Graph-Based Parameterization of Triangle Meshes with Arbitrary Genus

representing 2-manifolds with an arbitrary genus is described.
A topology-based decomposition of the shape is computed and used
to segment the shape into primitives, which define a chart
decomposition of the mesh. Then, each chart is parameterized
using an extension of the barycentric coordinates method.
The charts are all 0-genus and can be of three types only,
depending on the number of boundary components. The chart
decomposition and the parameterization are used to define
a shape graph where each node represents one primitive and
the arcs code the adjacency relationships between the primitives.
Conical and cylindrical primitives are coded together with their
skeletal lines that are computed from and aligned with their
parameterization. The application of the parameterization
approach to remeshing guarantees that extraordinary vertices
are localized only where two patches share a boundary and
they are not scattered on the whole surface.