Re: [Algorithms] Re : Re : R: Sphere to rectangle
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Re: [Algorithms] Re : Re : R: Sphere to rectangle
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From: Gino v. d. B. <gin...@gm...> - 2010-01-13 08:55:58
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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? > > > > ------------------------------------------------------------------------------ > 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 > GDA...@li... > <mailto:GDA...@li...> > 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 > GDA...@li... > <mailto:GDA...@li...> > 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 > GDA...@li... > https://lists.sourceforge.net/lists/listinfo/gdalgorithms-list > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithms-list |
