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Meanwhile, the simplified conjugate-gradient method (SCGM) is used as the optimization method which continuously updates the shape until the objective function is minimized.
The intervention presents a virtual representation of a physical object and updates the shape of the object based on the user's interactions.
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Update the shape parameter with the fixed pose parameter.
Further we implement level set methods to update the shape of the obstacle.
Then, we use the shape gradient functions in velocity analysis to update the shape of shell structures.
We design an algorithm to update the shape and the impedance function alternatively along the descent direction of the objective functional.
The optimal model parameters are determined by alternately updating the pose parameter (R θ T) at the fixed β and updating the shape parameter β at fixed (R θ T) until the shape residual error converges.
Update R θ and T with the fixed shape parameter arg min R θ, T k P R θ S ˜ + T ˜ − s ˜ 2 d β = β k − 1 2 Update the shape parameter with the fixed pose parameter arg min β k P R θ S ˜ + T ˜ − s ˜ 2 d R θ, T = R θ, T k 2 4.
Update the shape parameter with the fixed pose parameter arg min β k M ° P R θ S ˜ + T ˜ − s ˜ 2 d R θ, T = R θ, T k − 1 2 Update R θ and T with the fixed shape parameter arg min R θ, T k M ° P R θ S ˜ + T ˜ − s ˜ 2 d β = β k 2 4.
In the shape optimization process, we carry out frequency response analysis to calculate shape gradient function, and then use the shape gradient functions in velocity analysis to update the shape or position of the inlaid material based on the H1 gradient method.
Update R θ and T with the fixed shape parameter arg min R θ, T k P R θ S ˜ + T ˜ − s ˜ 2 d β = β k − 1 2. Update the shape parameter with the fixed pose parameter arg min β k P R θ S ˜ + T ˜ − s ˜ 2 d R θ, T = R θ, T k 2. Reconstruct (S 3d ) k using the shape parameter β k.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com