Let H2 be the group of isotopy classes of orientation-preserving homeomorphisms of S that preserve a Heegaard splitting of genus two. In this paper, we construct a tree in the barycentric subdivision of the disk complex of a handlebody of the splitting to obtain a finite presentation of H2.

We derive a generalization of barycentric coordinates which allows a vertex in a planar triangulation to be expressed as a convex combination of its neighbouring vertices. The coordinates are motivated by the Mean Value Theorem for harmonic functions and can be used to simplify and improve methods for parameterization and morphing.  2003 Elsevier Science B.V. All rights reserved.

In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...

The h-polynomial of the barycentric subdivision any n-dimensional cubical complex with nonnegative h-vector is shown to have only real roots and be interlaced by Eulerian polynomial type Bn. This result applies subdivisions shellable complexes and, in particular, convex polytopes answers affirmatively a question Brenti, Mohammadi Welker.

Three different polygon morphing methods are examined. The first one is based on the utilization of the trimmed skeleton of the symmetric difference of the source and target polygons as an intermediate polygon. The second one reduces the problem to the problem of morphing compatible planar triangulations and utilizes the representation of planar triangulations as a matrix constructed using bary...

In a recent paper by the first author, a simple proof was given of a result by Tutte on the validity of barycentric mappings, recast in terms of the injectivity of piecewise linear mappings over triangulations. In this note, we make a short extension to the proof to deal with arbitrary tilings. We also give a simple counterexample to show that convex combination mappings over tetrahedral meshes...

Printing with a large number of inks, also called N -ink printing, is a challenging task. The challenges comprise spectral modeling of the printer, color separation, halftoning, and limitations of the amount of inks. Juxtaposed halftoning, a perfectly dot-off-dot halftoning method, has proved to be useful to address some of these challenges. However, for juxtaposed halftones, prediction of colo...