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Math for Game Programmers 04 – Operations on vectors

69 points by Charles__L 14y ago

Xyzodiac 14y ago
Funny enough, vectors aren't usually discussed in a math setting until Calculus III. Despite being a relatively easy concept.
- psykotic 14y ago
  In my Danish high school we covered the algebra and geometry of vectors in two and three dimensions in our second year. The high school mathematics curriculum in Denmark is ridiculously unambitious; I'm certain my American friends covered more than this in their high school AP classes. There's a compelling argument for withholding the abstract theory of vector spaces and linear maps from non-mathematicians until multivariate calculus. Linear maps (as approximations to differentiable maps), determinants (as Jacobians measuring volume distortion under pullback), eigenvalues and quadratic forms (as Hessians measuring curvature with eigenvalues as principal curvatures) all make prominent appearances and become easy to motivate geometrically.
- prophetjohn 14y ago
  I learned about them in trigonometry and again in precalculus and again in linear algebra. Also, physics 1, but that doesn't count. The stuff in that post is exteremely simple.
- eckyptang 14y ago
  In the UK, we did vectors, matrices, calculus, discrete mathematics at A level (16-18 years old). I think they still do that sort of stuff now.
- deleted 14y ago
  [deleted]
- mirsadm 14y ago
  I did specialist maths during my high school years (~16-17 years old) which was quite involved and covered vectors and lots of other interesting things. One of the few good things about high school in Australia. Oddly enough the maths in Computer Science at a University level was much easier.
38leinad 14y ago
he also seems to have a nice article on 2d platformers: http://higherorderfun.com/blog/2012/05/20/the-guide-to-implementing-2d-platformers/ http://higherorderfun.com/blog/2012/05/20/the-guide-to-imple... marked for reading.
shanelja 14y ago
Thanks a lot, your advice on Vectors over your last few articles has really expanded my knowledge of what you can really do with Arrays if you think of them as pieces of an object rather than just a (generally) unordered list of "stuff".

69 points by Charles__L 14y ago

Funny enough, vectors aren't usually discussed in a math setting until Calculus III. Despite being a relatively easy concept.

psykotic 14y ago
In my Danish high school we covered the algebra and geometry of vectors in two and three dimensions in our second year. The high school mathematics curriculum in Denmark is ridiculously unambitious; I'm certain my American friends covered more than this in their high school AP classes. There's a compelling argument for withholding the abstract theory of vector spaces and linear maps from non-mathematicians until multivariate calculus. Linear maps (as approximations to differentiable maps), determinants (as Jacobians measuring volume distortion under pullback), eigenvalues and quadratic forms (as Hessians measuring curvature with eigenvalues as principal curvatures) all make prominent appearances and become easy to motivate geometrically.
prophetjohn 14y ago
I learned about them in trigonometry and again in precalculus and again in linear algebra. Also, physics 1, but that doesn't count. The stuff in that post is exteremely simple.
eckyptang 14y ago
In the UK, we did vectors, matrices, calculus, discrete mathematics at A level (16-18 years old). I think they still do that sort of stuff now.
deleted 14y ago
[deleted]
mirsadm 14y ago
I did specialist maths during my high school years (~16-17 years old) which was quite involved and covered vectors and lots of other interesting things. One of the few good things about high school in Australia. Oddly enough the maths in Computer Science at a University level was much easier.

38leinad 14y ago

he also seems to have a nice article on 2d platformers: http://higherorderfun.com/blog/2012/05/20/the-guide-to-implementing-2d-platformers/ http://higherorderfun.com/blog/2012/05/20/the-guide-to-imple... marked for reading.

shanelja 14y ago

Thanks a lot, your advice on Vectors over your last few articles has really expanded my knowledge of what you can really do with Arrays if you think of them as pieces of an object rather than just a (generally) unordered list of "stuff".