This seems like a really smart and clear way to make the triangles more uniform in size. Some of these steps seem like they would be tricky to implement in practice. For example, collapsing the edges could cause other edges to be deleted, making it really tricky to be able to loop through all edges.
tarangs
The remeshing does have some trade-off in the detail right? I see some loss of detail in the eyelids.
pw123
Is there a proof anywhere of why this algorithm is effective? I'd be interesting in reading that.
graphicstar11
are there different kinds of isotropic remeshing algorithms or has this been proven to be the most effective one? I feel like there may be other optimizations such as possibly deleting faces that could improve a mesh?
keenan
@tarangs Yes, absolutely---that is a fundamental trade off in surface triangulation. The triangulation has to serve as both a description of the geometry, and as a data structure that supports computation on the surface. So you have to balance between geometric accuracy and triangulation quality. (Or inflate the size of the triangulation, by using lots and lots of tiny-but-nice triangles.)
keenan
@pw123 There's no proof for this particular algorithm (it uses a bunch of heuristics---but does work well!). However, there's a related scheme called optimal Delaunay triangulation; the paper I just linked to does some nice analysis/explanation for why this kind of strategy works.
This seems like a really smart and clear way to make the triangles more uniform in size. Some of these steps seem like they would be tricky to implement in practice. For example, collapsing the edges could cause other edges to be deleted, making it really tricky to be able to loop through all edges.
The remeshing does have some trade-off in the detail right? I see some loss of detail in the eyelids.
Is there a proof anywhere of why this algorithm is effective? I'd be interesting in reading that.
are there different kinds of isotropic remeshing algorithms or has this been proven to be the most effective one? I feel like there may be other optimizations such as possibly deleting faces that could improve a mesh?
@tarangs Yes, absolutely---that is a fundamental trade off in surface triangulation. The triangulation has to serve as both a description of the geometry, and as a data structure that supports computation on the surface. So you have to balance between geometric accuracy and triangulation quality. (Or inflate the size of the triangulation, by using lots and lots of tiny-but-nice triangles.)
@pw123 There's no proof for this particular algorithm (it uses a bunch of heuristics---but does work well!). However, there's a related scheme called optimal Delaunay triangulation; the paper I just linked to does some nice analysis/explanation for why this kind of strategy works.