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Does Delaunay imply manifold?


Is delaunay an efficient metric to calculate? It looks like it contains quite a number of extra steps for each pair of triangles (although not all pairs are going to overlap). The angles check seem to be more efficient.


A followup to the previous question. Is delaunay used in real time for decision making? Or is it used to provide metrics on certain meshing scheme (online utility measurement tool that's not part of the critical path).


Wouldn't long triangles be good at approximating long smooth surfaces like that of the cylinder two slides ago?


For the given example that defines good triangles as all angles close to 60 degrees, how large would the range of acceptable values for each angle typically be (or is it just a situational thing/matter of preference)? e.g. would an isosceles right triangle (45/45/90) usually fall within an acceptable range, since visually it doesn't really fit long and skinny?


Does this rule of thumb always need to be followed? The cylinder from two slides ago (and for that matter, any curved rectangular surface) will most likely need to be drawn with long triangles like those.


Shouldn't the quality of mesh depend on specific task? If we would like to describe a needle, triangle mesh with "good" shape in the slides might be a worse idea than those with "bad" shape.


Would it be possible to break bad triangles into more smaller good triangles?


Is there a way to quantify those metrics?


Do the triangles have to be completely uniform or close in size? I’m thinking that the long skinny triangles could potentially be broken into smaller triangles to prevent the existence of “bad triangles”


Are the "bad" triangles necessarily even "bad" if we can just create a mesh of smaller "good" triangles in the shape of the "bad" one?


Is there any case that bas triangles is necessary? What to do in this situation?


For certain meshes we may need to use "bad" triangles to accurately describe things, how would this be factored in / considered?


Is the Delaunay triangulation unique? It doesn't seem immediately clear how many degrees of freedom the empty circumcircles requirement leaves.