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karansher / computer-graphics-kinematics

Computer Graphics Assignment about Kinematics
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Confusion on "choice of energy" #5

Open cherylchen2 opened 1 year ago

cherylchen2 commented 1 year ago

In the assignment, it explained that

The change in tip positions with respect to joint angles does not depend on the choice of energy . We call this matrix of changes the kinematic Jacobian

Can someone clarify what "choice of energy" means and why it doesn't depend on it?

FarzanehCS commented 1 year ago

By energy, we mean the energy function E(x(a)). In A7, we chose the energy function E(x(a)) to be a square distance, but it could theoretically be any other function.

The sentence you quoted says: The gradient of x with respect to the angle changes a is sth that does not depend on the choice of the energy function that we choose and hence we call this gradient, the kinematic Jacobian.