Introduction: Quadrangle geological maps from Mariner 10 data cover 45% [1] of the surface of Mercury at 1:5M scale, e.g. [2],[3]. Orbital MESSENGER data, which cover the entire planetary surface, can now be used to produce finer scale geological maps, including regions unseen by Mariner 10. Hokusai quadrangle (0–90° E; 22.5–66° N) is in the hemisphere unmapped by Mariner 10. It contains promin...

We define the notion of d i -regularity and regularity in generalized polygons, thus generalizing the notion of ‘regular point’ in a generalized quadrangle or hexagon. We show that a thick generalized polygon cannot contain too many regular points unless it is a projective plane, quadrangle or hexagon. For certain polygons (thick ‘odd’gons and 8-gons), we show that even a certain number of d2-r...

A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, 6, 1) design, the blocks being the hyperplane sections containing more than three (actually six) points of K. As such a point model is projectively unique, the present construction yields an easy coordinate–free approach t...

We propose an approach for automatically generating isotropic 2D quadrangle meshes from arbitrary domains with a fine control over sizing and orientation of the elements. At the heart of our algorithm is an optimization procedure that, from a coarse initial tiling of the 2D domain, enforces each of the desirable mesh quality criteria (size, shape, orientation, degree, regularity) one at a time,...

Let Q be a generalized quadrangle of order s with a regular point x. The set x⊥ together with all spans which are contained in x⊥ define a projective plane of order s. We introduce a property (Py) for every point y of Q noncollinear with x and prove that this property is equivalent with the regularity of the point y. We will use this to give an elementary proof for the following result: every g...

A hexagon quadrangle system of order n and index [HQS (n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of Kn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4) − HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a /2-fo...

We propose a framework for object extraction with accurate boundaries. A multilayer perceptron is used to identify seed points through examples, and regions are extracted and localized using a locally coupled network with weight adaptation. A functional system has been developed and applied to hydrographic region extraction from Digital Orthophoto Quarter–Quadrangle images.

A dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1, x2, ..., x12) and a 4-cycle (x1, x4, x7, x10). A dodecagon quadrangle system of order n and index ρ [DQS] is a pair (X, H), where X is a finite set of n vertices and H is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A dodecagon quadrangle ...

for the first time we have used eyelid skin expansion to facilitate reconstruction of selected patients with shortage of lid skin (e.g. for burn scar and after excision of tumors). this method allows for a controlled increase in skin, need for reconstruction, and offers many advantages over grafted skin transfered from a distance. color, texture, thinness, delicacy and adnexal structures are ae...

We show that a pointwise convergent sequence (n) n2IN of continuous collineations of a compact projective plane converges uniformly if and only if the pointwise limit of (n) n2IN has a quadrangle in its image. Moreover is then a continuous collineation. Furthermore, we derive that a homomorphism between topological projective planes is continuous if and only if it is continuous at some point.