Exercise · ZW-SMOOTH-DIFFEOMORPHIC-DEFORMATION-004 · ★★☆ Intermediate
Two deformations reach the same reference points, but one squashes a region until it forms a fold. Which one must be discarded?
Choose one option.
Show answer
- B. The one that forms the fold, even if it fits the points, because it is not diffeomorphic
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Explanation
The fold makes the Jacobian vanish in a region, so that deformation is not diffeomorphic even though it fits the reference points.
A smooth diffeomorphic deformation \(\varphi\) is a bijective, smooth transformation whose inverse is also smooth.
\[\varphi^{-1}\text{ is smooth}\]
More practice problems: smooth diffeomorphic deformation