Override trig functions for infinite precision in set cases

[eric-wieser]

This fixes #80

The underlying issue here is that lcMatrix44FromEulerAngles(LC_PI/2) was not returning an exact 90 degree rotation matrix.

Overriding sin/cos might be overkill, but it did solve the problem on my machine, and seems pretty harmless anyway

[leozide]

I've looked at this for a little bit today, I think using doubles instead of floats is a more generic solution and will work for more cases.

Changing:

RotationMatrix = lcMul(lcMatrix33RotationY(Angles[1] * M_PI / 180), RotationMatrix);

and:

inline lcMatrix33 lcMatrix33RotationY(const double Radians)
{
	float s, c;

	s = sin(Radians);
	c = cos(Radians);

	lcMatrix33 m;

	m.r[0] = lcVector3(   c, 0.0f,   -s);
	m.r[1] = lcVector3(0.0f, 1.0f, 0.0f);
	m.r[2] = lcVector3(   s, 0.0f,    c);

	return m;
}

Fixes the problem you described. I'll need to experiment some more to see where the loss of precision is causing problems (sinf/cosf or LC_DTOR).

[eric-wieser]

Thanks for taking a look. Moving to doubles would definitely help, but might just hide the problem.

The problem is that in C, sin(2*M_PI) != 0, because 2*M_PI is not actually 2pi, just a floating point number close to 2pi. Even casting to float doesn't discard enough precision for you to get away with it.

Of course, the approach in this patch is sketchy, as it uses equality comparisons of floats. Passing angles in degrees in these cases would work better.

[leozide]

I've updated the angle/pi defines and it seems to have solved the problem in a lot of cases.