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Usefulness of multivariable calc and more advanced calc topics?


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#1 Robot Ninja   Members   -  Reputation: 569

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Posted 28 November 2012 - 03:32 PM

Hey GameDev,

I'm not much a math guy (though I'm good with math), so I am not as knowledgeable with this kind of topic. My class registration was this morning, and both of the advanced calc classes at the local community college were already filled. I'm on the fence regarding whether or not to try to petition for the class, since I think that taking the class would be enlightening and potentially useful for me. On the other hand, both classes conflict with another one that I would like to take.

So I was wondering, how much would it hurt me if I didn't take this class? The course description says: "This course studies vectors and parametric equations, partial differentiation, functions of two or more variables, gradients, higher-order derivatives, multiple integrals, cylindrical and spherical coordinates, vector functions and their derivatives, vector fields, surface and line integrals, the theorems of Green and Stokes, and the Divergence Theorem." I can imagine that this level of calculus is useful in physics and engineering applications, but my interest lies more in computer graphics. I've probably missed a lot of other great applications for it, so please feel free to fill me in on other ones. Posted Image

My bachelor's is in Psych, but I'm in the middle of changing my career. I'm planning to begin applying for CS-related/programming jobs towards the end of spring through the summer, so I've been taking CS classes, a couple math classes, and working on some personal projects in my free time. I want to apply for game and non-game-related jobs. I understand that taking the class later on is always a possibility, but as far as employment goes I'm wondering how much of a let-down it will be to employers if I don't have this background knowledge when I apply. I'm already anticipating that it will be difficult enough getting an interview since my BA is not in CS, math, nor engineering. Posted Image

*EDIT* This thread would have been better titled: "Applications of multivariable calc and more advanced calc topics in game dev and graphics". They way it is now seem a little...condescending... Posted Image

Edited by Robot Ninja, 29 November 2012 - 03:25 AM.


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#2 Álvaro   Crossbones+   -  Reputation: 13311

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Posted 28 November 2012 - 03:44 PM

Some of those things are definitely useful for computer graphics. In particular, you'll find multiple integrals in the rendering equation, which is the key to realistic rendering.

#3 Robot Ninja   Members   -  Reputation: 569

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Posted 29 November 2012 - 03:15 AM

Interesting. I just googled it really quick and it just lead me to an UC Berkeley article on global illumination. I can see this being used in a raytracer, but are developers using this for real-time global illumination too? Please do share more! This is what gets me excited about math! Posted Image

#4 Bacterius   Crossbones+   -  Reputation: 8857

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Posted 29 November 2012 - 05:03 AM

Interesting. I just googled it really quick and it just lead me to an UC Berkeley article on global illumination. I can see this being used in a raytracer, but are developers using this for real-time global illumination too? Please do share more! This is what gets me excited about math!

Yes. Most of this equation can be used directly from within a shader (you might have issues with global illumination and multiple bounce lighting, but direct lighting + shadows + environment mapping is a pretty good approximation in most situations).

The slowsort algorithm is a perfect illustration of the multiply and surrender paradigm, which is perhaps the single most important paradigm in the development of reluctant algorithms. The basic multiply and surrender strategy consists in replacing the problem at hand by two or more subproblems, each slightly simpler than the original, and continue multiplying subproblems and subsubproblems recursively in this fashion as long as possible. At some point the subproblems will all become so simple that their solution can no longer be postponed, and we will have to surrender. Experience shows that, in most cases, by the time this point is reached the total work will be substantially higher than what could have been wasted by a more direct approach.

 

- Pessimal Algorithms and Simplexity Analysis


#5 Robot Ninja   Members   -  Reputation: 569

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Posted 29 November 2012 - 05:21 PM

Well I guess I'll try to pick up the mentioned calculus topics sooner rather than later. I'm going to email the professor to see what textbook they will be using for the course, and see if I can shadow the class on my own time. Are there any other calc topics that are important to graphics besides multiple integrals, particularly any others mentioned from the course description I provided? Also, if anyone has a suggestion for a good self-study textbook for calc, that would be awesome too!

*EDIT* Quick question about the rendering equation - in summary, what is the integration providing? The components in the equation make sense individually, but then I quickly lose it when I see the multiplication and integration of the 3 components together.

Edited by Robot Ninja, 29 November 2012 - 05:50 PM.





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