Mesh or surface, understanding the difference

Quick list of pros and cons.

Surface good:

  • Analytically defined geometry (it’s smooth no matter how far you zoom in).
  • Small memory/file footprint (you do not need many points to define a curvy surface, however the benefits are somewhat mitigated by the fact that every surface carries around a display mesh used for shading).
  • Simple topology (a surface is always a finite uv patch topologically speaking, makes it easier to develop algorithms for them).
  • Accuracy (because surfaces are analytical, things like intersections yield accurate results).

Surface bad:

  • The maths involved is difficult.
  • It’s difficult if not impossible to exchange surface data with other 3D applications.
  • Topologically limited (sort of the flip-side of the topological simplicity argument. Sometimes you need a higher genus shape and then a single surface will no longer cut the mustard).

Mesh good:

  • Simple definition (points, polygons connecting those points, there done).
  • Highly exchangeable with other apps.
  • Modern graphics hardware is really good at displaying meshes fast.
  • No topological constraints.
  • Lots of published research and algorithms for meshes, not so much for nurbs surfaces.
  • You can associate specific colours with specific points on the mesh.

Mesh bad:

  • It’s not smooth, it’s discrete.
  • It can be really difficult to perform operations on the mesh shape, because there is no intrinsic parameterisation.
  • There’s lots of ways in which a mesh can be invalid.
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