Optimal Angle Bounds for Quadrilateral Meshes

Quadrilateral Meshes for PSLGs

We prove that any PSLG has a conforming quadrilateral mesh with O(n) elements, all angles ≤ 120◦ and all new angles ≥ 60◦ (the complexity and the angle bounds are both sharp). Moreover, all but O(n) of the angles may be taken in a smaller interval, say [89◦, 91◦]. Date: January 2011. 1991 Mathematics Subject Classification. Primary: 30C62 Secondary:

Post Refinement Element Shape Improvement for Quadrilateral Meshes

Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. ...

Local Refinement of Quadrilateral Meshes

Subelement patterns using bisection of edges and schemes for selecting edges to be split are described for the local refinement of elements in all-quadrilateral and quadrilateral-dominant planar meshes. Subelement patterns using trisection of edges are also described for the local refinement of elements in all-quadrilateral planar meshes. These patterns and schemes are easily extendible to quad...

Upper and Lower Bounds for Stri tly Convex Quadrilateral Meshes of Point Sets

Small Stri tly Convex Quadrilateral Meshes of Point Sets

Abstract In this paper, we give upper and lower bounds on the number of Steiner points required to onstru t a stri tly onvex quadrilateral mesh for a planar point set. In parti ular, we show that 3⌊ 2 ⌋ internal Steiner points are always suÆ ient for a onvex quadrilateral mesh of n points in the plane. Furthermore, for any given n ≥ 4, there are point sets for whi h ⌈ 2 ⌉ − 1 Steiner points are...