Generalized Shader IK: Add angular constraints

[hai-vr]

Generalized Shader IK is a draft project to create a modified version of the Handholding Shader IK which would have more customization options and would be less specific to dancing. It does not aim to be a superset of the Handholding Shader IK.

The shader code for the Generalized Shader IK is to be kept separate from the Handholding Shader IK: If the Generalized Shader IK were to be implemented within Handholding Shader IK, it would introduce a whole lot of complexity to a piece of very specialized code that is small enough to be simple to understand.

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For some applications, we would limit the angles at which an IK can move around.

From a quick analysis, this may introduce a few challenges, taking the Mathematical guide as a reference. For instance, if we constrain the angle of forearmFlexAngle, then the distance to the target will be constrained. In effect, this changes the values that already have been used when applying the law of cosines to determine the angle of forearmFlexAngle, and may require us to recalculate the triangle using the law of cosines with the distance as an unknown and the forearmFlexAngle as known.

Further down the line, if the pitch is constrained, then the entirearmFlexAngle angle calculated as a result of applying the law of cosines may have to be modified again.

Therefore with my current knowledge I am unsure about the required strategy to stabilize the calculations with constrained angles.

This is to say that this feature seems non-trivial to me. There are also unknowns about the desired behavior when the target is located at ridiculous angles near an unstable threshold, i.e. exactly behind the IK.

As I have no knowledge of how real IK systems work, I might need to learn how a real IK system work, or empirically figure out a strategy to solve this.