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In the section, Inverse Kinetics in 2D of this article: http://freespace.virgin.net/hugo.elias/models/m_ik.htm

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There is Vector R. How could I find this vector R? I know the length of the bone and its angle, how could I then calculate vector R in this example?

Thanks

Would it simply be taking the vector of the angle and returning v.y, -v.x?

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The base of the vector $R$ is just $(L\cos(\theta),L\sin(\theta))$ where $L$ is the length of the bone and $\theta$ is its angle, usually measured from horizontal to the left. If the desired length of $R$ is $r$, the offset is $(-r\sin(\theta),r\cos(\theta))$, so the end point is $(L\cos(\theta)-r\sin(\theta),L\sin(\theta)+r\cos(\theta))$ . Is this what you are after? I don't see anything to set $r$ in the problem.