Finding the angles for the X, Y and Z axis in 3D - OpenGL/C++

Question

I am currently trying to use OpenGL (With SDL) to draw a cube to the location where I left click in the screen and then get it to point at the position in the screen where I right click.

I can successfully draw a cube at my desired location using gluUnproject - Meaning I already know the coordinates of which my cube is situated.

However I do not know how to calculate all of the angles required to make my cube point at the new location.

Of course I am still using gluUnproject to find the coordinates of my right click, but I only know how to rotate around the Z axis from using 2D graphics.

For example before, if I wanted to rotate a quad around the Z axis (Of course, this would be a top down view where the Z axis is still "going through" the screen) in 2D I would do something like:

angle = atan2(mouseCoordsY - quadPosY, mouseCoordsX - quadPosX);
glRotatef(angle*180/PI, 0, 0, 1);

My question is, how would I go about doing this in 3D?

• Do I need to calculate the angles for each axis as I did above?
• If so how do I calculate the angle for rotation around the X and Y axis?
• If not, what method should I use to achieve my desired results?

Any help is greatly appreciated.

Answer 1

If your cube is at A = (x0,y0,z0)

If your cube is currently looking at B=(x1,y1,z1)

and if you want it to look at C=(x2,y2,z2) then;

let v1 be the vector from A to B

v1 = B - A

and v2 be the one from A to C

v2 = C - A

First normalize them.

v1 = v1 / |v1|
v2 = v2 / |v2|

then calculate the rotation angle and the rotation axis as

angle = acos(v1*v2) //dot product
axis = v1 X v2 //cross product

You can call glRotate with

glRotate(angle, axis[0], axis[1], axis[2])