Help, Graphics Gurus please
Ok I'm at the point where mathematics is the only thing that is keeping me from doing advanced things in the graphics field. I have not taken calculus yet however I have taken precalculus (trig and algebra) and we stopped right before vector mathematics and combinatorics. I'm not so versed in matrix math but I've done some examples, nothing significant.
I know what a limit is but I have no idea how to apply its practicality in something other than theory. I know what derivatives are but I have no idea how to derive my own equations to come up with the formula for rotation and such. To the point my math knowledge is a bit broken thanks to the grade school education in my state and my complacency for math before stumbling onto programming 2-3 years ago as a sophmore in high school.
to the point what did you learn that made you realize that you could do just about anything professionally in a project to create graphics (model geometry for instance) using only mathematics. I've read a crap load and able to generate hand-coded models from picturing them in my mind but I'm in awe at how people somehow come up with methods of create spheres using only math skills and for loops. Im able to use api methods and use vertex buffers to load in pre-made vertex data but Its like greek trying to inductively reason as to how to generate data from a mathematical equation.
At my university I realize how abstract and intuitive math can really be but as a result it makes me feel like I'm missing something the more I know because it doesn't seem concrete. Over this past year at my university I've realized how far math could take me but its very daunting to try to tame even 1/8 of the beast that is calculus.
I know what a limit is but I have no idea how to apply its practicality in something other than theory. I know what derivatives are but I have no idea how to derive my own equations to come up with the formula for rotation and such. To the point my math knowledge is a bit broken thanks to the grade school education in my state and my complacency for math before stumbling onto programming 2-3 years ago as a sophmore in high school.
to the point what did you learn that made you realize that you could do just about anything professionally in a project to create graphics (model geometry for instance) using only mathematics. I've read a crap load and able to generate hand-coded models from picturing them in my mind but I'm in awe at how people somehow come up with methods of create spheres using only math skills and for loops. Im able to use api methods and use vertex buffers to load in pre-made vertex data but Its like greek trying to inductively reason as to how to generate data from a mathematical equation.
At my university I realize how abstract and intuitive math can really be but as a result it makes me feel like I'm missing something the more I know because it doesn't seem concrete. Over this past year at my university I've realized how far math could take me but its very daunting to try to tame even 1/8 of the beast that is calculus.
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I'm not sure what response you are expecting. This is the only concrete "question" I see in your post:
I am assuming that's a question. The answer I can give you is: I actually realized I CANNOT do anything I want in graphics. Sure I took 5 calculus for 3 years in college, but was it graphic-oriented? No. I studied Chemical engineering, not computing. I have learned what I have been able to learn, but there's a very real limit to where I can go. And of course this is aggravated by the fact that I don't really code graphic-intensive applications.
If I am missing the point or a question, then let me know.
| DeXecipher wrote: |
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| what did you learn that made you realize that you could do just about anything professionally in a project to create graphics (model geometry for instance) using only mathematics |
I am assuming that's a question. The answer I can give you is: I actually realized I CANNOT do anything I want in graphics. Sure I took 5 calculus for 3 years in college, but was it graphic-oriented? No. I studied Chemical engineering, not computing. I have learned what I have been able to learn, but there's a very real limit to where I can go. And of course this is aggravated by the fact that I don't really code graphic-intensive applications.
If I am missing the point or a question, then let me know.
I'm nearly at the end of Analysis II, right now. I know how to calculate and prove limits in R^n->R; I can derive R^n->R^m functions; I can find and prove maximums and minimums of functions (local and global, unrestricted and restricted by continuous functions); I can integrate in one, two, and three dimensions, and integrate improperly in one dimension; and a few other things I'm forgetting right now.
And let me tell you: absolutely none of it has any application to graphics programming whatsoever. At least not directly. Some of it might be useful to understand more advanced subjects that do have applications, but I'm not aware of any such subjects.
Geometry, trigonometry, and linear algebra are really all you need. You may occasionally need one or two things from other branches, but those three are the bread and butter of graphics programming.
I don't think such a thing exists. Fractals have some use in procedural generation (e.g. terrain generation), but saying you can do anything with them is going a little too far, I think.
I find your misuse of the word "induction" irritating.
To clarify, induction means either:
* In mathematics, if you can prove that a property P of the naturals is true for 1 (i.e. P(1)) and that P(n) implies P(n+1), then you've proven that P is true for all naturals.
* In empirical science, an inductive reasoning concludes that a statement must be true for all members of a set from the fact that it is true for some members of the set.
The former is a proof technique, not a reasoning technique.
The latter is a reasoning technique, but it's not useful in mathematics. Imagine concluding from the fact that the first four prime numbers are 2, 3, 5, and 7, that all odd numbers greater than 1 are prime. Popper would argue that induction is not useful in science, either.
This is generally not a terribly useful technique unless you're really hurting for space, you don't have artists to help you, the thing you're trying to render is bizarrely complex and/or large (for example, see Infinity. It's a game a guy is writing that uses procedural generation to generate and store planets, systems, galaxies, and so on. Ships and other artificial structures are still hand-designed, though), or you're out for a challenge.
And let me tell you: absolutely none of it has any application to graphics programming whatsoever. At least not directly. Some of it might be useful to understand more advanced subjects that do have applications, but I'm not aware of any such subjects.
Geometry, trigonometry, and linear algebra are really all you need. You may occasionally need one or two things from other branches, but those three are the bread and butter of graphics programming.
| what did you learn that made you realize that you could do just about anything professionally in a project to create graphics (model geometry for instance) using only mathematics |
| inductively reason as to how to generate data from a mathematical equation |
To clarify, induction means either:
* In mathematics, if you can prove that a property P of the naturals is true for 1 (i.e. P(1)) and that P(n) implies P(n+1), then you've proven that P is true for all naturals.
* In empirical science, an inductive reasoning concludes that a statement must be true for all members of a set from the fact that it is true for some members of the set.
The former is a proof technique, not a reasoning technique.
The latter is a reasoning technique, but it's not useful in mathematics. Imagine concluding from the fact that the first four prime numbers are 2, 3, 5, and 7, that all odd numbers greater than 1 are prime. Popper would argue that induction is not useful in science, either.
| Its like greek trying to reason as to how to generate data from a mathematical equation |
Generally, the process involves obtaining a data set that you want to meet (i.e. the coordinates of a sphere), noting patterns within that data set, and then attempting to match a mathematical function that, when graphed, matches the pattern seen in the data set. More often than not you'll see a trend that can only be met by using multiple functions, and that's where things get tricky. But the methodology is fairly simple, works well, and permits you to apply practically any component of mathematics that can output a graph.
Also, just to comment on a few things:
While there aren't many uses for calculus in the field, the fourier transform is pretty deeply founded in calculus, and is fundamental in quite a few areas of graphics. Water simulation is one of the more common ones, but it's also occasionally used in procedural regeneration of textures and meshes. However, most of the time I've seen it used in texts simply to present an understanding of a situation (that is to say, it's not used in implementation, only in analysis.)
The games industry is incredibly expensive, especially for AAA titles. If a programmer can remove a task for an artist by procedurally generating it, then less money will be spent on the artistic team on that project and future projects. This is especially the case with graphics becoming so advanced that nearly every mesh has ~4 other maps (not just a texture) that have to be designed or manipulated individually to get something to look right.
Finally, for anyone interested:
http://procworld.blogspot.com/
That guy's stuff is pretty amazing, and a significant chunk of it is procedurally generated.
Also, just to comment on a few things:
| Geometry, trigonometry, and linear algebra are really all you need. |
| This is generally not a terribly useful technique unless you're really hurting for space, you don't have artists to help you, the thing you're trying to render is bizarrely complex and/or large |
Finally, for anyone interested:
http://procworld.blogspot.com/
That guy's stuff is pretty amazing, and a significant chunk of it is procedurally generated.
Is helios our admin? Probably not, but i never seen anyone before with more than 9k posts, did I?
Anyways:
That's all of it in most cases.
Anyways:
| Geometry, trigonometry, and linear algebra are really all you need. |
That's all of it in most cases.
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I want to say thanks all for the personal information, this is really going to help me. I thought I was a bit broken because I see many examples of guys who post their implementation of an engine on their videos and it confounded me. Yes I realize that much of the api helps them, such as opengl, but it always amazed me. Also I know that much of the time its modeling software that handles the geometry for simple 3d primitives such at spheres, cubes, and such and I realize that its almost impossible to procedurely generate complex models procedurely unless they look like legos maybe.
Thanks all and I'm going to learn make sure to start learning linear algebra before schools begins.
Thanks all and I'm going to learn make sure to start learning linear algebra before schools begins.
As an aside (not very relevant here, but this being the lounge I can say it anyway) saying things like "I've done pre-calculus" and "I've just finished Analysis II" and what have you carry very little information to anyone not within the same education system at the same time. I've got no idea what pre-calculus might mean. Likewise Analysis II, and presumably every other rough-grouping.
Right now I'm at a community college. I'm signed up for Linear Algebra and Calc III next semester. The semester after that, I'll be taking differential equations.
At the school I am planning to transfer, linear analysis a required for a transfer student to be selected.
Anyways, apparently my differential equations course articulates with (counts for) linear analysis, even though the school I'm transferring to has separate linear analysis, and differential equations courses.
So what I wonder; what is the difference between differential equations and linear analysis?
Pre-Calc is basically a review of trigonometry and algebra, and designed to get students ready for Calc I. Linear analysis I believe is the fifth calculous class you would take at a university?
At the school I am planning to transfer, linear analysis a required for a transfer student to be selected.
Anyways, apparently my differential equations course articulates with (counts for) linear analysis, even though the school I'm transferring to has separate linear analysis, and differential equations courses.
So what I wonder; what is the difference between differential equations and linear analysis?
| "I've done pre-calculus" and "I've just finished Analysis II" and what have you carry very little information to anyone not within the same education system at the same time. |
Pre-Calc is basically a review of trigonometry and algebra, and designed to get students ready for Calc I. Linear analysis I believe is the fifth calculous class you would take at a university?
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| Linear analysis I believe is the fifth calculous class you would take at a university? |
Same thing again, dude! To anyone not in the same education system at the same time, it's just a label with mystery content. :)
| Same thing again, dude! To anyone not in the same education system at the same time, it's just a label with mystery content. :) |
I threw in the question mark because I would like to know the same thing as you. What exactly is analysis 2? All I know is that I think it's very advanced calculous. Mostly stuff me and you probably wouldn't know what is anyways.
edit: At the college I would like to go to, there are a lot of different analysis classes.
linear analysis I, II
vector analysis
complex analysis I, II
Introduction to analysis I, II
Applied analysis I, II
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| What exactly is analysis 2? All I know is that I think it's very advanced calculous. Mostly stuff me and you probably wouldn't know what is anyways. |
http://translate.google.com/translate?sl=es&tl=en&js=n&prev=_t&hl=en&ie=UTF-8&layout=2&eotf=1&u=http%3A%2F%2Fcms.dm.uba.ar%2Facademico%2Flic%2Fprogramas%2FAnalisis_I_M&act=url
It's just how we call multivariate calculus, since "multivariate calculus" is a bit of a mouthful. Some things from topology (open and closed sets, arc-connectedness) are also introduced for the sake of proving certain theorems, like the mean value theorem in R^n.
In my education system, multivariable calculous is usually Calc 3; although some of it spills over into differential equations.
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