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Inverse kinematics (IK) solvers often become mathematically intensive or computationally expensive with long kinematic chains or when functioning in higher dimensions. I am going to cover an approach to solving IK that is easy to understand, handles any number of joints, and is easy to implement in any dimension. We will walk through a two dimensional example and I'll present sample code to perform the algorithm.

A basic kinematic chain of joints with no rotational constraints can be viewed as a set of points (the joint positions) with distance constraints between pairs (bones with a fixed length). By iteratively stretching the bones towards our target and resolving these distance constraints, we will converge on a solution to the system. This approach to solving the IK problem is very similar to solving constraints in a verlet based physics system (for more information on verlet physics, I recommend reading Advanced Character Physics by Thomas Jakobsen). For a sample implementation of constraint relaxation based IK, you can download the RJ_Demo_IK application.

You might also be interested in the following articles on different IK solvers:

• Analytic Two-Bone IK in 2D
• Cyclic Coordinate Descent in 2D