Subdivision of mesh (half edge data), using various algorithms.

Extension to half-edge (code not included, note extension requires C++20).

Load mesh into half-data:

std::unique_ptr<Mesh::HalfEdge> p_mesh = Mesh::Import( "cube_tri.obj", Mesh::Type::Wavefront );

Select an algorithm (for example Doo with optional value):

std::unique_ptr<Mesh::Subdivision::Polymorphic> p_algorithm = std::make_unique<Mesh::Subdivision::Doo>( 0.6 );

Perform one subdivision (note that process() will return a nullptr on failure):

auto p_subdiv = p_algorithm->process( p_mesh );

Save subdivided mesh:

Mesh::Export( "mesh-subdiv.obj", p_subdiv, Mesh::FileType::Wavefront, Mesh::VertexNormal::Weighted );

N-gon:
Number of edges needed. Either a fixed value, or a minimal.
Special cases:
3*, process will turn mesh polygons into triangles.
4*, vertices must be order 4 (e.g. have four edges).

Surface:
Types of surfaces.
Closed, all edges are connected to two (2) polygons.
Open, one or two polygon(s) per edge.
Any, same as open, supports sharp/hard/creased edges.

M/T:
Support for material and/or texture coordinates.
If not supported, the data is is lost.

Optional:
Shading, if polygon is smooth or flat shaded. Lost if not supported\

Butterfly:
Butterfly-Tensor:
Nira Dyn, David Levine, John A. Gregory (1990)
A butterfly subdivision scheme for surface interpolation with tension control

Catmull-Clark:
Catmull-Clark-Quad:
E. Catmull, J Clark (1978)
Recursively generated B-spline surfaces on arbitrary topological meshes

Doo:
D. W. H. Doo (1978)
A subdivision algorithm for smoothing down irregularly shaped polyhedrons

Doo-Sabin:
D. Doo, M. Sabin (1978)
Behavior of recursive division surfaces near extraordinary points

Loop:
Loop, Charles Teorell (1987)
Smooth Subdivision Surfaces Based on Triangles

Root3:
Kobbelt, Leif (2000)
√3-subdivision

• C++20

• half-edge

More algorithms...

Improved butterfly:
???

DDS:
???

Habib-Warren (AKA midedge):
A. Habib, J. Warren (1999)
Edge and vertex insertion for a class of C1 subdivision surfaces

Kobbelt:
???

Peters-Reif (AKA midedge):
J. Peters, U. Reif (1997)
The simplest subdivision scheme for smoothing polyhedra

Chaikin (1974), An algorithm for high speed generation