The Newton polygon of the implicit equation of a rational plane curve is explicitly determined by the multiplicities of any of its parametrizations. We give an intersection-theoretical proof of this fact based on a refinement of the KušnirenkoBernštein theorem. We apply this result to the determination of the Newton polygon of a curve parameterized by generic Laurent polynomials or by generic r...

The paper studies local convexity properties of digital curves. We locally define convex and concave parts from the slope of maximal digital straight segments and arithmetically characterize the smallest digital pattern required for checking convexity. Moreover, we introduce the concepts of digital edge and digital hull, a digital hull being a sequence of increasing or decreasing digital edges....

In this paper, a representative algorithm convex hull with half-dividing and recurrence is commented; and according to the isomorphic fundamental theorem of the convex hull construction, and guided by the isomorphic distributing characteristics of a convex hull’s the apexes, a more efficient new algorithm to find a convex hull based on the dynamical base line with a maximum pitch of the dynamic...

The concept of convex polygon-offset distance function was introduced in 2001 by Barequet, Dickerson, and Goodrich. Using this notion of point-to-point distance, they showed how to compute the corresponding nearestand farthest-site Voronoi diagram for a set of points. In this paper we generalize the polygon-offset distance function to be from a point to any convex object with respect to an m-si...

We present a diagram that captures containment information for scalable rotated and translated versions of a convex polygon. For a given polygon P and a contact point q in a point set S, the diagram parameterizes possible translations, rotations, and scales of the polygon in order to represent containment regions for each additional point v in S. We present geometric and combinatorial propertie...

Instead of using the polygon defined by adjacent vertices to a vertex (called the ball) or its kernel [1], we propose a modified polygon that is easy to compute, convex and an approximation of the kernel. We call this polygon the “quick kernel ball region.” This novel algorithm is presented in details. It is easy to implement and effective in constraining a vertex to remain within its feasible ...

Given a simple polygon P , we consider the problem of finding a convex polygon Q contained in P that minimizes H(P, Q), where H denotes the Hausdorff distance. We call such a polygon Q a Hausdorff core of P . We describe polynomial-time approximations for both the minimization and decision versions of the Hausdorff core problem, and we provide an argument supporting the hardness of the problem.

VQ = {(q, a) ∈ Z : gcd(q, a) = 1, max{|a|, |q|} ≤ Q}. Then the Jarńık polygon PQ is the unique (up to translation) convex polygon whose sides are precisely the vectors in VQ. In other words, PQ is the polygon whose vertices can be obtained by starting from an arbitrary point in R and adding the vectors in VQ one by one, traversing those vectors in a counterclockwise direction. For example, the ...

Let S be used to denote a nite set of planar geometric objects. Deene a polygon transversal of S as a closed simple polygon that simultaneously intersects every object in S, and a minimum polygon transversal of S as a polygon transversal of S with minimum perimeter. If S is a set of points then the minimum polygon transversal of S is the convex hull of S. However, when the objects in S have som...

In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection of the ellipses are found in an efficient manner. To do so, the intersection points of the ellipses that fall on the boundary of the intersection region are d...