# what does AngleVectors method in quake 3 source code does

I know some of some linear algebra(basic vector math ie: dot,cross product).
However I can't decipher what below method does, I know what is yaw,pitch and roll.
But I can't connect these with vector.
Worse, I'm not sure this fall under what math 'category', so I don't really know how to google.
Hence the question here.
Anyone?

void AngleVectors( const vec3_t angles, vec3_t forward, vec3_t right, vec3_t up) {
float       angle;
static float        sr, sp, sy, cr, cp, cy;
// static to help MS compiler fp bugs

angle = angles[YAW] * (M_PI*2 / 360);
sy = sin(angle);
cy = cos(angle);
angle = angles[PITCH] * (M_PI*2 / 360);
sp = sin(angle);
cp = cos(angle);
angle = angles[ROLL] * (M_PI*2 / 360);
sr = sin(angle);
cr = cos(angle);

if (forward)
{
forward[0] = cp*cy;
forward[1] = cp*sy;
forward[2] = -sp;
}
if (right)
{
right[0] = (-1*sr*sp*cy+-1*cr*-sy);
right[1] = (-1*sr*sp*sy+-1*cr*cy);
right[2] = -1*sr*cp;
}
if (up)
{
up[0] = (cr*sp*cy+-sr*-sy);
up[1] = (cr*sp*sy+-sr*cy);
up[2] = cr*cp;
}
}


ddddd

It just computes a (slightly wacky, because of Quake's "entity pitches are negative" thing) 3x3 rotation matrix, with each column (or row, depending on your preference) being one of the forward/right/up vectors. This can then be used to position various objects/effects/etc relative to the view; Quake uses it for pushing muzzleflashes slightly forwards and for sprite billboarding, for example.

Compare with the matrix described at http://blogs.msdn.com/b/mikepelton/archive/2004/10/29/249501.aspx

• ah yes, the rotation matrix.It made sense now.I can't "read" math in code form, so I can't connect the dot. – kypronite Nov 7 '12 at 5:39

The function takes angles and calculates vectors that point in directions relative to angles.

For angles, and the operations sin cos and tangent, you'll want to look up trigonometry.

Multiplying an angle in degrees by M_PI*2 / 360 converts degrees to radians. (M_PI = 3.14).

forward is a vector that points in the direction that the angles form to create the forward facing direction.

right is a vector pointing to the right of where the angles representation is facing, and up' points directly up.

If angles represented the angles that you are looking at currently (i.e. your head), forward would point straight ahead of you, right' would point to your right, andup would point up from where your head is oriented.

• I forgotten about rotation matrix, so I think I got confused how angle relates to vector. – kypronite Nov 7 '12 at 5:41