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To sum up, I've introduced a new element quality metric for ensuring that tetrahedral elements meet the requirements of the Finite Element Method.

The implementation of our simplification and mesh improvement algorithm is robust and efficient and can process models made from high-resolution scanned geometry with millions of tetrahedral elements.

In practice the method ensures the removal of the poorest quality elements to allow interactive simulation.

We've found that the method encourages iterative modeling, as it is easy to tweak the parameters of the model (the thickness of the skin layer on the dog model, or the final tetrahedral count) and try it out in an interactive simulation.