Based om this illustration, it seems that remeshing through sampling may be another way to achieve this regularization effect as seen in many former problems we've studied.
It was brought up in lecture that isotropic remeshing is used to regularize triangles to make the mesh easier to process, but this could come at the cost of removing some of the high-frequency detail in the mesh. This is especially apparent near the nose in both images, as on the left, there's a clear groove in the nostril, but on the right, that groove is near nonexistent.
I was wondering if it was possible to perform isotropic remeshing without losing some of this detail or perhaps only targeted remeshing in specific areas. It would be nice to have faster processing while preserving some of the detail you want in specific areas of the mesh. Since remeshing speeds up the processing at the cost of losing some details at the higher frequencies, it seems very similar to antialiasing in a sense.
how do we "decide" where to implement isotropic remeshing? isotropic remeshing seems to perform well on smoother areas such as the cheek, but causes us to lose sharper detail such as the creases in the eyes, nose, and lips. is this a mathematical decision boundary in the algorithm (perhaps a tradeoff dependent on benefit of isotropic remeshing vs quadric error?) or a human decision :oo