I have a motion path in 3D space (a series of joined bezier curves). The application I'm working on allows the user to create graphics animations. Suppose I have a bitmap placed on a given motion path. I'm trying to align the front face of the bitmap to the motion path.
the problem basically boils down to this:
I have two vectors - the bitmaps surface normal vector (always <0,0,1>) and the vector defined by the object's xyz position at time t and t+1 - this vector would be (t+1x-tx,t+1y-ty,t+1z-tz);
now, I need to subject the bitmap to a certain series of rotations in order to align its normal vector to the vector defined by the path.
I had tried mapping the path vector first onto the xy plane, determining the y rotation needed, then mapping the vector onto the yz plane in order to figure out the x rotation. Apparently there's a z rotation element which I'm not able to figure out.
I hope I've made what I'm trying to do a little clear .
So, I don't want the object on the path to simply position itself at the XYZ positions but also face the direction it's going in.
Thanks for any help.