Convex hull is one of the most fundamental constructs in geometry and its construction has been extensively studied. There are many prior works on convex points. However, counterpart for weighted points not sufficiently addressed despite important applications. Here, we present a simple fast algorithm, QuickhullDisk, set disks R2 by generalizing quickhull algorithm QuickhullDisk takes O(nlog n) time average O(mn) worst case where m represents number extreme which contribute to boundary n...

Abstract In this article, we present an efficient algorithm to determine the convex hull of a finite planar set using idea Method Orienting Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung Großen mittels Orientierungskurven, Optimization, 18 (1987), pp. 65–81, for solving optimal control problems with state constraints). The is determined parts orienting lines and final line. Two advantages over some variations Graham's are presented. Keywords:...

A kind of generalized convex functions is said to be stable with respect some property (P) if this maintaincd during an arbitrary function from class disturbed by a linear functional sufficiently small norm. Unfortunately. known generallzed convexities iike quasicunvexity, explicit quasiconvexity. and pseudoconvexity are not such optimization properties which expected true these generalizations, even the domain ol compact. Therefore, we introduce notion s-quasiconvex functions. These...

This article describes an efficient convex hull algorithm for finite point sets in 3D based on the idea of Method Orienting Curves (introduced by Phu Optimization, 18 (1987) pp. 65–81, solving optimal control problems with state constraints). The actual run times our and known gift-wrapping set random points (in uniform distribution) show that runs significantly faster than one.

Abstract We show that the known types of generalized monotone maps are not stable with respect to their characterizations (i.e. maintained if an arbitrary map this type is disturbed by element sufficiently small norm) and introduce s-quasimonotone maps, which characterization. For gradient s-quasimonotonicity related s-quasiconvexity (introduced Phu in Optimization, 38, 1996) underlying function. A necessary sufficient condition for a univariate polynomial be given. Furthermore, some...

We present an efficient algorithm for finding the shortest path joining two points in a sequence of triangles three-dimensional space without planar unfolding. The concept funnel associated with common edge along is introduced, that similar to Lee and Preparata's one simple polygon. funnels all edges constructed then determined by cusps these funnels. Such are iteratively their Method Orienting Curves, which was introduced Phu [Ein konstruktives Lösungsverfahren für das Problem des...

In this paper, we present an efficient algorithm, namely Orienting and Final Circles (OFC)-Delaunay Triangulation, for constructing the Delaunay triangulation of a finite planar point set using idea Method Curves (introduced by Phu in Zur Lösung einer regulären Aufgabenklasse der optimalen Steuerung im Groen mittels Orientierungskurven, Optimization 18(1) (1987) 65–81 Ein konstruktives Lösungsverfahren für das Problem des Inpolygons kleinsten Umfangs von J. Steiner, 18(3) 349–359). The...

In this article, we deal with some computational aspects of geodesic convex sets. Motzkin-type theorem, Radon-type and Helly-type theorem for sets are shown. particular, given a finite collection in simple polygon an “oracle,” which accepts as input three the gives its output intersection point or reports nonexistence; present algorithm finding collection.

The following problem is very classical in motion planning: Let a and b be two vertices of polygon P (Q, respectively) the polyline formed by from to (from a, counterclockwise order. We find Euclidean shortest path between b. In this paper, an efficient algorithm based on incremental convex hulls presented. Under some assumption, consists extreme subpolylines respectively), first start advancing P, then Q, alternating until vertex reached. Each such hull delivered for subpolyline just before...

The convex rope problem, posed by Peshkin and Sanderson in <em>IEEE Journal of Robotics & Automation, 2,</em> 1986 53–58, is to find the counterclockwise clockwise ropes starting at vertex <em>a</em> ending <em>b</em> a simple polygon, where on boundary hull polygon visible from infinity (i.

A map F(·) defined on a nonempty and convex D⊂Rn, which remains pseudomonotone when disturbed by vectors in Rn with sufficiently small norm, is s-quasimonotone (P. T. An, Optimization, Vol. 55 (2006), pp. 289–299). In this paper, the stability radius of such introduced. We then present relationship between index D its line segments contained D. The closedness set that F(x)+a quasimonotone proved. Additionally, excess demand functions also given.

Abstract Detecting potholes is an ongoing problem that requires extensive investigations as significantly deteriorate urban beauty and can cause serious harm to commuters. Multiple techniques have been developed over the years address issue. However, there has no formal way define size, particularly width, of a pothole. This work presents An's mathematical definition for width arbitrary 2D pothole at point inside. Then, each calculated by taking supremum all values points in given subset We...

Y tế có vai trò quan trọng trong đời sống hiện nay, không chỉ giúp bảo vệ sức khỏe cho người dân, góp phần nâng cao cải thiện xã hội. Đi đôi với đó nguy cơ dẫn đến tai nạn lao động nhân viên y ngày càng gia tăng. Việc xây dựng biện pháp rất trọng. Mục tiêu của nghiên cứu tổng này nhằm các nguyên để phòng chống tế. Sử dụng phương văn, tìm kiếm tài liệu liên và công tác chống, Kết quả, thấy nhiều như: Tiếp xúc yếu tố hiểm - hại, môi trường làm việc đảm an toàn…...

Solving shortest path problems inside simple polygons is a very classical problem in motion planning. To date, it has usually relied on triangulation of the polygons. The question: "Can one devise O(n) time algorithm for computing between two points polygon (with n vertices), without resorting to (complicated) linear-time algorithm?" raised by J. S. B. Mitchell Handbook Computational Geometry (J. Sack and Urrutia, eds., Elsevier Science B.V., 2000), still open. aim this paper show that...