Game Creation with XNA/Mathematics Physics/Vectors and Matrices

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Vectors and Matrices[edit | edit source]

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 | edit source]

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:

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

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 | edit source]

Matrices[edit | edit source]

References[edit | edit source]

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