We use Jacobian extensively in the computer animation and robotics community, and as a result it is worth providing the reader with the technicalities that help understand its derivation and implementation. Named after mathematician Carl Gustav Jacob Jacobi (1804-1851), the Jacobian matrix provides an important tool to best describe a linear approximation of a function \(f\) near a point \(x\), given \(f\) is differentiable at that point. Jacobians are key component in many motion control and analysis techniques.
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