Touching points of s star-shaped set with an affine subspace

Approximate Star-Shaped Decomposition of Point Set Data

Simplification or decomposition is a common strategy to handle large geometric models, which otherwise require excessive computation to process. Star-shaped decomposition partitions a model into a set of star-shaped components. A model is star shaped if and only if there exists at least one point which can see all the points of the model. Due to this interesting property, decomposing a model in...

Coloring a set of touching strings

For a family of geometric objects in the plane F = {S1, . . . , Sn}, define χ(F) as the least integer l such that the elements of F can be colored with l colors, in such a way that any two intersecting objects have distinct colors. When F is a set of Jordan regions that may only intersect on their boundaries, and such that any point of the plane is contained in at most k regions, it can be prov...

Star-Shaped and L-Shaped Orthogonal Drawings

An orthogonal drawing of a plane graph G is a planar drawing of G, denoted by D(G), such that each vertex of G is drawn as a point on the plane, and each edge of G is drawn as a sequence of horizontal and vertical line segments with no crossings. An orthogonal polygon P is called orthogonally convex if the intersection of any horizontal or vertical line L and P is either a single line segment o...

Convexifying star-shaped polygons

Star-Shaped Conjugated Systems

The present review deals with the preparation and the properties of star-shaped conjugated compounds. Three, four or six conjugated arms are attached to crossconjugated cores, which consist of single atoms (B, C, N), benzene or azine rings or polycyclic ring systems, as for example triphenylene or tristriazolotriazine. Many of these shape-persistent [n]star compounds tend to -stacking and self...