Computing convex quadrangulations☆

Experimental results on quadrangulations of sets of fixed points

We consider the problem of obtaining “nice” quadrangulations of planar sets of points. For many applications “nice” means that the quadrilaterals obtained are convex if possible and as “fat” or squarish as possible. For a given set of points a quadrangulation, if it exists, may not admit all its quadrilaterals to be convex. In such cases we desire that the quadrangulations have as many convex q...

On the Approximation Power of Splines on Triangulated Quadrangulations

We study the approximation properties of the bivariate spline spaces S r 3r (} +) of smoothness r and degree 3r deened on triangulations } + which are obtained from arbitrary nondegenerate convex quadrangulations by adding the diagonals of each quadrilateral. Suppose } is a nondegenerate convex quadrangulation of a polygonal domain in IR 2 (see Sect. 6 for details on quadrangulations and techni...

SIZE AND GEOMETRY OPTIMIZATION OF TRUSS STRUCTURES USING THE COMBINATION OF DNA COMPUTING ALGORITHM AND GENERALIZED CONVEX APPROXIMATION METHOD

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

Small Convex Quadrangulations of Point Sets

Characterizing and efficiently computing quadrangulations of planar point sets

Given a set S of n points in the plane, a quadrangulation of S is a planar subdivision whose vertices are the points of S, whose outer face is the convex hull of S, and every face of the subdivision (except possibly the outer face) is a quadrilateral. We show that S admits a quadrangulation if and only if S does not have an odd number of extreme points. If S admits a quadrangulation, we present...