algorithms; dri...@li...
> *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 <dio...@ne...>
> *À :* dri...@li...; Game Development Algorithms 
> <gda...@li...>
> *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: dri...@li... <mailto:dri...@li...> 
> [mailto:dri...@li... <mailto:dri...@li...>]
> Sent: sexta-feira, 8 de Janeiro de 2010 13:54
> To: gda...@li... 
> <mailto:gda...@li...>
> Subject: [Algorithms] R: Sphere to rectangle
>
> ----Messaggio originale----
> Da: dio...@ne... <mailto:dio...@ne...>
> 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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