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From: Douglass Turner <douglass.turner@gm...>  20050921 23:43:38

Coolness. Thanks Stepahne. On 9/21/05, Stephane Popinet <s.popinet@...> wrote: > Douglass Turner wrote: > > I would love to use this package for my computer graphics surface > > generation but the lack of support for attaching UV params to > > surfaces is a show stopper. For starters, texture can't (easily) be > > attached to tessellations generated by gts. > > GTS is objectoriented. It is relatively simple to customise objects > according to your needs. Attaching UV params to vertices should be easy. > Have a look at GtsColorVertex in the source for an example of how this > can be done. > > cheers > > Stephane > > >  > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App Server. > Download it for free  and be entered to win a 42" plasma tv or your ver= y > own Sony(tm)PSP. Click here to play: http://sourceforge.net/geronimo.php > _______________________________________________ > Gtsgeneral mailing list > Gtsgeneral@... > https://lists.sourceforge.net/lists/listinfo/gtsgeneral >  Douglass Turner 
From: Stephane Popinet <s.popinet@ni...>  20050921 21:13:59

Douglass Turner wrote: > I would love to use this package for my computer graphics surface > generation but the lack of support for attaching UV params to > surfaces is a show stopper. For starters, texture can't (easily) be > attached to tessellations generated by gts. GTS is objectoriented. It is relatively simple to customise objects according to your needs. Attaching UV params to vertices should be easy. Have a look at GtsColorVertex in the source for an example of how this can be done. cheers Stephane 
From: Douglass Turner <douglass.turner@gm...>  20050921 19:17:09

I would love to use this package for my computer graphics surface generation but the lack of support for attaching UV params to surfaces is a show stopper. For starters, texture can't (easily) be attached to tessellations generated by gts. I've thought about hacking the source code to add UV to the vertex object but, well, that would be a hack. What's a computer graphicist to do? Cheers, Doug 
From: fsm <thepooh@gm...>  20050921 13:50:00

Hi, I'm searching a way to build up a mesh from given points in 3D. These points are resulting from a virtual projector that projects its pixels as rays onto surfaces / screens. Thus, besides the position of the points I also have the pixel coordinate of the projector's pixel where the ray originated. With these intersectiono points given, I'd like to generate a Mesh in order to visualize the projection. I found out that the GTS has functions to do a delauny triangulation in 2D. Now I'm wondering if there is an equivalent for 3D space. Any advice is highly appreciated since I'd never to do with triangulation. Regards, Felix  GMX DSL = Maximale Leistung zum minimalen Preis! 2000 MB nur 2,99, Flatrate ab 4,99 Euro/Monat: http://www.gmx.net/de/go/dsl 
From: Rob McDonald <robm@as...>  20050921 02:51:46

> > > On modern CPUs, trig functions (and their inverses) are > > evaluated via > > > expensive table lookups hard coded into microcode. > > There's pretty much nothing *less* expensive in terms of time than a single > table lookup in "ROMequivalent" memory. I assume you are referring to an > iterative algorithm involving multiple lookups here? I have to confess I am > not familiar with the operation of the FPUs in modern CPUs. > > I didn't catch the part where "spreads" are just anglesquared's. Well, > like I said, if distancesquared and anglesquared are going to set the > world of trigonometry on fire, far be it from me to squirt the extinguisher. > But I'm gonna wait to hold my breath. > I'm not sure of the exact technique they use, but in my tests, they are very expensive. I know that fp division is a hybrid of a table and an algorithm. Hence, the Pentium fp bug (an error in the table) recurred for various divisors as the table value got reused. I may have mistyped, but IIRC spread=(sin (theta))^2. All that said, I do think this guy is selling a potent mixture of snake oil. Rob 
From: Gary R. Van Sickle <g.r.vansickle@wo...>  20050921 02:40:10

> > On modern CPUs, trig functions (and their inverses) are > evaluated via > > expensive table lookups hard coded into microcode. There's pretty much nothing *less* expensive in terms of time than a single table lookup in "ROMequivalent" memory. I assume you are referring to an iterative algorithm involving multiple lookups here? I have to confess I am not familiar with the operation of the FPUs in modern CPUs. I didn't catch the part where "spreads" are just anglesquared's. Well, like I said, if distancesquared and anglesquared are going to set the world of trigonometry on fire, far be it from me to squirt the extinguisher. But I'm gonna wait to hold my breath.  Gary R. Van Sickle 
From: Rob McDonald <robm@as...>  20050921 01:39:31

> On modern CPUs, trig functions (and their inverses) are evaluated via > expensive table lookups hard coded into microcode. It is very interesting > to perform a microbenchmark for various elementary mathematical operations > (*). These table lookups force a predetermined and finite level of > accuracy. Oh yeah, I forgot the footnote... (*) Try it. Write a simple program to perform some large number (1e10 or so) of binary mathematical operators with random arguments. Make sure your compiler doesn't optimize away your code. Normalize the results by addition. Work with single or double precision floating point numbers. Addition, subtraction, multiplication, division, exponentiation arbitrary power (positive & negative), exponentiation integer powers (positive & negative), square root, exp, log2, log10, ln, sin, cos, tan, asin, acos, atan, etc. I know I was amazed by the results. You'll soon be multiplying by 0.5 instead of dividing by two. You'll be writing inline macros to multiply out small integer powers. And the only thing you'll avoid more than trig functions are their inverses. Rob 
From: Rob McDonald <robm@as...>  20050921 01:24:44

Don't take this as a defense of Rational Trig, I don't know enough about it to bother with a defense... However, his approach isn't as revolutionary as he lets on. And from its similarity to our existing system, we may observe its strengths. And from that, we may see where it should be applied. Despite the author's grandstanding style, occasionally he relates his technique to the old way. He admits that most trig problems can be solved without evaluating the trig functions. It just takes more algebraic manipulation. The quadrance is simply the distance squared. The spread is simply the square of the sine of an angle. How often do forms like distance squared or sine squared show up in trig formulas or identities. Fairly often I'd say. If all of our trig equations (law of sines, law of cosines, etc.) are rederived in these new terms, we can dispense with the traditional transcendental trig functions. We now have a capable tool set that does not rely on trig functions. On modern CPUs, trig functions (and their inverses) are evaluated via expensive table lookups hard coded into microcode. It is very interesting to perform a microbenchmark for various elementary mathematical operations (*). These table lookups force a predetermined and finite level of accuracy. I mentioned this technique in this forum because geometric algorithms like those in GTS are vexed by floating point rounding error. GTS uses adaptive floating point techniques to mitigate this problem. I suspect that GTS avoids the use of trig functions entirely (I haven't checked). However, if a new set of tools allow one to more easily derive geometric relations that avoid transcendentals, they will come in handy once in a while. And if GTS can easily be extended to facilitate this approach, then where is the harm? (gts_triangle_spread() gts_triangle_quadrance() etc.) Rob 
From: Gary R. Van Sickle <g.r.vansickle@wo...>  20050921 00:28:11

> From: David Sterling > Sent: Tuesday, September 20, 2005 11:02 AM > To: gtsgeneral@... > Subject: RE: [gtsgeneral] [RFC] Rational Trig > > > The presentation style left me a little skeptical as well, > but I'm tempted to browse through a copy when it comes out. I > personally think the Calculus is a stunningly powerful set of > tools Yeah, it's worked pretty well since about Newton's time, hasn't it? ;) > and to attempt to rework bits of mathematics to avoid > using it for practical (as oposed to pedagogical) purposes is > a bit like trying to redesign vehicles for transcontinental > travel without using the wheel. BUT THE WHEEL IS A CIRCLE!!! IT'S CONFUSING!!! AND SINCE IT IS CONFUSING, IT MUST BE FUNDAMENTALLY FLAWED!!!! ;) > That said, this chapter gives > a sense that we could sucessfully define Euclidean geometry > using squared distance and (roughly) ratios of sides of > triangles( and some of us might even find it asthetically > pleasing). There's a lot of things "We could" do. For approximately a billion years, generation upon generation of "We"s much smarter than the good Doctor or anybody here have successfully applied angles and lengths to all manner of problems, and haven't worried much about it. And despite the good Doctor's ramblings, no, the square of a distance is not more intuitive than the distance itself, nor is that "spread" of his more intuitive than the omnipresent angle. > I suspect these ideas become more compelling when > studying Euclidean geometry over more general fields, or in > number theoretic applications where there is genuine insight > to be gained from understaning the origin of particular > irrational numbers. > Maybe they is and maybe they ain't. Last night, I would have rated what I've seen of the treatment provisionally at maybe 50% burger, 50% bun. After sleeping on it, and after having read this article: http://physorg.com/news6555.html I am willing to bet anybody a Coke that it's 99% Kookdom, 1% SemiInteresting Mathematical Diversion Which Breaks No New Ground. And before you take me up on that, note what the guy says: "Generations of students have struggled with classical trigonometry because the framework is wrong." "The framework [of 'classical' trigonometry] is wrong" == the statement of a Kook. A further bet: his book has a claim somewhere in it that the Pyramids of Egypt could only have been designed and built using "Rational Trigonometry". That's a TWOCoke bet! You KNOW this guy makes a claim like that! ;) > btw: per your comment about rotation matrices and > quaternions: Applying these operator doesn't involve > trigonmetric functions but defining them sure does :) > I knew I would catch hell for that ;). Ok, then let's make it a "spreadular momentum" vector. Take a rigid body's "spreadular momentum", its "quadranertia tensor", whatever, and let's see how the body changes orientation. I'm guessing the formulation is vastly more complex than the 'classical' approach, but I would be delerious for the good Doctor to prove me wrong! > Just my 2 cents, > > David  Gary R. Van Sickle > Original Message > From: gtsgeneraladmin@... > [mailto:gtsgeneraladmin@...]On Behalf Of > Gary R. Van Sickle > Sent: Monday, September 19, 2005 6:44 PM > To: gtsgeneral@... > Subject: RE: [gtsgeneral] [RFC] Rational Trig > > > > From: gtsgeneraladmin@... > > [mailto:gtsgeneraladmin@...] On Behalf Of Rob > > McDonald > > Sent: Monday, September 19, 2005 7:18 AM > > To: gtsgeneral@... > > Subject: [gtsgeneral] [RFC] Rational Trig > > > > This book will soon be released from the land Down Under. > > I'm reserving judgement on whether he is crackpot or genius until > > after I take a closer look at his book, but I think some of > his ideas > > certainly have merit. > > > > Welp, read the first chapter. Whenever I see anything to the > effect of "why, we just use the length *squared* instead of > the length, and the fundamentally flawed concept of > trigonometry becomes mere childs' play!", the first thing I > ask is: "Well then, how come one of the geniuses you're > 'poohpooh'ing come up with it?" > > As to any possible applicability to things like GTS, well, > I'll have to wait to see how he handles rotations and > translations of his triangles without matrices or quaternions > before buying his book. No trig involved in rotating things > with matrices or quaternions. > >  > Gary R. Van Sickle > > > > >  > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App Server. > Download it for free  and be entered to win a 42" plasma tv > or your very > own Sony(tm)PSP. Click here to play: > http://sourceforge.net/geronimo.php > _______________________________________________ > Gtsgeneral mailing list > Gtsgeneral@... > https://lists.sourceforge.net/lists/listinfo/gtsgeneral > > >  > SF.Net email is sponsored by: > Tame your development challenges with Apache's Geronimo App Server. > Download it for free  and be entered to win a 42" plasma tv > or your very > own Sony(tm)PSP. Click here to play: > http://sourceforge.net/geronimo.php > _______________________________________________ > Gtsgeneral mailing list > Gtsgeneral@... > https://lists.sourceforge.net/lists/listinfo/gtsgeneral 