For my understanding, the left mesh contains more details or sharp features but the right mesh is more closed to Delaunay triangulation, which means it may be easier to do the geometry processing.
My question is, is there any mesh construction algorithm can do this trade-off between detail precision and global smooth triangulation?
For example, the triangulation in the smooth area (like the cheeks) is closed to Delaunay but the boundaries or sharp features (like the ears and the nose) is triangulated in some other better detail-preserved way?
@Leslie Yes, you can definitely have a mesh that is both Delaunay and spatially adapted to the size of local features, the local curvature, etc. One popular algorithm for obtaining such a mesh is Delaunay refinement (see for instance Figure 1 in this paper).