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Specializations

There are several notable exceptions to how Meshes.jl defines parametric functions.

  • Meshes.ConeSurface is essentially a composite type and has a parametric function that only maps the conical portion of the geometry, so the Meshes.Disk base element has to be integrated separately.
  • Meshes.CylinderSurface is essentially a composite type and has a parametric function that only maps the cylindrical portion of the geometry, so the Meshes.Disk element has to be integrated separately.
  • Meshes.FrustumSurface is essentially a composite type and has a parametric function that only maps the cylindrical portion of the geometry, so the top and bottom Meshes.Disk elements have to be integrated separately.
  • Meshes.Line represents a line of infinite length that passes through two points, and it has a parametric function that is valid on the domain $(-\infty, \infty)$.
  • Meshes.Plane represents a plane of infinite extent, and it has a parametric function that is valid on the domain $(-\infty, \infty)^2$.
  • Meshes.Ray represents a line that begins at a point and extends in a particular direction with infinite length, and it has a parametric function that is valid on the domain $[0, \infty)$.
  • Meshes.Ring is a composite type that lacks a parametric function, but can be decomposed into Meshes.Segments and then integrated by adding together the individual integrals.
  • Meshes.Rope is a composite type that lacks a parametric function, but can be decomposed into Meshes.Segments and then integrated by adding together the individual integrals.
  • Meshes.Triangle has a parametric function that takes coordinates on a 2D barycentric coordinate system. So, for (::Meshes.Triangle)(t1, t2), the coordinates must obey: $t_1, t_2 \in [0,1]$ where $t_1 + t_2 \le 1$.
  • Meshes.Tetrahedron has a parametric function that takes coordinates on a 3D barycentric coordinate system. So, for (::Meshes.Tetrahedron)(t1, t2), the coordinates must obey: $t_1, t_2, t_3 \in [0,1]$ where $t_1 + t_2 + t_3 \le 1$.