What kind of mathematics do I need to know to understand virtual reality very well? [closed]

In my life I want to develop the virtual reality industry and I wanted to know what kind of mathematics will help me get there, I'm sure that every mathematical subject is helpful, but I mean specifically.

Thanks :)

closed as too broad by Morgan Rodgers, quid♦, John B, Yagna Patel, Chris GodsilFeb 13 '16 at 23:10

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• If you are going to program, there are some engines, like Unity3D that can cover most of it. Which will almost neglect the mathematical side. – Ilan Aizelman WS Feb 13 '16 at 17:54
• I would guess analytical geometry would be useful. But honestly, I think computer science knowledge will be much more useful. There are already tons of libraries to do the math for you; if you just put some time into understanding what they provide, you should be able to use them well. – Brian Tung Feb 13 '16 at 17:55
• to start $3d$ programming you need to know : trigonometry, matrices and of course programming very very well. after that, the maths for the global illumination algorithms are quite complicated (non linear optimization / fixed point, spherical harmonics, etc. ). the maths for physics engines or AI are also far to be simple $\implies$ everything is complicated, algorithmic & mathematic, and very interesting – reuns Feb 13 '16 at 18:06

I am currently in computer graphics course at my uni. The mathematics we need is mostly linear algebra on a rather computational level. You need linear algebra to describe e.g. points, vectors, transformations (matrices) in three dimensions.

Further, some knowledge in calculus/analysis is helpful. For example, we learnt about graphic filters (e.g. gaussian blur filters) which use convolution. Also, we discussed Bezier curves and other parametric descriptions.

Also, knowledge in probability theory might be useful. We used the Monte-Carlo integration method to compute some multi-dimensional integrals.

If you want to program then Logic.

Anyway Linear Algebra will be useful (but just vectors, rotations of vectors and simple matrix transformations rules). The term Quaternion that appears in Unity3D hints just to that.

While I agree with the importance of Linear Algebra, calculus/analysis, and probability, in order to make really groundbreaking improvements Virtual Reality at this stage, depending on your interests, there is a wide variety of subjects you may want to look into.

For example, augmented reality is becoming a very exciting field related to virtual reality. Jobs in this field typically require a PhD in computer vision (CV). A lot of CV is related to signal processing, both discrete and continuous, and some numerical methods to solve PDEs and stuff. Now, however, it is all really machine learning, so for augmented reality, you would want to look into Numerical Analysis, PDEs, Statistics, and some machine learning stuff (maybe neural networks?).

In terms of graphics, the above list would probably also help you to develop new shading models, and meshing techniques.

For 3D reconstruction computer vision is really what you need.

There is also a lot needed in terms of developing the auditory and haptic feedback for virtual reality. This would probably also lead you to a signal processing kind of background.

One last thing that I think would be cool for VR would be an easy way to import real world objects into the VR. This would lead you towards 3D scanning, which is also related to CV.