Game Creation with XNA/Mathematics Physics/Vectors and Matrices

From Wikibooks, open books for an open world
< Game Creation with XNA
Jump to: navigation, search

Vectors and Matrices[edit]

We need to recall some basic facts about vector and matrix algebra, especially when trying to develop 3D games. A nice introduction with XNA examples can be found in the book by Cawood and McGee. [1]

A right triangle showing the relation between opposite, adjacent and hypotenuse.

Right Triangle[edit]

Once upon a time there was little Hypotenuse. He had two cousins: the Opposite and his sister the Adjacent. Both were usually just known by their nick names 'Sine'[2] and 'Cosine'[3]. They lived together in a right triangle close to the woods. They were related through his mother's sister, aunty Alpha. His father, who was a mathematician, used to say that:

\sin \alpha = \frac {\textrm{opposite}} {\textrm{hypotenuse}} = \frac {a} {h}
\cos \alpha = \frac {\textrm{adjacent}} {\textrm{hypotenuse}} = \frac {b} {h}.

Sometimes he also referred to uncle Tangent (who was married to aunty Alpha) and said that

\tan \alpha = \frac {\textrm{opposite}} {\textrm{adjacent}} = \frac {a} {b},

so in a sense uncle Tangent of aunty Alpha was Sine divided by Cosine. To us that didn't make any sense, but Hypotenuse's father said that was how it always was.


Vectors[edit]

Matrices[edit]

References[edit]

  1. S. Cawood and P. McGee (2009). Microsoft XNA Game Studio Creator’s Guide. McGraw-Hill.
  2. Wikipedia:Sine
  3. Wikipedia:Cosine