enolte / fe-public

fe-public

Test results for the fe mesh repo.

Simplex mesh induction from a point cloud.

Tested with:

• GNU g++ 11.2.0 (64-bit) Windows 7

Older compilers are not supported.

Mesh Construction Strategies

simple

• encounter-ordered subset search (n-dimensional "z-order" iteration)
• opportunistic first match
• no additional simplex binding
• no data assumptions

proximity

• proximity-sorted search (n-dimensional partial proximity-sorted search)
• opportunistic first match
• no additional simplex binding
• no data assumptions

Basis construction strategies

C⁰ isometric

• Identical knot selection strategy for any simplex
  • No dimension assumptions
  • No simplex geometry assumptions
• Direct construction of polynomials from simplex vertices
• L^∞-normalization (implicit)
• Continuous splines
• No differentiability guarantees
• min degree = 1

C¹ isometric

• Identical knot selection strategy for any simplex
  • No dimension assumptions
  • No simplex geometry assumptions
• Direct construction of polynomials from simplex vertices
• Differentiable splines (approximate normalization)
• min degree = 2

Test cases

Test cases are organized by geometric selection of input points. For the below,

• k = simplex dimension
• m = capacity dimension of source region

Various embedding dimension values (n) are tested.

m-cube vertices, case k = m

• unit cube
  • mesh
  • basis (pending)
• nested m-cubes (pending)
• two intersecting m-cubes (pending)
• m-cubic lattice (pending)

m-cube vertices, case k < m

• unit cube (pending)
• nested m-cubes (pending)
• two intersecting m-cubes (pending)
• m-cubic lattice (pending)

m-sphere

• co-spherical grid points (pending)
• spherical shell (pending)
• nested m-spheres (pending)
• two intersecting m-cubes (pending)

random n-dimensional point cloud

• constrained m-angle (pending)
• constrained point distance (pending)
• constrained simplex measure (pending)