[Algorithms] Nearest point on plane for 2D IK

[Jeff L. <je...@di...>]

Since we were talking about skeleton animation, I have a question.

For my IK system, I prefer to use actual 2D joints where appropriate rather then use the general 3D form and limit with DOF restrictions.  I have received some email asking me how to do this with my CCD IK routine so I wanted to write up a paragraph on the little math routine for the magazine.  I think it is pretty obvious to people familiar with vector math, but I have found that many developers don't have the background and need some help.  I will put this in with my continuing series on why dot product is your friend.

I want to sanity check it to make sure this is a good, fast way to do this.  I know that it works but it may not be the best method.

Given a bone object in 3 space, B, and a desired 3D target to attempt to reach, T.  The method is to determine the plane that B is allowed to rotate, then project T into that plane.  Then I solve for the rotation angle.

To project T onto B's free rotational plane:

N = free axis of rotation

V = T - B		// Creates vector from base to target
P = T - N ( N dot V)	// Project V onto axis and subtract that from the target

Now, P is my new target point for the IK routine.  Continue as usual, dot product to get the angle to rotate, ...
I will explain why this works and such but you get the idea.

-Jeff