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Atheist

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About Atheist

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  1. Assuming no polys in the hi-res model correspond to more than one poly in the low-res one, I´d try this: For each poly i in the low-res model: - calcluate the plane Pi it lies in - For each poly j in the hi-res model: -- Project j on Pi. Also remember a distance d_ij of j from Pi (I´d try average distance of j´s points). -- if projection lies within Pi mark it as possible possession of j. Now, the problem is that for polys j it´s possible to meet the "possessed by" criteria of more than one poly i. That´s why a 2nd step is nessecary to determine which of the possible owners j has. This one would be as simple as: j belongs to the poly i that it´s closest to: Owner = i: d_ij=min. That´s just my first guess what I´d do. There may be professional algorithms that are better or it might be able to simplify above. It will probably not work if polys of the hi-res model do not project into a poly of the low-res model. I assumed you get the low-res model by removing points from the hi-res one. It should give ok results, then.
  2. Atheist

    normal of implicit function

    ... because the gradient (d/dx, d/dy, d/dz)F gives you the direction where F raises most and since your surface is defined by "points where F doesn´t change" that´s perpendicular (losely speaking, but maybe helping to understand it).
  3. Atheist

    one special point from plane and 3 points

    Definitely solveable if I undestood you correctly. My first idea for a solution (short version because I am tired): P4 = P1 + a(P2-P1) + b(P3-P1) the plane equation in it´s explicit form with Pn being the coordinates (coordinate vectors) of point n is true in 2D as well as in 3D, so: 1) with the 2D-coordinates Pn -which you know all n=1..4 of- calculate a and b. 2) plug a and b in the equation with the 3D-coordinates to determine P4.
  4. Atheist

    Symbolic Integration!

    1st off: This is one of my "noone answered so far and I have to distract myself so I´ll give you a non-competent answer with suggestions hoping it helps you"-posts. So don´t assume what I´m going to tell you is anywhere close to the current state of research. I once wrote a parser to plot 2D-surfaces several years ago (was my first contact with OpenGL, I think). The parser created a (mostly binary) tree from a string entered. Each node/leaf represented a mathematical operation. When created the node looks for the operation with the lowest orde in the string given to it, remembers it, splits up the string accordingly and gives the two substrings to the next-level nodes. Example: s = f(x)="5*x+2" Type: Addition, s1="5*x", s2="5" Right "2": Type: Constant=2 => Creation terminated Left "5*x": Type: Multiplication, s1="2", s2="x" Left "5": Constant as above Right "x": Variable. Creation terminated. Plug in Value at call. To get for example f(2) you call the tree and plug in 2 wherever you have a "variable"-leaf. Of course you can have more than one variable x and you could even give a string like "f(a,fg,e)=..." and determine the names/number of the variables and the name of the function by parsing the left side of the "=" sign. Using such a structure differentiation shouldn´t be much of a problem. Simply apply rules of differentiation on each node like "Sin(f(x))' = Cos(f(x))*f'(x)" and "f*g = f'*g + g'*f". This should work but needs a lot of optimization (like a subtree that only contains constants to be crunshed into a single leaf) to be halfways efficiently. As for integration: As long as you stick to polynomials that´s no problem, of course. When it comes to more complicated things ... oh, I have to go. No, honestly, I dunno if that parser structure is capable of doing that.
  5. Atheist

    Check my maths

    yep, that´s one of the "additional assumptions" I spoke about.
  6. Atheist

    Check my maths

    Quote:Original post by Atheist If the four points don´t lie in a plane ... well as I said I think you can´t even define the surface without additional assumptions. I´d split the quad into two triangles and use the triangle that applies to the point you´re looking for. Well, maybe I should add that of course having an algo to determine a height of the point withing the 2D-quad (the projection of your four heightpoints on the ground) you of course implicitely have defined your additional assumptions how the surface looks like. The advantage of splitting the quad into two triangles is that you know you´re dealing with flat surfaces which is the easiest geometry imaginable because plain linear algebra applies. Intuitively I´d think that will come handy if you want to do other things with your terrain than simply put an orc on it. Collision detection for example. In short: Splitting up the quad into triangles might not be the best option and it´s defenitely not the only one, but I think it´s the easiest one.
  7. Atheist

    Graduate schools (astrophysics)

    Can´t help you much with your questions because I don´t have the slightest clue about the US university system and I dont know the abbrevations GPA and GRE ("subject GRE" = "General Relativity"?). But I don´t think you´ll find many people here that can give you an anwer to your questions (maybe try calling the info-lanes of the universities and ask them) so I´ll give a few comments: >> My B.S. degree is in computer science. Would that be a >> problem if I wish to purse an M.S. in physics? I´d bet on it. Having studied CS you should have more or less the same mathematical background as a physicist (both parties would argue that theirs is better but I´ve got some friends studying CS and they´re having the same classes as I had) but you lack all "physics". If you want to study astrophysics (can one study astrophysics without studying normal physics in the US?) you should be aware that astrophysics not only uses General Relativity (which shouldn´t be much of a problem) but also elementary particle physics (which can become very hard if you dig deep enough ... Quantum Field Theories and stuff) and Thermodynamics/Statistics (maybe not on the Quantum Statistics level but I wouldn´t count on that). Only thing you could leave out from a normal physics study would be solid state physics and optics. Well, maybe even Quantum Theories though I would be quite surprised if someone would get a MS in physics without even knowing QM. In Germany, if you want to change "career path" it´s up to the university which parts of your education they accept and which courses you have to retake and I bet it´s quite the same in the US. So you´ll have to ask them. >> Would they consider the fact that I've been fairly >> successful in CS industry? I don´t know if a university would care about that. However: Modern theoretical physics uses computers a lot. In fact I don´t know one theoretical physicst who can´t code (but this won´t help you much since there´s no mandatory programming courses for physicsist - it´s simply assumed that they can code). Your experiences in CS industry might at least help you to get a job, later. If you only want to improve your math you should consider Applied Mathematics (Numerics). This should be much closer to your original education and I´d expect less problems with switching to this. Oh, and: >> Can I present them with personal projects (perhaps do some >> physics simulations?) If you ever do this you shouldn´t do stuff that is called physics simulation in this forums. I hardly doubt you´re going to impress someone with Newtonian Mechanics (unless they tell you otherwise, of course), regardless of how accurate, stable and fast it is. Final words: As said above I don´t know the US system. In fact I don´t even know what a Bachelor is because there´s no equivalent in germany (a Master would be something like a german Diploma which is the lowest rank there is in germany). So if something above is obviously bullshit, then it´s probably because of that. I just tried to give my statement as a (not yet-) physicist.
  8. Atheist

    Check my maths

    Three points allways lie in a plane. That´s not true for four points. If the four points of your quad don´t lie in a plane you´d even have trouble defining the area of your quad. If the four points of your quad lie in a plane then you can do the height interpolation as you´d do in a triangle (you´re talking about heightfields, no?) and don´t have to bother about the 4th point (but clx and cly can be >1, then). If they don´t lie in a plane ... well as I said I think you can´t even define the surface without additional assumptions. I´d split the quad into two triangles and use the triangle that applies to the point you´re looking for.
  9. Atheist

    collision woes

    Take a sphere (a sphere has a center and a radius) that encloses your object (as close as possible) and check for collision with the sphere (something closer to center than radius) instead of every triangle (or check the triangles only if there is collision/interstection) within the sphere. Oh, and ... 2D sphere = circle.
  10. Atheist

    What do you do when someone PM's you ...

    lol, wonder if my last post in this thread raised someone´s attention. Just also got such a PM... [headshake]
  11. Atheist

    What do you do when someone PM's you ...

    Reply or ignore, just as with any other message.
  12. Atheist

    collision woes

    Don´t know the book you´re talking about and I doubt that any collicion detection can be more accurate than checking for every single triangle (or whatever your shape consists of). Nevertheless, hierarchy of spheres for me sounds like a tree-structure: A big bounding circle around your whole object that includes smaller circles which fir your geometry better (which can of course also contain further smaller circles or triangles or whatever). Implementation would be "if collision with sphere then check all objects included in this sphere" starting with the big sphere around your whole object. Like I said it doesn´t make your collision more accurate than checking every triangle but it makes it faster because you can reject some triangles early. I don´t know if that´s what you were asking for (I never read any papers for collision detection myself since I feel able to write my own without any external help which is much more satisfying if it works). I merely gave a reply because noone else did so far. [Edited by - Atheist on June 24, 2004 9:31:54 AM]
  13. Atheist

    3D Matrix...

    "Layer" would be my favorite, I think.
  14. Atheist

    Origins Of The Universe

    Quote:Original post by Raduprv Quote:Original post by Atheist - Force is a term/concept that is used in Newtonian Physics (which is the standard for "everyday-physics") only. General Relativity and elementary particle physics take a different approach called "Path Integrals". This common feature of both approaches also led string theories (the one paper I read about it) take this approach. Generally spoken, there is no force in modern physics. - While force is very successful in Newtonian Physics, Newtonian Physics fails for spacetimes with much gravity which I´d expect in a Big-Bang scenario. This is strange, because I thought the quantum mechanics makes use of the nuclear and electric forces... Like I said: You might find this interesting (classical QM isn´t used in elementary particle physics, btw). The correct terms would be weak/strong/electromagnectic interactions. But this is getting offtopic ...
  15. Atheist

    Origins Of The Universe

    Preword: I usually don´t participate in threads that deal with superlatives like "infinity" (uh, oh ... "Big Bang" comes close ...). They imho tend to attract a lot of strange folk that either say stupid things they once heard but failed to understand or "i know better than you"-types (when it comes to pure math, there are certainly some people around this forum who actually do knwo better than me). I´m writing this because try_catch_this asked for it. Feel free to correct/add anything but don´t expect me to react. Infinities cannot be treatened directly. You usually treat them as limits of functions. At least I´d know no direct example right now, aside from "you can leave out any number of countable points when doing Lebesque Integrals under certain conditions". But these conditions are most likely also defined by limits (don´t want to look that up at nearly 4am). Let´s choose an example quite close to the one you just presented: A sphere with radius r that has a total mass of m uniformly spread in it. The mass-density (which is also a limit, btw) -which you seemed to call p in your post- will be: p(r) = m/(4/3*pi*r³) now, decrease the radius of the sphere by whatever means (we´re talking about math here, so don´t bother about "but they´ll get kinetic engery" and such stuff for now) and let the total mass remain the same (where should it go, anyways): The only parameter in p(r) that changes is r. If it gets smaller p becomes greater (remember that the mass of your sphere doesn´t change). In fact, p will exceed any positive number if you only choose r small enough. That´s the mathematical definition of a value approaching infinity and thus you say p is infinite when the radius becomes 0. The total mass m, however, remained unchanged by definition. => limit(r->0) p(r) = infinity, limit(r->0) m = m = finite. Nevertheless, as I allready mentioned: Problems with the big bang start even before you reach r=0 (r being something like the "radius" of your universe, now). I´ll take the opportunity to comment on Raduprv: Commenting on the examples you brought would lead to far, be pedantic at many points and especially would exceed my knowledge in cosmology. Some things that might interest you, though: - Force is a term/concept that is used in Newtonian Physics (which is the standard for "everyday-physics") only. General Relativity and elementary particle physics take a different approach called "Path Integrals". This common feature of both approaches also led string theories (the one paper I read about it) take this approach. Generally spoken, there is no force in modern physics. - While force is very successful in Newtonian Physics, Newtonian Physics fails for spacetimes with much gravity which I´d expect in a Big-Bang scenario.
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