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From: <phil_wilkins@pl...>  20020918 18:06:48

I use a parametric model for my particle system, that includes drag by using an exp(kt) component. But then VU1 can do that in parallel with the rest of the particle code, as it has a dedicated unit (the EFU) with it's own fmac and fdiv for that sort of thing. Cheers, Phil "Hansen, Daniel" <Daniel.Hansen@...> To: gdalgorithmslist@... Sent by: cc: gdalgorithmslistadmin@... Subject: RE: [Algorithms] Simple Air Resistance Simulation eforge.net for Shells 09/18/2002 01:21 AM Has anyone parametricized the velocity and position taking airresistance into consideration. I.e v(t) = v0 + a * t p(t) = p0 + (v0 + 0.5 * a * t) * t ..could be used when there's no airresistance. I'd like something similar with airresistance. I've seen some formulas with alot of nasty exponents in them, I'm looking for a simpler hack. Anyone? Original Message From: Charles Bloom [mailto:cbloom@...] Sent: den 11 september 2002 07:58 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells This "midpoint method" is 2nd order RungeKutta. See, for example : http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html http://csep1.phy.ornl.gov/ode/node7.html The traditional socalled "RungeKutta method" is the 4th order method. Anyway, all silliness, but some of the stuff on the web is pretty good. At 12:19 AM 9/11/2002 0400, jack@... wrote: >Thanks to all. Using the midpoint method combined with a small enough time >step appears to provide a reasonable amount of accuracy for my use. I'll >keep RungeKutta in mind for future use if it proves necessary. > >Jack > >Original Message >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] >Sent: Monday, September 09, 2002 2:52 PM >To: Jon Watte; jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >Even using something as simple as the midpoint method (a secondorder >integrator) will give much better results for minimal effort. RungeKutta >is probably overkill... ? > >v_intermediate= v  0.5*k(v^2)t; >v_final= v  k(v_intermediate^2)t; > > >Chris Butcher >Rendering & Simulation Lead >Halo 2  Bungie Studios >butcher@... > > >Original Message >From: Jon Watte [mailto:hplus@...] >Sent: Monday, September 09, 2002 12:43 >To: jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >> I'm trying to do a simple ballistics model for shells. The formula I'm >> using is: >> >> v' = v  k(v^2)t; > >This is a firstorder Euler integrator (I believe). These are known >to be unstable at any time step  as you notice :) > >The typical answer when faced with numerical integration problems >is to turn to a fourthorder RungeKutta integrator. I'm sure if you >plug that into Google, you'll get a massive number of hits. It might >show up on MathWorld, too. > >Cheers, > > / h+ > > > > > >mail2web  Check your email from the web at >http://mail2web.com/ . > > > > > >In remembrance >www.osdn.com/911/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88 >  Charles Bloom cb@... http://www.cbloom.com  In remembrance http://www.osdn.com/911/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: PeterPike Sloan <ppsloan@mi...>  20020918 18:00:33

I believe this is just the differential solid angle for the sphere map parameterization. Using sin(theta) would only be correct for a lat/long parameterization... PeterPike (I don't think this has anything to do with low pass filters...) Original Message From: Bert.Peers@... [mailto:Bert.Peers@...]=20 Sent: Wednesday, September 18, 2002 4:48 AM To: gdalgorithmslist@... Subject: RE: [Algorithms] Solid angle calculation > > > domega =3D (2*PI/width)*(2*PI/width)*sinc(theta) ; > > >=20 > > > I understand where the / width comes from since you are > > integrating in > > > steps of 1/width over the sphere, but I fail to understand what > > > sinc(theta) means. > We know what sinc _is_  Joris even gave the code for it. The > question is > why is it being used here? On a hunch : because they are using proper monte carlo integration around (rather than just taking a single point=20 sample at) the angle of interest, during which they use the sync as a lowpass filter to remove frequencies=20 beyond the nyquist limit ? So that would basically be a misleading name  it's not just the differential angle required by the numerical integration, it's also carrying the value of the filter being convolved with. I would expect to see a double loop, whereas the net samples you mention that don't use sinc, only have one loop. Or maybe not :) Bert  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=3D6188 
From: Jon Watte <hplus@mi...>  20020918 17:12:55

> Well an analytic solution is what I'm after. I've only seen very nasty > long (read slow) equations. I need somethinbg simpler (faster). Here's one possible approach to the problem of finding a "fast" analytical approximation of some possibly "slow" differential equation (such as the thingtravellingthroughair one): 1) Run the solution analytically in Mathematica or something 2) Look at the curves in X and Y 3) Fit a highorder polynomial to X and Y (I'd start with a fifthorder) 4) Hope it's good enough Cheers, / h+ 
From: Christopher Phillips <cphillips@re...>  20020918 13:36:57

The analytical solution should look pretty close to an exponential decay towards 'falling at terminal velocity'. Could just approximate the exponential bit as 1/(low order poly). Even exp(x) = 1/(1+x*(1+x*0.5)) will probably be close enough, as it's going to vanish pretty quickly anyway. here's a derivation of the 1d case here: (assumes air resistance is proprortional to V rather than V**2, but the principles pretty similar) http://www.mapleapps.com/categories/education/university/html/shottraj.html > Original Message > From: Hansen, Daniel [mailto:Daniel.Hansen@...] > Sent: 18 September 2002 12:26 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > Well an analytic solution is what I'm after. I've only seen very nasty > long (read slow) equations. I need somethinbg simpler (faster). > > Original Message > From: Jamie Fowlston [mailto:jamief@...] > Sent: den 18 september 2002 12:44 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > take your pick, really. just have some acceleration opposing > your velocity. > you can have a factor of your velocity, or the square of your > velocity, or > whatever. all are variously inaccurate, but may well give you > the effect > you're after. > > then it's simple integration to get your velocity and > position. but you may > well not find an analytic solution, if that's what you're > after, as they > don't always exist. > > jamie > > > Original Message > From: gdalgorithmslistadmin@... > [mailto:gdalgorithmslistadmin@...]On Behalf Of > Hansen, Daniel > Sent: 18 September 2002 09:22 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > Has anyone parametricized the velocity and position taking > airresistance > into consideration. I.e > > v(t) = v0 + a * t > p(t) = p0 + (v0 + 0.5 * a * t) * t > > ..could be used when there's no airresistance. > I'd like something similar with airresistance. > I've seen some formulas with alot of nasty exponents in them, > I'm looking > for a simpler hack. Anyone? > > > Original Message > From: Charles Bloom [mailto:cbloom@...] > Sent: den 11 september 2002 07:58 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > This "midpoint method" is 2nd order RungeKutta. See, for example : > > http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html > http://csep1.phy.ornl.gov/ode/node7.html > > The traditional socalled "RungeKutta method" is the 4th > order method. > Anyway, all silliness, but some of the stuff on the web is > pretty good. > > At 12:19 AM 9/11/2002 0400, jack@... wrote: > >Thanks to all. Using the midpoint method combined with a > small enough time > >step appears to provide a reasonable amount of accuracy for > my use. I'll > >keep RungeKutta in mind for future use if it proves necessary. > > > >Jack > > > >Original Message > >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] > >Sent: Monday, September 09, 2002 2:52 PM > >To: Jon Watte; jack@...; > gdalgorithmslist@... > >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > > >Even using something as simple as the midpoint method (a secondorder > >integrator) will give much better results for minimal > effort. RungeKutta > >is probably overkill... ? > > > >v_intermediate= v  0.5*k(v^2)t; > >v_final= v  k(v_intermediate^2)t; > > > > > >Chris Butcher > >Rendering & Simulation Lead > >Halo 2  Bungie Studios > >butcher@... > > > > > >Original Message > >From: Jon Watte [mailto:hplus@...] > >Sent: Monday, September 09, 2002 12:43 > >To: jack@...; gdalgorithmslist@... > >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > > >> I'm trying to do a simple ballistics model for shells. The > formula I'm > >> using is: > >> > >> v' = v  k(v^2)t; > > > >This is a firstorder Euler integrator (I believe). These are known > >to be unstable at any time step  as you notice :) > > > >The typical answer when faced with numerical integration problems > >is to turn to a fourthorder RungeKutta integrator. I'm sure if you > >plug that into Google, you'll get a massive number of hits. It might > >show up on MathWorld, too. > > > >Cheers, > > > > / h+ > > > > > > > > > > > >mail2web  Check your email from the web at > >http://mail2web.com/ . > > > > > > > > > > > >In remembrance > >www.osdn.com/911/ > >_______________________________________________ > >GDAlgorithmslist mailing list > >GDAlgorithmslist@... > >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > >Archives: > >http://sourceforge.net/mailarchive/forum.php?forum_ida88 > > >  > Charles Bloom cb@... http://www.cbloom.com > > > >  > In remembrance > http://www.osdn.com/911/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > Virus scanned and cleared ok 
From: neo binedell <neoji@mw...>  20020918 12:50:07

What about precomputing the arc/final position at the missile launch/creation time using the accel/velocity/dir vect, adding in your drag component and then just interpolating to that over time? Seems you'll have to do the heavyweight (prob. nonlinear) calc once and then it's just a lerp/xerp??? layder neo binedell ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Many spacetimes contain infinite distances in time, or in space, or both. They have four or more dimensions, and they are generally not flat. All of these features make it difficult to draw a spacetime on a piece of paper. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Original Message From: gdalgorithmslistadmin@... [mailto:gdalgorithmslistadmin@...]On Behalf Of Tom Forsyth Sent: 18 September 2002 02:14 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells If this is just for things like particle systems (e.g. bits coming off something exploding), then damping the horizontal movement to zero over time, but leaving the vertical as a standard parabola looks perfectly good. Tom Forsyth  purely hypothetical Muckyfoot bloke. This email is the product of your deranged imagination, and does not in any way imply existence of the author. > Original Message > From: Andrew Jones [mailto:andrew@...] > Sent: 18 September 2002 13:01 > To: Hansen, Daniel; gdalgorithmslist@... > Subject: Re: [Algorithms] Simple Air Resistance Simulation for Shells > > > You don't have any requirement for the ballistics of these shells > to be absolutely realistic with respect to air resistance, so as you > say a fudged solution is appropriate. If the analytical solution for > velocitysquared air resistance is too slow for you, then think > about a lesser model which will have a qualitatively similar effect, > but has a much simpler analytical solution. At the low end, try > having a constant accelleration in the opposite of the launch > direction > of the projectile. You could calculate the value of this accelleration > using vsquared from the launch velocity of the projectile. As the > projectile alters direction under gravity the 'air resistance' will be > acting in the wrong direction and as it slows the decelleration due > to air resistance will be too large, but why not just run the > 'correct' > reference fricition model against it and see what you get. Compare > the shapes of the ballistic arcs they give you, and see if > you can live > with a lesser version of reality. Of course, a constant accelleration > drag model may be quite poor, but you can try anything you want > provided it has a quick analytical solution. As a final > suggestion, you > may think that the correct analytical solution seems a bit > slow, but is this > really going to matter? If you're coding it up as a reference > you could > just leave it and see if it is ever too slow. Can you post a reference > with an analytical solution to ballistics with vsquared > drag? I'd like > to see one myself. How intensively is this being used? Bear > in mind that > your solver for this may not be a bottleneck anywhere at all if that > particular piece of code is memory bandwidth bound. > > Andrew Jones > Empire Interactive > > > > > Well an analytic solution is what I'm after. I've only seen > very nasty > > long (read slow) equations. I need somethinbg simpler (faster). > > > > Original Message > > From: Jamie Fowlston [mailto:jamief@...] > > Sent: den 18 september 2002 12:44 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > take your pick, really. just have some acceleration opposing your > velocity. > > you can have a factor of your velocity, or the square of > your velocity, or > > whatever. all are variously inaccurate, but may well give > you the effect > > you're after. > > > > then it's simple integration to get your velocity and > position. but you > may > > well not find an analytic solution, if that's what you're > after, as they > > don't always exist. > > > > jamie > > > > > > Original Message > > From: gdalgorithmslistadmin@... > > [mailto:gdalgorithmslistadmin@...]On Behalf Of > > Hansen, Daniel > > Sent: 18 September 2002 09:22 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > Has anyone parametricized the velocity and position taking > airresistance > > into consideration. I.e > > > > v(t) = v0 + a * t > > p(t) = p0 + (v0 + 0.5 * a * t) * t > > > > ..could be used when there's no airresistance. > > I'd like something similar with airresistance. > > I've seen some formulas with alot of nasty exponents in > them, I'm looking > > for a simpler hack. Anyone? > > > > > > Original Message > > From: Charles Bloom [mailto:cbloom@...] > > Sent: den 11 september 2002 07:58 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > This "midpoint method" is 2nd order RungeKutta. See, for example : > > > > http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html > > http://csep1.phy.ornl.gov/ode/node7.html > > > > The traditional socalled "RungeKutta method" is the 4th > order method. > > Anyway, all silliness, but some of the stuff on the web is > pretty good. > > > > At 12:19 AM 9/11/2002 0400, jack@... wrote: > > >Thanks to all. Using the midpoint method combined with a > small enough > time > > >step appears to provide a reasonable amount of accuracy > for my use. I'll > > > >keep RungeKutta in mind for future use if it proves necessary. > > > > > >Jack > > > > > >Original Message > > >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] > > >Sent: Monday, September 09, 2002 2:52 PM > > >To: Jon Watte; jack@...; > > gdalgorithmslist@... > > >Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > >Even using something as simple as the midpoint method (a > secondorder > > >integrator) will give much better results for minimal > effort. RungeKutta > > >is probably overkill... ? > > > > > >v_intermediate= v  0.5*k(v^2)t; > > >v_final= v  k(v_intermediate^2)t; > > > > > > > > >Chris Butcher > > >Rendering & Simulation Lead > > >Halo 2  Bungie Studios > > >butcher@... > > > > > > > > >Original Message > > >From: Jon Watte [mailto:hplus@...] > > >Sent: Monday, September 09, 2002 12:43 > > >To: jack@...; gdalgorithmslist@... > > >Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > >> I'm trying to do a simple ballistics model for shells. > The formula I'm > > >> using is: > > >> > > >> v' = v  k(v^2)t; > > > > > >This is a firstorder Euler integrator (I believe). These are known > > >to be unstable at any time step  as you notice :) > > > > > >The typical answer when faced with numerical integration problems > > >is to turn to a fourthorder RungeKutta integrator. I'm > sure if you > > >plug that into Google, you'll get a massive number of > hits. It might > > >show up on MathWorld, too. > > > > > >Cheers, > > > > > > / h+ > > > > > > > > > > > > > > > > > > >mail2web  Check your email from the web at > > >http://mail2web.com/ . > > > > > > > > > > > > > > > > > >In remembrance > > >www.osdn.com/911/ > > >_______________________________________________ > > >GDAlgorithmslist mailing list > > >GDAlgorithmslist@... > > >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > >Archives: > > >http://sourceforge.net/mailarchive/forum.php?forum_ida88 > > > > >  > > Charles Bloom cb@... http://www.cbloom.com > > > > > > > >  > > In remembrance > > http://www.osdn.com/911/ > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 >  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: Tom Forsyth <tomf@mu...>  20020918 12:18:09

If this is just for things like particle systems (e.g. bits coming off something exploding), then damping the horizontal movement to zero over time, but leaving the vertical as a standard parabola looks perfectly good. Tom Forsyth  purely hypothetical Muckyfoot bloke. This email is the product of your deranged imagination, and does not in any way imply existence of the author. > Original Message > From: Andrew Jones [mailto:andrew@...] > Sent: 18 September 2002 13:01 > To: Hansen, Daniel; gdalgorithmslist@... > Subject: Re: [Algorithms] Simple Air Resistance Simulation for Shells > > > You don't have any requirement for the ballistics of these shells > to be absolutely realistic with respect to air resistance, so as you > say a fudged solution is appropriate. If the analytical solution for > velocitysquared air resistance is too slow for you, then think > about a lesser model which will have a qualitatively similar effect, > but has a much simpler analytical solution. At the low end, try > having a constant accelleration in the opposite of the launch > direction > of the projectile. You could calculate the value of this accelleration > using vsquared from the launch velocity of the projectile. As the > projectile alters direction under gravity the 'air resistance' will be > acting in the wrong direction and as it slows the decelleration due > to air resistance will be too large, but why not just run the > 'correct' > reference fricition model against it and see what you get. Compare > the shapes of the ballistic arcs they give you, and see if > you can live > with a lesser version of reality. Of course, a constant accelleration > drag model may be quite poor, but you can try anything you want > provided it has a quick analytical solution. As a final > suggestion, you > may think that the correct analytical solution seems a bit > slow, but is this > really going to matter? If you're coding it up as a reference > you could > just leave it and see if it is ever too slow. Can you post a reference > with an analytical solution to ballistics with vsquared > drag? I'd like > to see one myself. How intensively is this being used? Bear > in mind that > your solver for this may not be a bottleneck anywhere at all if that > particular piece of code is memory bandwidth bound. > > Andrew Jones > Empire Interactive > > > > > Well an analytic solution is what I'm after. I've only seen > very nasty > > long (read slow) equations. I need somethinbg simpler (faster). > > > > Original Message > > From: Jamie Fowlston [mailto:jamief@...] > > Sent: den 18 september 2002 12:44 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > take your pick, really. just have some acceleration opposing your > velocity. > > you can have a factor of your velocity, or the square of > your velocity, or > > whatever. all are variously inaccurate, but may well give > you the effect > > you're after. > > > > then it's simple integration to get your velocity and > position. but you > may > > well not find an analytic solution, if that's what you're > after, as they > > don't always exist. > > > > jamie > > > > > > Original Message > > From: gdalgorithmslistadmin@... > > [mailto:gdalgorithmslistadmin@...]On Behalf Of > > Hansen, Daniel > > Sent: 18 September 2002 09:22 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > Has anyone parametricized the velocity and position taking > airresistance > > into consideration. I.e > > > > v(t) = v0 + a * t > > p(t) = p0 + (v0 + 0.5 * a * t) * t > > > > ..could be used when there's no airresistance. > > I'd like something similar with airresistance. > > I've seen some formulas with alot of nasty exponents in > them, I'm looking > > for a simpler hack. Anyone? > > > > > > Original Message > > From: Charles Bloom [mailto:cbloom@...] > > Sent: den 11 september 2002 07:58 > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > This "midpoint method" is 2nd order RungeKutta. See, for example : > > > > http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html > > http://csep1.phy.ornl.gov/ode/node7.html > > > > The traditional socalled "RungeKutta method" is the 4th > order method. > > Anyway, all silliness, but some of the stuff on the web is > pretty good. > > > > At 12:19 AM 9/11/2002 0400, jack@... wrote: > > >Thanks to all. Using the midpoint method combined with a > small enough > time > > >step appears to provide a reasonable amount of accuracy > for my use. I'll > > > >keep RungeKutta in mind for future use if it proves necessary. > > > > > >Jack > > > > > >Original Message > > >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] > > >Sent: Monday, September 09, 2002 2:52 PM > > >To: Jon Watte; jack@...; > > gdalgorithmslist@... > > >Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > >Even using something as simple as the midpoint method (a > secondorder > > >integrator) will give much better results for minimal > effort. RungeKutta > > >is probably overkill... ? > > > > > >v_intermediate= v  0.5*k(v^2)t; > > >v_final= v  k(v_intermediate^2)t; > > > > > > > > >Chris Butcher > > >Rendering & Simulation Lead > > >Halo 2  Bungie Studios > > >butcher@... > > > > > > > > >Original Message > > >From: Jon Watte [mailto:hplus@...] > > >Sent: Monday, September 09, 2002 12:43 > > >To: jack@...; gdalgorithmslist@... > > >Subject: RE: [Algorithms] Simple Air Resistance Simulation > for Shells > > > > > > > > >> I'm trying to do a simple ballistics model for shells. > The formula I'm > > >> using is: > > >> > > >> v' = v  k(v^2)t; > > > > > >This is a firstorder Euler integrator (I believe). These are known > > >to be unstable at any time step  as you notice :) > > > > > >The typical answer when faced with numerical integration problems > > >is to turn to a fourthorder RungeKutta integrator. I'm > sure if you > > >plug that into Google, you'll get a massive number of > hits. It might > > >show up on MathWorld, too. > > > > > >Cheers, > > > > > > / h+ > > > > > > > > > > > > > > > > > > >mail2web  Check your email from the web at > > >http://mail2web.com/ . > > > > > > > > > > > > > > > > > >In remembrance > > >www.osdn.com/911/ > > >_______________________________________________ > > >GDAlgorithmslist mailing list > > >GDAlgorithmslist@... > > >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > >Archives: > > >http://sourceforge.net/mailarchive/forum.php?forum_ida88 > > > > >  > > Charles Bloom cb@... http://www.cbloom.com > > > > > > > >  > > In remembrance > > http://www.osdn.com/911/ > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the experts > > on Hammer Technology! Open Source & Linux Developers, register now > > for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Andrew Jones <andrew@em...>  20020918 12:01:28

You don't have any requirement for the ballistics of these shells to be absolutely realistic with respect to air resistance, so as you say a fudged solution is appropriate. If the analytical solution for velocitysquared air resistance is too slow for you, then think about a lesser model which will have a qualitatively similar effect, but has a much simpler analytical solution. At the low end, try having a constant accelleration in the opposite of the launch direction of the projectile. You could calculate the value of this accelleration using vsquared from the launch velocity of the projectile. As the projectile alters direction under gravity the 'air resistance' will be acting in the wrong direction and as it slows the decelleration due to air resistance will be too large, but why not just run the 'correct' reference fricition model against it and see what you get. Compare the shapes of the ballistic arcs they give you, and see if you can live with a lesser version of reality. Of course, a constant accelleration drag model may be quite poor, but you can try anything you want provided it has a quick analytical solution. As a final suggestion, you may think that the correct analytical solution seems a bit slow, but is this really going to matter? If you're coding it up as a reference you could just leave it and see if it is ever too slow. Can you post a reference with an analytical solution to ballistics with vsquared drag? I'd like to see one myself. How intensively is this being used? Bear in mind that your solver for this may not be a bottleneck anywhere at all if that particular piece of code is memory bandwidth bound. Andrew Jones Empire Interactive > Well an analytic solution is what I'm after. I've only seen very nasty > long (read slow) equations. I need somethinbg simpler (faster). > > Original Message > From: Jamie Fowlston [mailto:jamief@...] > Sent: den 18 september 2002 12:44 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > take your pick, really. just have some acceleration opposing your velocity. > you can have a factor of your velocity, or the square of your velocity, or > whatever. all are variously inaccurate, but may well give you the effect > you're after. > > then it's simple integration to get your velocity and position. but you may > well not find an analytic solution, if that's what you're after, as they > don't always exist. > > jamie > > > Original Message > From: gdalgorithmslistadmin@... > [mailto:gdalgorithmslistadmin@...]On Behalf Of > Hansen, Daniel > Sent: 18 September 2002 09:22 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > Has anyone parametricized the velocity and position taking airresistance > into consideration. I.e > > v(t) = v0 + a * t > p(t) = p0 + (v0 + 0.5 * a * t) * t > > ..could be used when there's no airresistance. > I'd like something similar with airresistance. > I've seen some formulas with alot of nasty exponents in them, I'm looking > for a simpler hack. Anyone? > > > Original Message > From: Charles Bloom [mailto:cbloom@...] > Sent: den 11 september 2002 07:58 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > This "midpoint method" is 2nd order RungeKutta. See, for example : > > http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html > http://csep1.phy.ornl.gov/ode/node7.html > > The traditional socalled "RungeKutta method" is the 4th order method. > Anyway, all silliness, but some of the stuff on the web is pretty good. > > At 12:19 AM 9/11/2002 0400, jack@... wrote: > >Thanks to all. Using the midpoint method combined with a small enough time > >step appears to provide a reasonable amount of accuracy for my use. I'll > >keep RungeKutta in mind for future use if it proves necessary. > > > >Jack > > > >Original Message > >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] > >Sent: Monday, September 09, 2002 2:52 PM > >To: Jon Watte; jack@...; > gdalgorithmslist@... > >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > > >Even using something as simple as the midpoint method (a secondorder > >integrator) will give much better results for minimal effort. RungeKutta > >is probably overkill... ? > > > >v_intermediate= v  0.5*k(v^2)t; > >v_final= v  k(v_intermediate^2)t; > > > > > >Chris Butcher > >Rendering & Simulation Lead > >Halo 2  Bungie Studios > >butcher@... > > > > > >Original Message > >From: Jon Watte [mailto:hplus@...] > >Sent: Monday, September 09, 2002 12:43 > >To: jack@...; gdalgorithmslist@... > >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > > > > >> I'm trying to do a simple ballistics model for shells. The formula I'm > >> using is: > >> > >> v' = v  k(v^2)t; > > > >This is a firstorder Euler integrator (I believe). These are known > >to be unstable at any time step  as you notice :) > > > >The typical answer when faced with numerical integration problems > >is to turn to a fourthorder RungeKutta integrator. I'm sure if you > >plug that into Google, you'll get a massive number of hits. It might > >show up on MathWorld, too. > > > >Cheers, > > > > / h+ > > > > > > > > > > > >mail2web  Check your email from the web at > >http://mail2web.com/ . > > > > > > > > > > > >In remembrance > >www.osdn.com/911/ > >_______________________________________________ > >GDAlgorithmslist mailing list > >GDAlgorithmslist@... > >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > >Archives: > >http://sourceforge.net/mailarchive/forum.php?forum_ida88 > > >  > Charles Bloom cb@... http://www.cbloom.com > > > >  > In remembrance > http://www.osdn.com/911/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Bert.P<eers@ma...>  20020918 11:53:54

> > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > > > > > I understand where the / width comes from since you are > > integrating in > > > steps of 1/width over the sphere, but I fail to understand what > > > sinc(theta) means. > We know what sinc _is_  Joris even gave the code for it. The > question is > why is it being used here? On a hunch : because they are using proper monte carlo integration around (rather than just taking a single point sample at) the angle of interest, during which they use the sync as a lowpass filter to remove frequencies beyond the nyquist limit ? So that would basically be a misleading name  it's not just the differential angle required by the numerical integration, it's also carrying the value of the filter being convolved with. I would expect to see a double loop, whereas the net samples you mention that don't use sinc, only have one loop. Or maybe not :) Bert 
From: Joris Mans <joris.mans@pa...>  20020918 11:49:10

Here ya go http://graphics.stanford.edu/papers/envmap/prefilter.c > Original Message > From: gdalgorithmslistadmin@... > [mailto:gdalgorithmslistadmin@...] On > Behalf Of Joris Mans > Sent: Wednesday, September 18, 2002 1:19 PM > To: 'Nick Pelling'; gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > Ok, I understand that, but I fail to see how this function > can be used to calculate the differential solid angle as the > formulae found on the net do not use sinc for that. > > Does anyone know? > > Joris > > > Original Message > > From: gdalgorithmslistadmin@... > > [mailto:gdalgorithmslistadmin@...] On > > Behalf Of Nick Pelling > > Sent: Wednesday, September 18, 2002 12:42 PM > > To: gdalgorithmslist@... > > Subject: RE: [Algorithms] Solid angle calculation > > > > > > sinc() is actually a wellknown maths function, and is often > > used in code for rescaling / resampling. > > > > Search for "sinc function" on Google, and you'll hit loads of > > maths sites explaining it, such as: > > > > http://mathworld.wolfram.com/SincFunction.html > > > > Cheers, .....Nick Pelling..... > > > > Original Message > > From: Tom Forsyth [mailto:tomf@...] > > Sent: 16 September 2002 12:51 > > To: Joris Mans; gdalgorithmslist@... > > Subject: RE: [Algorithms] Solid angle calculation > > > > > > I assumed that was a typo, and they mean "sine(theta)". But I > > didn't worry about it too hard since, using cubemaps and > > just ignoring the spherical distortion (i.e. every sample is > > evenly weighted) seemed to work just fine  at least to > > within the tolerance of my eye :). It also bins all the > > angle stuff and uses the SH components directly (since you > > already have x,y,z to plug into the component calculations), > > so there's no trig anywhere in any equations. Which is very > > good news for speed. > > > > > > Tom Forsyth  purely hypothetical Muckyfoot bloke. > > > > This email is the product of your deranged imagination, > > and does not in any way imply existence of the author. > > > > > Original Message > > > From: Joris Mans [mailto:joris.mans@...] > > > Sent: 12 September 2002 02:17 > > > To: gdalgorithmslist@... > > > Subject: [Algorithms] Solid angle calculation > > > > > > > > > Hi > > > > > > I am currently trying to understand/implement the > > integration scheme > > > used in "An efficient rep. for Irradiance env maps" and I think my > > > math skills have some holes in them, because I don't > understand the > > > formula for calculating the solid angle. > > > This is the c sample code: > > > > > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > > > > > I understand where the / width comes from since you are > > integrating in > > > steps of 1/width over the sphere, but I fail to understand what > > > sinc(theta) means. > > > > > > FYI: > > > > > > float sinc(float x) { /* Supporting sinc function */ > > > if (fabs(x) < 1.0e4) return 1.0 ; > > > else return(sin(x)/x) ; > > > } > > > > > > How does this term calculate the solid angle? > > > > > > Thanks > > > > > > Joris > > > > > > > > > > > >  > > > In remembrance > > > http://www.osdn.com/911/ _______________________________________________ > > > GDAlgorithmslist mailing list > > > GDAlgorithmslist@... > > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > > > > >  > > This sf.net email is sponsored by:ThinkGeek > > Welcome to geek heaven. > > http://thinkgeek.com/sf > > _______________________________________________ > > GDAlgorithmslist mailing list > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > > This SF.NET email is sponsored by: AMD  Your access to the > > experts on Hammer Technology! Open Source & Linux Developers, > > register now for the AMD Developer Symposium. Code: EX8664 > > http://www.developwithamd.com/developerlab > > > > _______________________________________________ > > GDAlgorithmslist mailing list > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Nick Pelling <NP<elling@cl...>  20020918 11:40:34

In their prefilter() routine, the authors calculate theta as the angle from the normal to the (u,v) plane. That's the solid angle... that's all. The sinc() function is then using that solid angle to do the resampling. As I flagged, it's pretty useful for that kind of thing. It seems pretty simple. Cheers, ....Nick Pelling.... Original Message From: Joris Mans [mailto:joris.mans@...] Sent: 18 September 2002 12:19 To: 'Nick Pelling'; gdalgorithmslist@... Subject: RE: [Algorithms] Solid angle calculation Ok, I understand that, but I fail to see how this function can be used to calculate the differential solid angle as the formulae found on the net do not use sinc for that. Does anyone know? Joris > Original Message > From: gdalgorithmslistadmin@... > [mailto:gdalgorithmslistadmin@...] On > Behalf Of Nick Pelling > Sent: Wednesday, September 18, 2002 12:42 PM > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > sinc() is actually a wellknown maths function, and is often > used in code for rescaling / resampling. > > Search for "sinc function" on Google, and you'll hit loads of > maths sites explaining it, such as: > > http://mathworld.wolfram.com/SincFunction.html > > Cheers, .....Nick Pelling..... > > Original Message > From: Tom Forsyth [mailto:tomf@...] > Sent: 16 September 2002 12:51 > To: Joris Mans; gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > I assumed that was a typo, and they mean "sine(theta)". But I > didn't worry about it too hard since, using cubemaps and > just ignoring the spherical distortion (i.e. every sample is > evenly weighted) seemed to work just fine  at least to > within the tolerance of my eye :). It also bins all the > angle stuff and uses the SH components directly (since you > already have x,y,z to plug into the component calculations), > so there's no trig anywhere in any equations. Which is very > good news for speed. > > > Tom Forsyth  purely hypothetical Muckyfoot bloke. > > This email is the product of your deranged imagination, > and does not in any way imply existence of the author. > > > Original Message > > From: Joris Mans [mailto:joris.mans@...] > > Sent: 12 September 2002 02:17 > > To: gdalgorithmslist@... > > Subject: [Algorithms] Solid angle calculation > > > > > > Hi > > > > I am currently trying to understand/implement the > integration scheme > > used in "An efficient rep. for Irradiance env maps" and I think my > > math skills have some holes in them, because I don't understand the > > formula for calculating the solid angle. > > This is the c sample code: > > > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > > > I understand where the / width comes from since you are > integrating in > > steps of 1/width over the sphere, but I fail to understand what > > sinc(theta) means. > > > > FYI: > > > > float sinc(float x) { /* Supporting sinc function */ > > if (fabs(x) < 1.0e4) return 1.0 ; > > else return(sin(x)/x) ; > > } > > > > How does this term calculate the solid angle? > > > > Thanks > > > > Joris > > > > > > > >  > > In remembrance > > http://www.osdn.com/911/ _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > >  > This sf.net email is sponsored by:ThinkGeek > Welcome to geek heaven. > http://thinkgeek.com/sf > _______________________________________________ > GDAlgorithmslist mailing list GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the > experts on Hammer Technology! Open Source & Linux Developers, > register now for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > > _______________________________________________ > GDAlgorithmslist mailing list GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Jim Offerman <j.offerman@cr...>  20020918 11:40:04

Daniel, > Well an analytic solution is what I'm after. I've only seen very nasty > long (read slow) equations. I need somethinbg simpler (faster). Can't you just (as Jamie already suggested) approximate the behaviour using a very simple function like: Far = C * V Where Far is the computed force due to air resistance, V is the object's current velocity and C is some constant value used to approximate the velocity to air resistance ratio. Scientifically speaking, this is anything but accurate, but given a well chosen value for C it might feel just right. Jim Offerman Crevace Games http://www.crevace.com http://www.jimofferman.nl 
From: Jamie Fowlston <jamief@qu...>  20020918 11:34:32

good luck, i think you'll need it. jamie Original Message From: gdalgorithmslistadmin@... [mailto:gdalgorithmslistadmin@...]On Behalf Of Hansen, Daniel Sent: 18 September 2002 12:26 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells Well an analytic solution is what I'm after. I've only seen very nasty long (read slow) equations. I need somethinbg simpler (faster). Original Message From: Jamie Fowlston [mailto:jamief@...] Sent: den 18 september 2002 12:44 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells take your pick, really. just have some acceleration opposing your velocity. you can have a factor of your velocity, or the square of your velocity, or whatever. all are variously inaccurate, but may well give you the effect you're after. then it's simple integration to get your velocity and position. but you may well not find an analytic solution, if that's what you're after, as they don't always exist. jamie Original Message From: gdalgorithmslistadmin@... [mailto:gdalgorithmslistadmin@...]On Behalf Of Hansen, Daniel Sent: 18 September 2002 09:22 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells Has anyone parametricized the velocity and position taking airresistance into consideration. I.e v(t) = v0 + a * t p(t) = p0 + (v0 + 0.5 * a * t) * t ..could be used when there's no airresistance. I'd like something similar with airresistance. I've seen some formulas with alot of nasty exponents in them, I'm looking for a simpler hack. Anyone? Original Message From: Charles Bloom [mailto:cbloom@...] Sent: den 11 september 2002 07:58 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells This "midpoint method" is 2nd order RungeKutta. See, for example : http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html http://csep1.phy.ornl.gov/ode/node7.html The traditional socalled "RungeKutta method" is the 4th order method. Anyway, all silliness, but some of the stuff on the web is pretty good. At 12:19 AM 9/11/2002 0400, jack@... wrote: >Thanks to all. Using the midpoint method combined with a small enough time >step appears to provide a reasonable amount of accuracy for my use. I'll >keep RungeKutta in mind for future use if it proves necessary. > >Jack > >Original Message >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] >Sent: Monday, September 09, 2002 2:52 PM >To: Jon Watte; jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >Even using something as simple as the midpoint method (a secondorder >integrator) will give much better results for minimal effort. RungeKutta >is probably overkill... ? > >v_intermediate= v  0.5*k(v^2)t; >v_final= v  k(v_intermediate^2)t; > > >Chris Butcher >Rendering & Simulation Lead >Halo 2  Bungie Studios >butcher@... > > >Original Message >From: Jon Watte [mailto:hplus@...] >Sent: Monday, September 09, 2002 12:43 >To: jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >> I'm trying to do a simple ballistics model for shells. The formula I'm >> using is: >> >> v' = v  k(v^2)t; > >This is a firstorder Euler integrator (I believe). These are known >to be unstable at any time step  as you notice :) > >The typical answer when faced with numerical integration problems >is to turn to a fourthorder RungeKutta integrator. I'm sure if you >plug that into Google, you'll get a massive number of hits. It might >show up on MathWorld, too. > >Cheers, > > / h+ > > > > > >mail2web  Check your email from the web at >http://mail2web.com/ . > > > > > >In remembrance >www.osdn.com/911/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88 >  Charles Bloom cb@... http://www.cbloom.com  In remembrance http://www.osdn.com/911/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: Hansen, Daniel <Daniel.H<ansen@di...>  20020918 11:25:25

Well an analytic solution is what I'm after. I've only seen very nasty long (read slow) equations. I need somethinbg simpler (faster). Original Message From: Jamie Fowlston [mailto:jamief@...] Sent: den 18 september 2002 12:44 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells take your pick, really. just have some acceleration opposing your velocity. you can have a factor of your velocity, or the square of your velocity, or whatever. all are variously inaccurate, but may well give you the effect you're after. then it's simple integration to get your velocity and position. but you may well not find an analytic solution, if that's what you're after, as they don't always exist. jamie Original Message From: gdalgorithmslistadmin@... [mailto:gdalgorithmslistadmin@...]On Behalf Of Hansen, Daniel Sent: 18 September 2002 09:22 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells Has anyone parametricized the velocity and position taking airresistance into consideration. I.e v(t) = v0 + a * t p(t) = p0 + (v0 + 0.5 * a * t) * t ..could be used when there's no airresistance. I'd like something similar with airresistance. I've seen some formulas with alot of nasty exponents in them, I'm looking for a simpler hack. Anyone? Original Message From: Charles Bloom [mailto:cbloom@...] Sent: den 11 september 2002 07:58 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells This "midpoint method" is 2nd order RungeKutta. See, for example : http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html http://csep1.phy.ornl.gov/ode/node7.html The traditional socalled "RungeKutta method" is the 4th order method. Anyway, all silliness, but some of the stuff on the web is pretty good. At 12:19 AM 9/11/2002 0400, jack@... wrote: >Thanks to all. Using the midpoint method combined with a small enough time >step appears to provide a reasonable amount of accuracy for my use. I'll >keep RungeKutta in mind for future use if it proves necessary. > >Jack > >Original Message >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] >Sent: Monday, September 09, 2002 2:52 PM >To: Jon Watte; jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >Even using something as simple as the midpoint method (a secondorder >integrator) will give much better results for minimal effort. RungeKutta >is probably overkill... ? > >v_intermediate= v  0.5*k(v^2)t; >v_final= v  k(v_intermediate^2)t; > > >Chris Butcher >Rendering & Simulation Lead >Halo 2  Bungie Studios >butcher@... > > >Original Message >From: Jon Watte [mailto:hplus@...] >Sent: Monday, September 09, 2002 12:43 >To: jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >> I'm trying to do a simple ballistics model for shells. The formula I'm >> using is: >> >> v' = v  k(v^2)t; > >This is a firstorder Euler integrator (I believe). These are known >to be unstable at any time step  as you notice :) > >The typical answer when faced with numerical integration problems >is to turn to a fourthorder RungeKutta integrator. I'm sure if you >plug that into Google, you'll get a massive number of hits. It might >show up on MathWorld, too. > >Cheers, > > / h+ > > > > > >mail2web  Check your email from the web at >http://mail2web.com/ . > > > > > >In remembrance >www.osdn.com/911/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88 >  Charles Bloom cb@... http://www.cbloom.com  In remembrance http://www.osdn.com/911/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: Joris Mans <joris.mans@pa...>  20020918 11:18:59

Ok, I understand that, but I fail to see how this function can be used to calculate the differential solid angle as the formulae found on the net do not use sinc for that. Does anyone know? Joris > Original Message > From: gdalgorithmslistadmin@... > [mailto:gdalgorithmslistadmin@...] On > Behalf Of Nick Pelling > Sent: Wednesday, September 18, 2002 12:42 PM > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > sinc() is actually a wellknown maths function, and is often > used in code for rescaling / resampling. > > Search for "sinc function" on Google, and you'll hit loads of > maths sites explaining it, such as: > > http://mathworld.wolfram.com/SincFunction.html > > Cheers, .....Nick Pelling..... > > Original Message > From: Tom Forsyth [mailto:tomf@...] > Sent: 16 September 2002 12:51 > To: Joris Mans; gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > I assumed that was a typo, and they mean "sine(theta)". But I > didn't worry about it too hard since, using cubemaps and > just ignoring the spherical distortion (i.e. every sample is > evenly weighted) seemed to work just fine  at least to > within the tolerance of my eye :). It also bins all the > angle stuff and uses the SH components directly (since you > already have x,y,z to plug into the component calculations), > so there's no trig anywhere in any equations. Which is very > good news for speed. > > > Tom Forsyth  purely hypothetical Muckyfoot bloke. > > This email is the product of your deranged imagination, > and does not in any way imply existence of the author. > > > Original Message > > From: Joris Mans [mailto:joris.mans@...] > > Sent: 12 September 2002 02:17 > > To: gdalgorithmslist@... > > Subject: [Algorithms] Solid angle calculation > > > > > > Hi > > > > I am currently trying to understand/implement the > integration scheme > > used in "An efficient rep. for Irradiance env maps" and I think my > > math skills have some holes in them, because I don't understand the > > formula for calculating the solid angle. > > This is the c sample code: > > > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > > > I understand where the / width comes from since you are > integrating in > > steps of 1/width over the sphere, but I fail to understand what > > sinc(theta) means. > > > > FYI: > > > > float sinc(float x) { /* Supporting sinc function */ > > if (fabs(x) < 1.0e4) return 1.0 ; > > else return(sin(x)/x) ; > > } > > > > How does this term calculate the solid angle? > > > > Thanks > > > > Joris > > > > > > > >  > > In remembrance > > http://www.osdn.com/911/ _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > >  > This sf.net email is sponsored by:ThinkGeek > Welcome to geek heaven. > http://thinkgeek.com/sf > _______________________________________________ > GDAlgorithmslist mailing list GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the > experts on Hammer Technology! Open Source & Linux Developers, > register now for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > > _______________________________________________ > GDAlgorithmslist mailing list GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Tom Forsyth <tomf@mu...>  20020918 11:02:58

We know what sinc _is_  Joris even gave the code for it. The question is why is it being used here? Tom Forsyth  purely hypothetical Muckyfoot bloke. This email is the product of your deranged imagination, and does not in any way imply existence of the author. > Original Message > From: Nick Pelling [mailto:NPelling@...] > Sent: 18 September 2002 11:42 > To: gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > sinc() is actually a wellknown maths function, and is often > used in code > for rescaling / resampling. > > Search for "sinc function" on Google, and you'll hit loads of > maths sites > explaining it, such as: > > http://mathworld.wolfram.com/SincFunction.html > > Cheers, .....Nick Pelling..... > > Original Message > From: Tom Forsyth [mailto:tomf@...] > Sent: 16 September 2002 12:51 > To: Joris Mans; gdalgorithmslist@... > Subject: RE: [Algorithms] Solid angle calculation > > > I assumed that was a typo, and they mean "sine(theta)". But I > didn't worry > about it too hard since, using cubemaps and just ignoring > the spherical > distortion (i.e. every sample is evenly weighted) seemed to > work just fine  > at least to within the tolerance of my eye :). It also bins > all the angle > stuff and uses the SH components directly (since you already > have x,y,z to > plug into the component calculations), so there's no trig > anywhere in any > equations. Which is very good news for speed. > > > Tom Forsyth  purely hypothetical Muckyfoot bloke. > > This email is the product of your deranged imagination, > and does not in any way imply existence of the author. > > > Original Message > > From: Joris Mans [mailto:joris.mans@...] > > Sent: 12 September 2002 02:17 > > To: gdalgorithmslist@... > > Subject: [Algorithms] Solid angle calculation > > > > > > Hi > > > > I am currently trying to understand/implement the integration scheme > > used in "An efficient rep. for Irradiance env maps" and I > > think my math > > skills have some holes in them, because I don't understand > the formula > > for calculating the solid angle. > > This is the c sample code: > > > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > > > I understand where the / width comes from since you are > integrating in > > steps of 1/width over the sphere, but I fail to understand what > > sinc(theta) means. > > > > FYI: > > > > float sinc(float x) { /* Supporting sinc function */ > > if (fabs(x) < 1.0e4) return 1.0 ; > > else return(sin(x)/x) ; > > } > > > > How does this term calculate the solid angle? > > > > Thanks > > > > Joris > > > > > > > >  > > In remembrance > > http://www.osdn.com/911/ > > _______________________________________________ > > GDAlgorithmslist mailing list > > GDAlgorithmslist@... > > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > > Archives: > > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > > > >  > This sf.net email is sponsored by:ThinkGeek > Welcome to geek heaven. > http://thinkgeek.com/sf > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > > >  > This SF.NET email is sponsored by: AMD  Your access to the experts > on Hammer Technology! Open Source & Linux Developers, register now > for the AMD Developer Symposium. Code: EX8664 > http://www.developwithamd.com/developerlab > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 > 
From: Jamie Fowlston <jamief@qu...>  20020918 10:43:39

take your pick, really. just have some acceleration opposing your velocity. you can have a factor of your velocity, or the square of your velocity, or whatever. all are variously inaccurate, but may well give you the effect you're after. then it's simple integration to get your velocity and position. but you may well not find an analytic solution, if that's what you're after, as they don't always exist. jamie Original Message From: gdalgorithmslistadmin@... [mailto:gdalgorithmslistadmin@...]On Behalf Of Hansen, Daniel Sent: 18 September 2002 09:22 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells Has anyone parametricized the velocity and position taking airresistance into consideration. I.e v(t) = v0 + a * t p(t) = p0 + (v0 + 0.5 * a * t) * t ..could be used when there's no airresistance. I'd like something similar with airresistance. I've seen some formulas with alot of nasty exponents in them, I'm looking for a simpler hack. Anyone? Original Message From: Charles Bloom [mailto:cbloom@...] Sent: den 11 september 2002 07:58 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells This "midpoint method" is 2nd order RungeKutta. See, for example : http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html http://csep1.phy.ornl.gov/ode/node7.html The traditional socalled "RungeKutta method" is the 4th order method. Anyway, all silliness, but some of the stuff on the web is pretty good. At 12:19 AM 9/11/2002 0400, jack@... wrote: >Thanks to all. Using the midpoint method combined with a small enough time >step appears to provide a reasonable amount of accuracy for my use. I'll >keep RungeKutta in mind for future use if it proves necessary. > >Jack > >Original Message >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] >Sent: Monday, September 09, 2002 2:52 PM >To: Jon Watte; jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >Even using something as simple as the midpoint method (a secondorder >integrator) will give much better results for minimal effort. RungeKutta >is probably overkill... ? > >v_intermediate= v  0.5*k(v^2)t; >v_final= v  k(v_intermediate^2)t; > > >Chris Butcher >Rendering & Simulation Lead >Halo 2  Bungie Studios >butcher@... > > >Original Message >From: Jon Watte [mailto:hplus@...] >Sent: Monday, September 09, 2002 12:43 >To: jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >> I'm trying to do a simple ballistics model for shells. The formula I'm >> using is: >> >> v' = v  k(v^2)t; > >This is a firstorder Euler integrator (I believe). These are known >to be unstable at any time step  as you notice :) > >The typical answer when faced with numerical integration problems >is to turn to a fourthorder RungeKutta integrator. I'm sure if you >plug that into Google, you'll get a massive number of hits. It might >show up on MathWorld, too. > >Cheers, > > / h+ > > > > > >mail2web  Check your email from the web at >http://mail2web.com/ . > > > > > >In remembrance >www.osdn.com/911/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88 >  Charles Bloom cb@... http://www.cbloom.com  In remembrance http://www.osdn.com/911/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188  This SF.NET email is sponsored by: AMD  Your access to the experts on Hammer Technology! Open Source & Linux Developers, register now for the AMD Developer Symposium. Code: EX8664 http://www.developwithamd.com/developerlab _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: Nick Pelling <NP<elling@cl...>  20020918 10:42:45

sinc() is actually a wellknown maths function, and is often used in code for rescaling / resampling. Search for "sinc function" on Google, and you'll hit loads of maths sites explaining it, such as: http://mathworld.wolfram.com/SincFunction.html Cheers, .....Nick Pelling..... Original Message From: Tom Forsyth [mailto:tomf@...] Sent: 16 September 2002 12:51 To: Joris Mans; gdalgorithmslist@... Subject: RE: [Algorithms] Solid angle calculation I assumed that was a typo, and they mean "sine(theta)". But I didn't worry about it too hard since, using cubemaps and just ignoring the spherical distortion (i.e. every sample is evenly weighted) seemed to work just fine  at least to within the tolerance of my eye :). It also bins all the angle stuff and uses the SH components directly (since you already have x,y,z to plug into the component calculations), so there's no trig anywhere in any equations. Which is very good news for speed. Tom Forsyth  purely hypothetical Muckyfoot bloke. This email is the product of your deranged imagination, and does not in any way imply existence of the author. > Original Message > From: Joris Mans [mailto:joris.mans@...] > Sent: 12 September 2002 02:17 > To: gdalgorithmslist@... > Subject: [Algorithms] Solid angle calculation > > > Hi > > I am currently trying to understand/implement the integration scheme > used in "An efficient rep. for Irradiance env maps" and I > think my math > skills have some holes in them, because I don't understand the formula > for calculating the solid angle. > This is the c sample code: > > domega = (2*PI/width)*(2*PI/width)*sinc(theta) ; > > I understand where the / width comes from since you are integrating in > steps of 1/width over the sphere, but I fail to understand what > sinc(theta) means. > > FYI: > > float sinc(float x) { /* Supporting sinc function */ > if (fabs(x) < 1.0e4) return 1.0 ; > else return(sin(x)/x) ; > } > > How does this term calculate the solid angle? > > Thanks > > Joris > > > >  > In remembrance > http://www.osdn.com/911/ > _______________________________________________ > GDAlgorithmslist mailing list > GDAlgorithmslist@... > https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist > Archives: > http://sourceforge.net/mailarchive/forum.php?forum_id=6188 >  This sf.net email is sponsored by:ThinkGeek Welcome to geek heaven. http://thinkgeek.com/sf _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: Dirk Gregorius <dirk@di...>  20020918 10:04:30

Hi, this is my first post to this mailing list, so if anything is not = correct please just tell. I have just taken a job at my university as a student. The faculty = reasearches motion with a motion capture system. They developed a system = which produces joint coordintaes for any time t in absolute cartesian = world coodinates. These joints build a joint hierachy, which is constant = over time. My task now is to connect this data with a skinmesh and = deform it. Does anybody of you has experience in connecting a mesh with motion = capture data? How did you do this and what constraints did you use? Is = ist possible to normalize the mocap data such data the lenght between = all joints is one and the root joint has the coordinates (0,0,0,)? Any = other suggestions are welcome. When this task is done I thought of the following to deform the mesh: First I want to create a bone hierachy from the joint hierachy? ( BTW: = What is the difference? My problem is that I don't know how to define an = orientation for a joint. ) I define the following. Every bone has an orientation and a position. = Given two joints A and B the position is always the joint higher in the = hierachy, here: A. If I store the orientation as three vectors, one is = given by vector AB  now always the xaxis. I define that the xaxis = should always point to the next joint. Now I thought of hardcoding the other two in the restpose. I thought of constraining the zaxis vector to (0,0,1). With the AB = initialvector which I call now AiBi =3D (Xi,Yi,Zi) I find the the yaxis vector simply through the crossproduct ( Xi, Yi, = Zi ) x ( 0, 0, 1 ) =3D ( Yi, Xi, 0 ) This results in a bone hierachy for the the restpose where every bone = has the following representation:  Xi Yi 0 Ax   Yi Xi 0 Ay  =20  Zi 0 1 Az   0 0 0 1  With this information I can build the bone hierachy for any given time t = this way, i hope. I have the initial data and I also get the the joint coordinates for any = given time t in absolute world coordinates: The position of each bone is simply A(t) and the first vector of the = orientation is AB  my new xaxis. Now I can calculate the transform of AiBi to AB. The axis of rotation is the crossproduct of AiBi and AB and the angle = omega is acos( dot( AiBi, AB ) ) Now I can calculate a matrix of this information and transform the y = and z axis this way or put the axis and the angle in a quaternion and do qNew =3D q^1 * q0 * q. This leads to a transition matrix Mtrans =3D M(initialBone)^1 * = M(Bone(t) ) The mesh can then be deformed calculating: NewVertex =3D w1 * Mtrans(BoneOfInfluence) * OldVertex + ....+ wn * = Mtrans(BoneOfInfluence) * OldVertex=20 I couldn't try this out because I first have to connect the mesh with = the joints, what is for me transforming the joint data in the coordinate = system of the mesh data or vice versa and scale everything untill it = fits. But I don't know if this destroys the mocap data. If you have any experience with this task please tell!! Dirk 
From: Hansen, Daniel <Daniel.H<ansen@di...>  20020918 08:20:48

Has anyone parametricized the velocity and position taking airresistance into consideration. I.e v(t) = v0 + a * t p(t) = p0 + (v0 + 0.5 * a * t) * t ..could be used when there's no airresistance. I'd like something similar with airresistance. I've seen some formulas with alot of nasty exponents in them, I'm looking for a simpler hack. Anyone? Original Message From: Charles Bloom [mailto:cbloom@...] Sent: den 11 september 2002 07:58 To: gdalgorithmslist@... Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells This "midpoint method" is 2nd order RungeKutta. See, for example : http://www.sst.ph.ic.ac.uk/angus/Lectures/compphys/node11.html http://csep1.phy.ornl.gov/ode/node7.html The traditional socalled "RungeKutta method" is the 4th order method. Anyway, all silliness, but some of the stuff on the web is pretty good. At 12:19 AM 9/11/2002 0400, jack@... wrote: >Thanks to all. Using the midpoint method combined with a small enough time >step appears to provide a reasonable amount of accuracy for my use. I'll >keep RungeKutta in mind for future use if it proves necessary. > >Jack > >Original Message >From: Chris Butcher (BUNGIE) [mailto:cbutcher@...] >Sent: Monday, September 09, 2002 2:52 PM >To: Jon Watte; jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >Even using something as simple as the midpoint method (a secondorder >integrator) will give much better results for minimal effort. RungeKutta >is probably overkill... ? > >v_intermediate= v  0.5*k(v^2)t; >v_final= v  k(v_intermediate^2)t; > > >Chris Butcher >Rendering & Simulation Lead >Halo 2  Bungie Studios >butcher@... > > >Original Message >From: Jon Watte [mailto:hplus@...] >Sent: Monday, September 09, 2002 12:43 >To: jack@...; gdalgorithmslist@... >Subject: RE: [Algorithms] Simple Air Resistance Simulation for Shells > > >> I'm trying to do a simple ballistics model for shells. The formula I'm >> using is: >> >> v' = v  k(v^2)t; > >This is a firstorder Euler integrator (I believe). These are known >to be unstable at any time step  as you notice :) > >The typical answer when faced with numerical integration problems >is to turn to a fourthorder RungeKutta integrator. I'm sure if you >plug that into Google, you'll get a massive number of hits. It might >show up on MathWorld, too. > >Cheers, > > / h+ > > > > > >mail2web  Check your email from the web at >http://mail2web.com/ . > > > > > >In remembrance >www.osdn.com/911/ >_______________________________________________ >GDAlgorithmslist mailing list >GDAlgorithmslist@... >https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist >Archives: >http://sourceforge.net/mailarchive/forum.php?forum_ida88 >  Charles Bloom cb@... http://www.cbloom.com  In remembrance http://www.osdn.com/911/ _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=6188 
From: T.M. Evans <tmadoc@ti...>  20020918 07:44:57

You can convert a cubemap to a sphere map, I have a demo (with source) = by Terry Welsh that does this in realtime using OpenGL. I tried looking = for it so I could post the link but I am unable to find it, I think I = probably originally foud it on the OpenGL headlines. I suppose that if you can't find it I can mail it to you, it's pretty = small. Cheers, Madoc  Original Message =20 From: Gareth Lewin=20 To: Nguyen Binh ; gdalgorithmslistadmin@... ; = Gareth Lewin=20 Cc: GdalgorithmsList=20 Sent: Monday, September 16, 2002 9:54 AM Subject: RE: Re[2]: [Algorithms] Sphere map generation. Please help!!! > Hi Gareth, Hi. > GL> Try to imaging what a Sphere map is. It is basically a=20 > fisheye view with a > GL> 180 degree lens of the scene from a certain point. > GL> >=20 > Thanks though I knew that before but I'm seeking for a=20 > more "technically" > definition of sphere map. Ok, didn't know you knew that. Maybe you can explain where you are = struck then ? Because basically all you need is to set up a camera with a 180 degree fov and render your scene. If you want to generate a sphere map = for an object in Max ( Slightly offtopic ) then you can hide the object, = find it's center point, render the sphere map ( or two ) from that point = and reshow the object. >=20 >=20 > GL> OT: > GL> I know that max can autogenerate cube maps for you,=20 > maybe it can generate > GL> sphere maps too ? >=20 > Yes, I see in 3DSMax we can use "Reflect/Refract" material to > generate cube map but no way we can do with sphere map. If I'm not mistaken, the Reflect?Refract material comes with source = code in the maxsdk. Sorry for not being sure, but we here use Maya (Sadly :)) = and I don't have the maxsdk installed anymore. _____________________ Regards, Gareth Lewin  This sf.net email is sponsored by:ThinkGeek Welcome to geek heaven. http://thinkgeek.com/sf _______________________________________________ GDAlgorithmslist mailing list GDAlgorithmslist@... https://lists.sourceforge.net/lists/listinfo/gdalgorithmslist Archives: http://sourceforge.net/mailarchive/forum.php?forum_id=3D6188 