Michael George schrieb:
Hello,
For my game I need to represent right isosceles triangles, and do
operations including translation and rotation in 15 degree
increments. Unfortunately, I cannot tolerate rounding error, because
it will cause bad visual and gameplay artifacts. I'm thinking of
representing points as vectors where the components are of the form
a + b * sqrt(2) + c * sqrt(3) + d * sqrt(6)
where a, b, c, and d are rationals. I believe numbers of this form
are sufficient for my purposes, although I haven't worked out all the
proofs yet. Anyway, I was wondering if anyone has done anything
similar and can suggest a library I can use for manipulating such
vectors before I go off and implement it myself.
Thanks!
--Mike
Hi
I don't think that you can avoid rounding errors, unless you use a math
library that takes the math errors of the computer into account (which
can differ from hardware to hardware).
I'm not sure, why you want to represent points in such a complicated
way, but I don't know the theory about it and I'm not a mathematician.
One way to go is to accumulate the angle of a rotation (same for
translation) and use the accumulated angle on a object to transform it
into the right orientation (if you do use a previously rotated object
then you will get much more rounding errors over time!). Using that way
one would have a variable 'angle' which would be incremented in 15
degree steps (15, 30, 45,...) and use it to construct the rotation
matrix (or whatever it is used to rotate). This should be precise enough.
Unless you can draw using subpixels, you will have rounding errors when
trying to draw the points on integer coordinates of the screen anyway.
Maybe I'm wrong.
~DR0ID
