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From: Robert Blum <r.blum@gm...>  20081230 22:31:24

> is there any interpolation code I can look at Yes, there is. It firstly depends on the viewer  spherical projection, cylindrical projection, or hacked up? For either of the first two, you *really* do want to read up on polar coordinates. For the 3rd, you'll need to reverse the projection used, whatever it is.  R 
From: Tom Sparks <tom_a_sparks@ya...>  20081216 10:41:41

the image is a Equirectangular the image is viewed in panorama viewer is there a way to use interpolation to map x,y to pan,tilt angles is there any interpolation code I can look at  Original Message  From: Jim Offerman <jofferman@...> To: Game Development Algorithms <gdalgorithmslist@...> Sent: Tuesday, 16 December, 2008 7:01:44 PM Subject: Re: [Algorithms] image map to degree (angle) There is only one angle in a 2D situation... the pan / tilt concept only makes sense in a 3D space. Are you, perhaps, looking for a way to determine the polar coordinates? If so, check this out: http://en.wikipedia.org/wiki/Polar_coordinates Jim.  Jim Offerman Nixxes Software http://www.nixxes.com >  Original Message  > Subject: [Algorithms] image map to degree (angle) > From: Tom Sparks <tom_a_sparks@...> > To: GDAlgorithmslist@... > Date: 12/16/2008 6:41 AM > > > > I am using the HTML image map ( http://www.maschek.hu/imagemap/imgmap ) to define the location > > I need to be able to translate the x,y to Pan ( 180 and 180 degrees) and tilt ( 90 and 90 degrees) angles > I am using php > > > Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. > The future of the web can't happen without you. Join us at MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist > >  SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. The future of the web can't happen without you. Join us at MIX09 to help pave the way to the Next Web now. Learn more and register at http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline 
From: Jim Offerman <jofferman@ni...>  20081216 09:23:03

There is only one angle in a 2D situation... the pan / tilt concept only makes sense in a 3D space. Are you, perhaps, looking for a way to determine the polar coordinates? If so, check this out: http://en.wikipedia.org/wiki/Polar_coordinates Jim.  Jim Offerman Nixxes Software http://www.nixxes.com >  Original Message  > Subject: [Algorithms] image map to degree (angle) > From: Tom Sparks <tom_a_sparks@...> > To: GDAlgorithmslist@... > Date: 12/16/2008 6:41 AM > > > > I am using the HTML image map ( http://www.maschek.hu/imagemap/imgmap ) to define the location > > I need to be able to translate the x,y to Pan ( 180 and 180 degrees) and tilt ( 90 and 90 degrees) angles > I am using php > > > Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. > The future of the web can't happen without you. Join us at MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist > > 
From: Tom Sparks <tom_a_sparks@ya...>  20081216 05:41:44

I am using the HTML image map ( http://www.maschek.hu/imagemap/imgmap ) to define the location I need to be able to translate the x,y to Pan ( 180 and 180 degrees) and tilt ( 90 and 90 degrees) angles I am using php Start your day with Yahoo!7 and win a Sony Bravia TV. Enter now http://au.docs.yahoo.com/homepageset/?p1=other&p2=au&p3=tagline 
From: Jason Hughes <jason_hughes@di...>  20081211 17:25:56

Ah. If you can tolerate a little error, you could make your object into a hierarchy of spheres rather than just a single level. If a sphere is completely above, it's above. If it's below, it's below. If it's split, traverse to the next level of the hierarchy and check again. The good thing about spheres is you can more or less use any orientation for them because you want them to fill space. So, there's only a need to generate the initial layer of spheres, then translate and scale some fixed pattern of subspheres inside the one you're currently testing. Best of luck, JH John McCutchan wrote: > Thanks everyone for your suggestions and interesting conversation. The > reason I asked was that I'm trying to determine how much volume of an > object (discretized into spheres) is submerged under a height field > (discretized into AABBs) and need to do this many times per frame. I > think I've figured out a cheap solution that should give reasonable > results (never count a submerged sphere twice.) > > Thanks, > John > > On Sun, Dec 7, 2008 at 5:24 AM, Willem H. de Boer <willem@...> wrote: > >> Do you need an accurate answer? If accuracy is something >> you wouldn't mind say compute over several frames, then >> you could use a simple Monte Carlolike scheme. (Though >> I think the number of sample points required is low enough >> to be able to compute the volume in realtime) >> >> One could proceed by generating random points inside >> the union of the AABB and the sphere, the total volume, >> V, of which is easy to calculate ofcourse. >> >> Then only keep those points that lie within the intersection >> of the AABB and the sphere and keep track of the ratio of >> points within to the total number of points generated, call >> this r_n. >> >> Then after a suitable number of points generated, the volume is >> roughly r_n * V. >> >> The trouble with finding an analytic description of the volume >> is that the domain of integration (i.e. the intersection of AABB >> and sphere) is usually difficult to parametrise. In such cases >> MClike schemes work very well. >> >> Cheers, >> Willem >> >>  Original Message  >> From: "John McCutchan" <john@...> >> To: "Game Development Algorithms" <gdalgorithmslist@...> >> Sent: Friday, December 05, 2008 10:00 PM >> Subject: [Algorithms] Volume of intersection of sphere and AABB >> >> >> >>> Hi, >>> >>> I'm wondering if anyone has an idea of how to compute the volume of >>> the intersection of a sphere (center, radius) and an AABB(max,min) ? >>> >>> The idea being if the sphere is completely inside the AABB that the >>> volume returned would be that of the sphere and as the sphere moves >>> out of the AABB the volume drops to zero. >>> >>> I've googled but haven't been able to find anything. >>> >>> Thanks, >>>  >>> John McCutchan <john@...> >>> >>>  >>> SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, >>> Nevada. >>> The future of the web can't happen without you. Join us at MIX09 to help >>> pave the way to the Next Web now. Learn more and register at >>> http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ >>> _______________________________________________ >>> GDAlgorithmslist mailing list >>> GDAlgorithmslist@... >>> https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >>> Archives: >>> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist >>> >>> >>  >> SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. >> The future of the web can't happen without you. Join us at MIX09 to help >> pave the way to the Next Web now. Learn more and register at >> http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ >> _______________________________________________ >> GDAlgorithmslist mailing list >> GDAlgorithmslist@... >> https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >> Archives: >> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist >> >> > > > > 
From: Jay Stelly <J<ay@va...>  20081208 22:21:15

I really think whoever suggested building it back up from an integral had the right idea. Without putting a ton of thought into it, I would expect you could start with something like this: http://celtickane.com/school/math_circle.php Then you'd remove the symmetry and build this up to a sphere/volume. Then you need to factor in the intersection's effect on the bounds of each dimension's integral. I think that will give you four sets of integral bounds (sphere or box at each min/max) per dimension so 64 possible equations? Then you'd just do the intersection and that would select and parameterize the analytic integral solution from the set of 64. Then you evaluate that equation. I'd definitely do it numerically if you could because that would be a 5minute coding job. The analytical answer seems like a fair amount more work but still doable  but then I haven't done the work so I'm probably still missing something. Is there some way to use symmetry to eliminate a bunch of those equations? Maybe there's a more clever way involving determining the overlapping volume so you could do each dimension independently or something? Jay > Original Message > From: Jon Watte [mailto:jwatte@...] > Sent: Monday, December 08, 2008 12:28 PM > To: Game Development Algorithms > Subject: Re: [Algorithms] Volume of intersection of sphere and AABB > > > Yes, I agree, you also have to test for sphere/face penetration cases > separately. The corner vertex test is useful when the center of the > sphere is outside the union of the slabs that define the box. > > Sincerely, > > jw > > > Osman, Brian wrote: > > But that doesn't catch all cases, does it? What about when > the sphere > > penetrates one side of the box, but with a shallow enough > penetration > > that it never reaches any of the corners. The trivial > version of this is > > when the sphere's radius is much smaller than the sides of > the box, and > > the sphere centered on one side of the box. > > > > I can't imagine solving this from scratch ... I'd certainly > seek out the > > existing CSG methods, and work from there. > > > > Brian > > > > > > Original Message > > From: Jon Watte [mailto:jwatte@...] > > Sent: Friday, December 05, 2008 7:25 PM > > To: Game Development Algorithms > > Subject: Re: [Algorithms] Volume of intersection of sphere and AABB > > > > > > Oh, and I forgot to mention: one way to classify which of the cases > > you're dealing with is to check whether each vertex of the > box is inside > > > > or outside the sphere. The sphere intersects the sides > where at least > > one vertex is inside the sphere (I think a side that's fully inside > > still should be treated as a cutting plane). > > > > Sincerely, > > > > jw > > > > >  >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las > Vegas, Nevada. > The future of the web can't happen without you. Join us at > MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009 > .visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgo > rithmslist > 
From: Vincent Scheib <vsglists@gm...>  20081208 21:59:04

For the people who found the photoshop blend mode article handy, I thought I'd offer this link. I've found it most useful for a quick photoshop blend math reference: http://dunnbypaul.net/blends/ 
From: metanet software <metanet_gda4@ya...>  20081208 21:57:53

thanks! Right now I'm getting pretty good results by initializing all r = rMax and then solving the s<t constraints; the main problem with this is that each frame I have to start from scratch.. your idea sounds promising in that it will let me "warm start" things using the previous frame's solution.  On Mon, 12/8/08, Patrick Betremieux <Patrick@...> wrote: > From: Patrick Betremieux <Patrick@...> > Subject: Re: [Algorithms] Solving a system of line equations  SimpleVersion ; ) > To: "Game Development Algorithms" <gdalgorithmslist@...> > Received: Monday, December 8, 2008, 1:30 PM > I see two problems with those two constraints being in the > same solver > pass. First, the two constraints are really opposite of > each other. And > since this problem has a range of solutions per segment, > and no local > minimum, you will likely get the solver to just ping pong > back and forth > around valid solutions. And if you run this as the user > moves a point, > you might very well get all the segments to randomly switch > between > valid solutions each frame. > > Since one of your constraints is softer then the other (s > < t is an > absolute, whereas r being close to rMax is just to make it > better), I > would just iteratively expand the r's one segment at a > time until they > all reach their max, or would cause s >= t. First > compute for all > segments by how much it could grow its r without causing > problems. Then > iteratively pick the segment that has the least room to > grow its r and > expand it as much as possible. Recompute the new growth > potential of the > two neighbours, and repeat until you've gone through > all the segments. > At least, this would have the benefit of giving you the > same answer each > time you run it, but you'd have to add some heuristic > for which solution > you're more interested in (Maximizing one r might make > another one > needing to be zero, which might not be good) > > Patrick. > > Original Message > From: metanet software [mailto:metanet_gda4@...] > Sent: Friday, December 05, 2008 12:08 PM > To: gdalgorithmslist@... > Subject: Re: [Algorithms] Solving a system of line > equations  > SimpleVersion ; ) > > I've gotten the basic solver working, but I'm still > struggling with how > to deal with additional constraints, such as: > > drive r[] values towards targets (minimize targ[i]  > r[i]) > enforce a minimum allowable r value (make sure r[i] > > rmin) > > Currently I'm adding these as additional constraints > the solver has to > deal with; this makes sense for enforcing the minimum > allowable value, > but it seems wrong to drive r[] values towards targets > using > constraints, since they almost always directly > "fight" with the main > constraints.. causing the solver to fail to converge to a > solution. > > Raigan > > > >  On Fri, 12/5/08, metanet software > <metanet_gda4@...> wrote: > > > From: metanet software <metanet_gda4@...> > > Subject: [Algorithms] Solving a system of line > equations  Simple > Version ; ) > > To: gdalgorithmslist@... > > Received: Friday, December 5, 2008, 10:20 AM > > My first form of this question was needlessly obtuse, > this > > version should be much more comprehensible! > > > > I have the following system: > > http://www.harveycartel.org/raigan/system.jpg > > > > I'd like to solve for r0,r1,r2 such that s < t; > > obviously setting r0=r1=r2=0 is a trivial solution; > I'm > > more interested in driving r0,r1,r2 towards target > values > > r0max,r1max,r2max while maintaining the constraint s > < t. > > > > My current plan is to construct the constraint > equation C = > > s  t < 0 and then solve for the r values (by > calculating > > the partial derivatives of C wrt r[i] and doing a > > nonlinearleastsquares fit as in > > > http://www.matthiasmueller.info/publications/posBasedDyn.pdf > > ). > > > > However even if this works, I have no idea how to > > simultaneously minimize (rmax[i]  r[i]), i.e how I > should > > drive the r values towards target values while obeying > C. > > > > Sorry for the totally obfuscated initial question.. > thanks > > for your time! > > > > Raigan > > > > p.s  Just in case it's not clear from the > diagram, s > > and t are the parametric times of intersection between > > lines; each line is parallel to a segment (p[i+1]  > p[i]) > > and passes through the point p[i] + r[i]*Perp(p[i+1]  > > p[i])/Len(p[i+1]  p[i]).. i.e each line is just a > > linesegment offset along its normal. > > > > > > > > > > > __________________________________________________________________ > > Looking for the perfect gift? Give the gift of Flickr! > > > > > http://www.flickr.com/gift/ > > > > >  >  > > SF.Net email is Sponsored by MIX09, March 1820, 2009 > in > > Las Vegas, Nevada. > > The future of the web can't happen without you. > Join > > us at MIX09 to help > > pave the way to the Next Web now. Learn more and > register > > at > > > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. > com/ > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis > t > > > > __________________________________________________________________ > Yahoo! Canada Toolbar: Search from anywhere on the web, and > bookmark > your favourite sites. Download it now at > http://ca.toolbar.yahoo.com. > >  >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in > Las Vegas, > Nevada. > The future of the web can't happen without you. Join > us at MIX09 to > help > pave the way to the Next Web now. Learn more and register > at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. > com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis > t > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in > Las Vegas, Nevada. > The future of the web can't happen without you. Join > us at MIX09 to help > pave the way to the Next Web now. Learn more and register > at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist __________________________________________________________________ Yahoo! Canada Toolbar: Search from anywhere on the web, and bookmark your favourite sites. Download it now at http://ca.toolbar.yahoo.com. 
From: Jon Watte <jwatte@gm...>  20081208 20:30:34

Yes, I agree, you also have to test for sphere/face penetration cases separately. The corner vertex test is useful when the center of the sphere is outside the union of the slabs that define the box. Sincerely, jw Osman, Brian wrote: > But that doesn't catch all cases, does it? What about when the sphere > penetrates one side of the box, but with a shallow enough penetration > that it never reaches any of the corners. The trivial version of this is > when the sphere's radius is much smaller than the sides of the box, and > the sphere centered on one side of the box. > > I can't imagine solving this from scratch ... I'd certainly seek out the > existing CSG methods, and work from there. > > Brian > > > Original Message > From: Jon Watte [mailto:jwatte@...] > Sent: Friday, December 05, 2008 7:25 PM > To: Game Development Algorithms > Subject: Re: [Algorithms] Volume of intersection of sphere and AABB > > > Oh, and I forgot to mention: one way to classify which of the cases > you're dealing with is to check whether each vertex of the box is inside > > or outside the sphere. The sphere intersects the sides where at least > one vertex is inside the sphere (I think a side that's fully inside > still should be treated as a cutting plane). > > Sincerely, > > jw > 
From: Jon Watte <jwatte@gm...>  20081208 20:30:29

Stefan Dänzer wrote: > I want to implement an opensource library for fast mesh skinning. > Mesh skinning is widely used in character animation. I want to > implement such an algorithm for surgical training simulation. The idea > is to have different resolutions of a 3D model, usually this model > represents a human organ. Deformations are applied to a lowres > version of the model. A highres model is coupled by mesh skinning to > the lowres model. The highres model is then rendered. I was > wondering if someone has experience in this filed and could provide me > with useful references for a start. What you talk about doesn't sound like skinning. In skinning, you "drape" a skin across a skeleton of articulated joints. It sounds like what you're trying to do would be better served by treating the lowerresolution mesh as a control cage for some higherorder surface. Sincerely, jw 
From: Patrick Betremieux <P<atrick@li...>  20081208 18:25:25

I see two problems with those two constraints being in the same solver pass. First, the two constraints are really opposite of each other. And since this problem has a range of solutions per segment, and no local minimum, you will likely get the solver to just ping pong back and forth around valid solutions. And if you run this as the user moves a point, you might very well get all the segments to randomly switch between valid solutions each frame. Since one of your constraints is softer then the other (s < t is an absolute, whereas r being close to rMax is just to make it better), I would just iteratively expand the r's one segment at a time until they all reach their max, or would cause s >= t. First compute for all segments by how much it could grow its r without causing problems. Then iteratively pick the segment that has the least room to grow its r and expand it as much as possible. Recompute the new growth potential of the two neighbours, and repeat until you've gone through all the segments. At least, this would have the benefit of giving you the same answer each time you run it, but you'd have to add some heuristic for which solution you're more interested in (Maximizing one r might make another one needing to be zero, which might not be good) Patrick. Original Message From: metanet software [mailto:metanet_gda4@...] Sent: Friday, December 05, 2008 12:08 PM To: gdalgorithmslist@... Subject: Re: [Algorithms] Solving a system of line equations  SimpleVersion ; ) I've gotten the basic solver working, but I'm still struggling with how to deal with additional constraints, such as: drive r[] values towards targets (minimize targ[i]  r[i]) enforce a minimum allowable r value (make sure r[i] > rmin) Currently I'm adding these as additional constraints the solver has to deal with; this makes sense for enforcing the minimum allowable value, but it seems wrong to drive r[] values towards targets using constraints, since they almost always directly "fight" with the main constraints.. causing the solver to fail to converge to a solution. Raigan  On Fri, 12/5/08, metanet software <metanet_gda4@...> wrote: > From: metanet software <metanet_gda4@...> > Subject: [Algorithms] Solving a system of line equations  Simple Version ; ) > To: gdalgorithmslist@... > Received: Friday, December 5, 2008, 10:20 AM > My first form of this question was needlessly obtuse, this > version should be much more comprehensible! > > I have the following system: > http://www.harveycartel.org/raigan/system.jpg > > I'd like to solve for r0,r1,r2 such that s < t; > obviously setting r0=r1=r2=0 is a trivial solution; I'm > more interested in driving r0,r1,r2 towards target values > r0max,r1max,r2max while maintaining the constraint s < t. > > My current plan is to construct the constraint equation C = > s  t < 0 and then solve for the r values (by calculating > the partial derivatives of C wrt r[i] and doing a > nonlinearleastsquares fit as in > http://www.matthiasmueller.info/publications/posBasedDyn.pdf > ). > > However even if this works, I have no idea how to > simultaneously minimize (rmax[i]  r[i]), i.e how I should > drive the r values towards target values while obeying C. > > Sorry for the totally obfuscated initial question.. thanks > for your time! > > Raigan > > p.s  Just in case it's not clear from the diagram, s > and t are the parametric times of intersection between > lines; each line is parallel to a segment (p[i+1]  p[i]) > and passes through the point p[i] + r[i]*Perp(p[i+1]  > p[i])/Len(p[i+1]  p[i]).. i.e each line is just a > linesegment offset along its normal. > > > > > __________________________________________________________________ > Looking for the perfect gift? Give the gift of Flickr! > > http://www.flickr.com/gift/ > >   > SF.Net email is Sponsored by MIX09, March 1820, 2009 in > Las Vegas, Nevada. > The future of the web can't happen without you. Join > us at MIX09 to help > pave the way to the Next Web now. Learn more and register > at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis t __________________________________________________________________ Yahoo! Canada Toolbar: Search from anywhere on the web, and bookmark your favourite sites. Download it now at http://ca.toolbar.yahoo.com.   SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. The future of the web can't happen without you. Join us at MIX09 to help pave the way to the Next Web now. Learn more and register at http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. com/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis t 
From: John McCutchan <john@jo...>  20081207 16:30:45

Thanks everyone for your suggestions and interesting conversation. The reason I asked was that I'm trying to determine how much volume of an object (discretized into spheres) is submerged under a height field (discretized into AABBs) and need to do this many times per frame. I think I've figured out a cheap solution that should give reasonable results (never count a submerged sphere twice.) Thanks, John On Sun, Dec 7, 2008 at 5:24 AM, Willem H. de Boer <willem@...> wrote: > Do you need an accurate answer? If accuracy is something > you wouldn't mind say compute over several frames, then > you could use a simple Monte Carlolike scheme. (Though > I think the number of sample points required is low enough > to be able to compute the volume in realtime) > > One could proceed by generating random points inside > the union of the AABB and the sphere, the total volume, > V, of which is easy to calculate ofcourse. > > Then only keep those points that lie within the intersection > of the AABB and the sphere and keep track of the ratio of > points within to the total number of points generated, call > this r_n. > > Then after a suitable number of points generated, the volume is > roughly r_n * V. > > The trouble with finding an analytic description of the volume > is that the domain of integration (i.e. the intersection of AABB > and sphere) is usually difficult to parametrise. In such cases > MClike schemes work very well. > > Cheers, > Willem > >  Original Message  > From: "John McCutchan" <john@...> > To: "Game Development Algorithms" <gdalgorithmslist@...> > Sent: Friday, December 05, 2008 10:00 PM > Subject: [Algorithms] Volume of intersection of sphere and AABB > > >> Hi, >> >> I'm wondering if anyone has an idea of how to compute the volume of >> the intersection of a sphere (center, radius) and an AABB(max,min) ? >> >> The idea being if the sphere is completely inside the AABB that the >> volume returned would be that of the sphere and as the sphere moves >> out of the AABB the volume drops to zero. >> >> I've googled but haven't been able to find anything. >> >> Thanks, >>  >> John McCutchan <john@...> >> >>  >> SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, >> Nevada. >> The future of the web can't happen without you. Join us at MIX09 to help >> pave the way to the Next Web now. Learn more and register at >> http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ >> _______________________________________________ >> GDAlgorithmslist mailing list >> GDAlgorithmslist@... >> https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >> Archives: >> http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist >> > > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. > The future of the web can't happen without you. Join us at MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist >  John McCutchan <john@...> 
From: Stefan Dänzer <stefan.daenzer@gm...>  20081207 14:34:41

Hi, I want to implement an opensource library for fast mesh skinning. Mesh skinning is widely used in character animation. I want to implement such an algorithm for surgical training simulation. The idea is to have different resolutions of a 3D model, usually this model represents a human organ. Deformations are applied to a lowres version of the model. A highres model is coupled by mesh skinning to the lowres model. The highres model is then rendered. I was wondering if someone has experience in this filed and could provide me with useful references for a start. Stefan  "Work like you don't need the money, love like you've never been hurt and dance like no one is watching."  Randall G Leighton 
From: Willem H. de Boer <willem@wh...>  20081207 13:24:49

Do you need an accurate answer? If accuracy is something you wouldn't mind say compute over several frames, then you could use a simple Monte Carlolike scheme. (Though I think the number of sample points required is low enough to be able to compute the volume in realtime) One could proceed by generating random points inside the union of the AABB and the sphere, the total volume, V, of which is easy to calculate ofcourse. Then only keep those points that lie within the intersection of the AABB and the sphere and keep track of the ratio of points within to the total number of points generated, call this r_n. Then after a suitable number of points generated, the volume is roughly r_n * V. The trouble with finding an analytic description of the volume is that the domain of integration (i.e. the intersection of AABB and sphere) is usually difficult to parametrise. In such cases MClike schemes work very well. Cheers, Willem  Original Message  From: "John McCutchan" <john@...> To: "Game Development Algorithms" <gdalgorithmslist@...> Sent: Friday, December 05, 2008 10:00 PM Subject: [Algorithms] Volume of intersection of sphere and AABB > Hi, > > I'm wondering if anyone has an idea of how to compute the volume of > the intersection of a sphere (center, radius) and an AABB(max,min) ? > > The idea being if the sphere is completely inside the AABB that the > volume returned would be that of the sphere and as the sphere moves > out of the AABB the volume drops to zero. > > I've googled but haven't been able to find anything. > > Thanks, >  > John McCutchan <john@...> > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, > Nevada. > The future of the web can't happen without you. Join us at MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist > 
From: Ben SunshineHill <sneftel@gm...>  20081206 20:49:47

On Fri, Dec 5, 2008 at 5:00 PM, John McCutchan <john@...> wrote: > Hi, > > I'm wondering if anyone has an idea of how to compute the volume of > the intersection of a sphere (center, radius) and an AABB(max,min) ? Doesn't sound like too difficult of a problem. The candidate points, the extrema of which form the resultant AABB, will come from the extrema of the intersections of the sphere with each face of the original AABB, and the extrema of the sphere itself (the six intersection points of the sphere and the faces of its own AABB) which are inside the original AABB. Determine which planes on the original AABB intersect the sphere, find the extrema of any intersection between the corresponding faces and the sphere, and union the results, plus the aforementioned sphere extrema, into an AABB. Ben 
From: David Dynerman <dynerman@cs...>  20081206 19:55:27

Just a thought  is the volume removed from a sphere by a cutting plane proportional to the distance from the origin of the sphere to the plane? That probably wouldn't work for the sphere intersecting more than one side though. Osman, Brian wrote: > But that doesn't catch all cases, does it? What about when the sphere > penetrates one side of the box, but with a shallow enough penetration > that it never reaches any of the corners. The trivial version of this is > when the sphere's radius is much smaller than the sides of the box, and > the sphere centered on one side of the box. > > I can't imagine solving this from scratch ... I'd certainly seek out the > existing CSG methods, and work from there. > > Brian > > > Original Message > From: Jon Watte [mailto:jwatte@...] > Sent: Friday, December 05, 2008 7:25 PM > To: Game Development Algorithms > Subject: Re: [Algorithms] Volume of intersection of sphere and AABB > > > Oh, and I forgot to mention: one way to classify which of the cases > you're dealing with is to check whether each vertex of the box is inside > > or outside the sphere. The sphere intersects the sides where at least > one vertex is inside the sphere (I think a side that's fully inside > still should be treated as a cutting plane). > > Sincerely, > > jw > > > John McCutchan wrote: >> Hi, >> >> I'm wondering if anyone has an idea of how to compute the volume of >> the intersection of a sphere (center, radius) and an AABB(max,min) ? >> >> The idea being if the sphere is completely inside the AABB that the >> volume returned would be that of the sphere and as the sphere moves >> out of the AABB the volume drops to zero. >> >> I've googled but haven't been able to find anything. >> >> Thanks, >> > > >  >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, > Nevada. > The future of the web can't happen without you. Join us at MIX09 to > help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. > com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis > t > >  > SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. > The future of the web can't happen without you. Join us at MIX09 to help > pave the way to the Next Web now. Learn more and register at > http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist 
From: Osman, Brian <BO<sman@vv...>  20081206 16:52:32

But that doesn't catch all cases, does it? What about when the sphere penetrates one side of the box, but with a shallow enough penetration that it never reaches any of the corners. The trivial version of this is when the sphere's radius is much smaller than the sides of the box, and the sphere centered on one side of the box. I can't imagine solving this from scratch ... I'd certainly seek out the existing CSG methods, and work from there. Brian Original Message From: Jon Watte [mailto:jwatte@...] Sent: Friday, December 05, 2008 7:25 PM To: Game Development Algorithms Subject: Re: [Algorithms] Volume of intersection of sphere and AABB Oh, and I forgot to mention: one way to classify which of the cases you're dealing with is to check whether each vertex of the box is inside or outside the sphere. The sphere intersects the sides where at least one vertex is inside the sphere (I think a side that's fully inside still should be treated as a cutting plane). Sincerely, jw John McCutchan wrote: > Hi, > > I'm wondering if anyone has an idea of how to compute the volume of > the intersection of a sphere (center, radius) and an AABB(max,min) ? > > The idea being if the sphere is completely inside the AABB that the > volume returned would be that of the sphere and as the sphere moves > out of the AABB the volume drops to zero. > > I've googled but haven't been able to find anything. > > Thanks, >   SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. The future of the web can't happen without you. Join us at MIX09 to help pave the way to the Next Web now. Learn more and register at http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix. com/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslis t 
From: Alen Ladavac <alenlml@cr...>  20081206 12:04:13

Saturday, December 6, 2008, 1:12:17 AM, Wessam wrote: >> The last time I checked (CS2?), an option for linear space operation was available only for some operations >> (image resizing?), but not for general blending, and was in some obscure place in the prefs. > It’s been in Photoshop a while ago. Edit >> Color Settings > (Check) Advanced Mode > (Check) Blend RGB Colors Using Gamma. > It affects all transparency blends (including layer transparencies). Sorry, my bad. Yes that's the option. I've misremembered the way it works. It applies to blending, but it curiously doesn't apply to image resizing. I remember it seemed strange, because resizing is the textbook example of how operating in gamma space can produce wrong results: #1 Create an image filled with pixelwide black/white stripe pattern. #2 Downscale it 2x2 using bilinear filtering. #3 Upscale it back. #4 Compare it visually with the original when viewed from a distance. If resampling was done in gamma space, the result will _much_ darker than the original. When I was trying to demonstrate this kind of artefact to our artists, I was expecting that I would be able to demonstrate how Photoshop is able to do the resizing correctly if the color settings are right, but alas.... To do a correct image resize in PS, one has to do strange tricks with converting the image to linear color using the levels dialog (a strange place for a gamma conversion tool, isn't it?), then resize, then go back to gamma space. And this has to be done with 16bit per component precision of course. In the end it is really complicated, so I gave up and let our artists continue to do image resizing the wrong way. Sadly, Gimp seems to follow the stray path of PS, and even the gamma conversion is placed in the same dialog, etc. :( If you know of a way to do resizing correctly in PS, please do let me know! Cheers, Alen 
From: Wessam Bahnassi <wbahnassi@in...>  20081206 00:35:59

> Yes, Photoshop is "backward compatible" with the way image blending was done "back in the early days...". > The last time I checked (CS2?), an option for linear space operation was available only for some operations > (image resizing?), but not for general blending, and was in some obscure place in the prefs. It’s been in Photoshop a while ago. Edit > Color Settings > (Check) Advanced Mode > (Check) Blend RGB Colors Using Gamma. It affects all transparency blends (including layer transparencies). وسام البهنسي مبرمج  إليكترونيك آرتس  Wessam Bahnassi Microsoft DirectX MVP, Programmer  Electronic Arts Inc.  الشبكة العربية لمطوري الألعاب Arabic Game Developer Network http://www.agdnonline.com From: Alen Ladavac [mailto:alenlml@...] Sent: Thursday, December 04, 2008 10:15 AM To: Jesús de Santos García Cc: Game Development Algorithms Subject: Re: [Algorithms] Common Src/DestAlphaBlend mode combinations Yes, Photoshop is "backward compatible" with the way image blending was done "back in the early days...". The last time I checked (CS2?), an option for linear space operation was available only for some operations (image resizing?), but not for general blending, and was in some obscure place in the prefs. I'm still stunned that such a large bunch of experienced programmers working on the most popular graphics app in the world have not come to fix this for so long. Probably because 99% users consider this as "correct behaviour". Then again, other apps, like Gimp, are no better (AFAIK), so go figure... JM2C, Alen Jesús wrote: > To avoid driver issues and the card not behaving like it should I took screenshots from Photoshop and ExpressionBlend to analyze how the blending was being done. And my conclusion was that is was being done in sRGB space (in theory the wrong one). May be, my photoshop configuration was not right and playing with the profiles can change the result, or may be the technique of taking screenshots and analyzing the raw bytes is not correct. But it was a surprise to me and we decided to do the blend in sRGB space to exactly have the same result that the artist was having. I'd like to know if more people experimented with this. On Wed, Dec 3, 2008 at 17:42, Jason Hughes < <mailto:jason_hughes@...> jason_hughes@...> wrote: I'm not sure if this is the same issue you experienced or not, but when I went down the premultiplied alpha path and learned how to set up my textures and blend modes to take advantage of it, I ran across some unexpected roadblocks with low end hardware. Fixed function intel chips, specifically, which I am guessing are similar to earlier fixed function hardware. I could set the texture surface to be linear, but that destroyed my color fidelity in the low end (darks) which gave me banding. I could set the rendered surface to be linear, as well as setting the presentation to require linear>sRGB conversion, but that only seemed to darken the scene and reduce color fidelity. In the end, it appeared (though I didn't test numerically or exhaustively) that the GPU was automatically converting sRGB to linear when fetching from the texture and frame buffer, then converting back when storing out. The PMA looked right but only when I didn't try to be fancy about the surfaces involved. YMMV, JH Jesús de Santos García wrote: I wonder if those formulas are exactly correct... I mean, for example in the additive mode the sum operation is being done in sRGB space (not in linear as it should be in theory). We had a similar problem when interpreting XAML for our gui. We wanted the final render to look exactly as it appeared in an editor (Expression Blend) and we had do switch off the blending in linear space. On Tue, Dec 2, 2008 at 00:46, Guido Henkel < <mailto:ghenkel@...> ghenkel@...> wrote: You may want to take a look at this page <http://www.pegtop.net/delphi/articles/blendmodes/>; http://www.pegtop.net/delphi/articles/blendmodes/ Guido Henkel, CEO G3 Studios  <http://www.g3studios.com>; http://www.g3studios.com  BLACK JACK PRO is now available also for the iPhone! Don't miss the best version yet <http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=288915774&mt=8>; http://phobos.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=288915774&mt=8  This response and any files transmitted with it are confidential and intended solely for the use of the individual or entity to whom they are addressed. If you are not the intended recipient, you should not copy it, retransmit it, use it, disclose its contents, but should return it to the sender immediately and delete your copy from your system. On Dec 1, 2008, at 3:24 PM, Peter Higley wrote: > Hello, > > I recently wanted to provide a list of common/useful combination of > source and destination blend modes for a DirectX graphics > application. I know that it is common to use custom pixel shaders > to do almost everything these days, but I thought a set of "classic" > hardwired blend modes would be easy enough to add. Odd thing is, I > couldn't find a list of common combinations. There is a > multiplicative/normal mode (srcblend = srcalpha, destblend = > invsrcalpha), there is an additive mode (srcblend = srcalpha, > destblend = one). I worked out a "screen" mode (srcblend = one, > destblend = invsrccolor) which is similar to PhotoShop's screen mode. > > I know that there are other useful combinations. What have you used? > > Peter >  > This SF.Net email is sponsored by the Moblin Your Move Developer's > challenge > Build the coolest Linux based applications with Moblin SDK & win > great prizes > Grand prize is a trip for two to an Open Source event anywhere in > the world > <http://moblincontest.org/redirect.php?banner_id=100&url=/_______________________________________________>; http://moblincontest.org/redirect.php?banner_id=100&url=/_______________________________________________ > GDAlgorithmslist mailing list > <mailto:GDAlgorithmslist@...> GDAlgorithmslist@... > <https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist>; https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > <http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist>; http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist  This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world <http://moblincontest.org/redirect.php?banner_id=100&url=/>; http://moblincontest.org/redirect.php?banner_id=100&url=/ _______________________________________________ GDAlgorithmslist mailing list <mailto:GDAlgorithmslist@...> GDAlgorithmslist@... <https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist>; https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: <http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist>; http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist _____  This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the wo <http://moblincontest.org/redirect.php?banner_id=100&url=/>; http://moblincontest.org/redirect.php?banner_id=100&url=/ _____ _______________________________________________ GDAlgorithmslist mailing lis <mailto:GDAlgorithmslist@...> GDAlgorithmslist@... <https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist>; https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives <http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist>; http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist  This SF.Net email is sponsored by the Moblin Your Move Developer's challenge Build the coolest Linux based applications with Moblin SDK & win great prizes Grand prize is a trip for two to an Open Source event anywhere in the world <http://moblincontest.org/redirect.php?banner_id=100&url=/>; http://moblincontest.org/redirect.php?banner_id=100&url=/ _______________________________________________ GDAlgorithmslist mailing list <mailto:GDAlgorithmslist@...> GDAlgorithmslist@... <https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist>; https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: <http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist>; http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist  Alen 
From: Jon Watte <jwatte@gm...>  20081206 00:25:18

Oh, and I forgot to mention: one way to classify which of the cases you're dealing with is to check whether each vertex of the box is inside or outside the sphere. The sphere intersects the sides where at least one vertex is inside the sphere (I think a side that's fully inside still should be treated as a cutting plane). Sincerely, jw John McCutchan wrote: > Hi, > > I'm wondering if anyone has an idea of how to compute the volume of > the intersection of a sphere (center, radius) and an AABB(max,min) ? > > The idea being if the sphere is completely inside the AABB that the > volume returned would be that of the sphere and as the sphere moves > out of the AABB the volume drops to zero. > > I've googled but haven't been able to find anything. > > Thanks, > 
From: Darren Grant <dgrant@ke...>  20081205 23:59:04

The first thing that comes to mind is to start with 'the integral of circular slabs' approach. That will get you an easy volume by integrating across a box axis instead of the entire sphere. Modifying the slab (circle) area equation similarly so that each circle is bounded by the four remaining edges should get you the rest of the way. (Haven't tried this so I can't say it won't be ugly, but it does help that the edges are mutually orthogonal so their equations become constant values.) It also seems like this would be a fairly common csg problem.. and approximating the initial sphere with a convex polytope and clipping that against the planes of the box is another option in that field. Regards, Darren At 02:00 PM 12/5/2008, John McCutchan wrote: >Hi, > >I'm wondering if anyone has an idea of how to compute the volume of >the intersection of a sphere (center, radius) and an AABB(max,min) ? > >The idea being if the sphere is completely inside the AABB that the >volume returned would be that of the sphere and as the sphere moves >out of the AABB the volume drops to zero. > >I've googled but haven't been able to find anything. > >Thanks, > >John McCutchan <john@...> > > >SF.Net email is Sponsored by MIX09, March 1820, 2009 in Las Vegas, Nevada. >The future of the web can't happen without you. Join us at MIX09 to help >pave the way to the Next Web now. Learn more and register at >http://ad.doubleclick.net/clk;208669438;13503038;i?http://2009.visitmix.com/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_name=gdalgorithmslist > > > >No virus found in this incoming message. >Checked by AVG. >Version: 7.5.552 / Virus Database: 270.9.14/1832  Release Date: >12/5/2008 9:57 AM 
From: Gregory Junker <gjunker@da...>  20081205 23:41:33

> On Fri, Dec 5, 2008 at 2:41 PM, Gregory Junker > <gjunker@...> wrote: > >> > >> I'm wondering if anyone has an idea of how to compute the volume of > >> the intersection of a sphere (center, radius) and an > AABB(max,min) ? > >> > >> The idea being if the sphere is completely inside the AABB that the > >> volume returned would be that of the sphere and as the sphere moves > >> out of the AABB the volume drops to zero. > >> > >> I've googled but haven't been able to find anything. > >> > > > > I think you are looking for Constructive Solid Geometry algorithms? > > Am I? I don't want the geometry, I'm looking for the scalar > measurement of the volume of space contained in the geometry. > CSG is all about intersections of objects in 3D space. Once you have completed the boolean operation on your shapes, then you have something with which you can compute a volume. Given that the relative positions of your two objects can be completely arbitrary, there is no analytical solution of which I am aware. Is the sphere intersecting one face? Two? Three? All 6? I have to say, this isn't something you likely are going to want to do every frame. Is there a higherlevel goal you are trying to achieve? Perhaps there is a different solution that serves your needs. Greg 
From: John McCutchan <john@jo...>  20081205 23:23:12

On Fri, Dec 5, 2008 at 2:41 PM, Gregory Junker <gjunker@...> wrote: >> >> I'm wondering if anyone has an idea of how to compute the volume of >> the intersection of a sphere (center, radius) and an AABB(max,min) ? >> >> The idea being if the sphere is completely inside the AABB that the >> volume returned would be that of the sphere and as the sphere moves >> out of the AABB the volume drops to zero. >> >> I've googled but haven't been able to find anything. >> > > I think you are looking for Constructive Solid Geometry algorithms? Am I? I don't want the geometry, I'm looking for the scalar measurement of the volume of space contained in the geometry.  John McCutchan <john@...> 
From: Gregory Junker <gjunker@da...>  20081205 23:09:16

> > I'm wondering if anyone has an idea of how to compute the volume of > the intersection of a sphere (center, radius) and an AABB(max,min) ? > > The idea being if the sphere is completely inside the AABB that the > volume returned would be that of the sphere and as the sphere moves > out of the AABB the volume drops to zero. > > I've googled but haven't been able to find anything. > I think you are looking for Constructive Solid Geometry algorithms? Greg 
From: John McCutchan <john@jo...>  20081205 22:30:47

Hi, I'm wondering if anyone has an idea of how to compute the volume of the intersection of a sphere (center, radius) and an AABB(max,min) ? The idea being if the sphere is completely inside the AABB that the volume returned would be that of the sphere and as the sphere moves out of the AABB the volume drops to zero. I've googled but haven't been able to find anything. Thanks,  John McCutchan <john@...> 