Circular rotation around an arbitrary axis

Question

I am programming Starcraft 2 custom maps and got some proglems with math in 3D. Currently I am trying to create and rotate a point around an arbitrary axis, given by x,y and z (the xyz vector is normalized).

I've been trying around a lot and read through a lot of stuff on the internet, but I just cant get how it works correctly. My current script (you probably dont know the language, but it's nothing special) is the result of breaking everything for hours (doesn't work correctly):

    point CP; fixed AXY; point D; point DnoZ; point DXY_Z; fixed AZ; fixed LXY; missile[Missile].Angle = (missile[Missile].Angle + missile[Missile].Acceleration) % 360.0; missile[Missile].Acceleration += missile[Missile].AirResistance; if (missile[Missile].Parent > -1) {     D = missile[missile[Missile].Parent].Direction;     DnoZ = Point(PointGetX(D),0.0);     DXY_Z = Normalize(Point(SquareRoot(PointDot(DnoZ,DnoZ)),PointGetHeight(D)));     AZ = MaxF(ACos(PointGetX(DXY_Z)),ASin(PointGetY(DXY_Z)))+missile[Missile].Angle;     DnoZ = Normalize(DnoZ);     AXY = MaxF(ACos(PointGetX(DnoZ)),ASin(PointGetY(DnoZ)));     CP = Point(Cos(AXY+90),Sin(AXY+90));     LXY = SquareRoot(PointDot(CP,CP));     if (LXY > 0) {         CP = PointMult(CP,Cos(AZ)/LXY);         PointSetHeight(CP,Sin(AZ));     } else {         CP = Point3(0.0,0.0,1.0);     } } else {     CP = Point(Cos(missile[Missile].Angle),Sin(missile[Missile].Angle)); } missile[Missile].Direction = Normalize(CP); missile[Missile].Position = PointAdd(missile[Missile].Position,PointMult(missile[Missile].Direction,missile[Missile].Distance)); 

I just cant get my mind around the math. If you can explain it in simple terms that would be the best solution, a code snipped would be good as well (but not quite as helpful, because I plan to do more 3D stuff in the future).

Answer 1

http://en.wikipedia.org/wiki/Rotation_matrix. Look under the section Rotation matrix from axis and angle. For your convenience, here's the matrix you need. It's a bit hairy. theta is the angle, and ux, uy, and uz are the x, y, and z components of the normalized axis vector

If you don't understand matrices and vectors, post back and I'll help you.