1,040 research outputs found
Metrics with four conic singularities and spherical quadrilaterals
A spherical quadrilateral is a bordered surface homeomorphic to a closed
disk, with four distinguished boundary points called corners, equipped with a
Riemannian metric of constant curvature 1, except at the corners, and such that
the boundary arcs between the corners are geodesic. We discuss the problem of
classification of these quadrilaterals and perform the classification up to
isometry in the case that two angles at the corners are multiples of pi. The
problem is equivalent to classification of Heun's equations with real
parameters and unitary monodromy.Comment: 68 pges, 25 figure
Linear Complexity Hexahedral Mesh Generation
We show that any polyhedron forming a topological ball with an even number of
quadrilateral sides can be partitioned into O(n) topological cubes, meeting
face to face. The result generalizes to non-simply-connected polyhedra
satisfying an additional bipartiteness condition. The same techniques can also
be used to reduce the geometric version of the hexahedral mesh generation
problem to a finite case analysis amenable to machine solution.Comment: 12 pages, 17 figures. A preliminary version of this paper appeared at
the 12th ACM Symp. on Computational Geometry. This is the final version, and
will appear in a special issue of Computational Geometry: Theory and
Applications for papers from SCG '9
Spherical quadrilaterals with three non-integer angles
We classify spherical quadrilaterals up to isometry in the case when one
inner angle is a multiple of pi while the other three are not. This is
equivalent to classification of Heun's equations with real parameters and one
apparent singularity such that the monodromy consists of unitary
transformations.Comment: 38 pages, 16 figures. arXiv admin note: text overlap with
arXiv:1409.152
- …