Minimum Enclosing Circle of a Set of Fixed Points and a Mobile Point
نویسندگان
چکیده
Given a set S of n static points and a mobile point p in R, we study the variations of the smallest circle that encloses S ∪ {p} when p moves along a straight line `. In this work, a complete characterization of the locus of the center of the minimum enclosing circle (MEC) of S ∪{p}, for p ∈ `, is presented. The locus is a continuous and piecewise differentiable linear function, and each of its differentiable pieces lies either on the edges of the farthest-point Voronoi diagram of S, or on a line segment parallel to the line `. Moreover, the locus has O(n) differentiable pieces, which can be computed in linear time, given the farthest-point Voronoi diagram of S.
منابع مشابه
بازیابی مبتنی بر شکل اجسام با توصیفگرهای بدست آمده از فرآیند رشد کانتوری
In this paper, a novel shape descriptor for shape-based object retrieval is proposed. A growing process is introduced in which a contour is reconstructed from the bounding circle of the shape. In this growing process, circle points move toward the shape in normal direction until they get to the shape contour. Three different shape descriptors are extracted from this process: the first descript...
متن کاملMinimum Enclosing Circle of a Set of Static Points with Dynamic Weight from One Free Point
Given a set S of n static points and a free point p in the Euclidean plane, we study a new variation of the minimum enclosing circle problem, in which a dynamic weight that equals to the reciprocal of the distance from the free point p to the undetermined circle center is included. In this work, we prove the optimal solution of the new problem is unique and lies on the boundary of the farthest-...
متن کاملStrong convergence of variational inequality problem Over the set of common fixed points of a family of demi-contractive mappings
In this paper, by using the viscosity iterative method and the hybrid steepest-descent method, we present a new algorithm for solving the variational inequality problem. The sequence generated by this algorithm is strong convergence to a common element of the set of common zero points of a finite family of inverse strongly monotone operators and the set of common fixed points of a finite family...
متن کاملMinimum Enclosing Circle with Few Extra Variables
Asano et al. [JoCG 2011] proposed an open problem of computing the minimum enclosing circle of a set of n points in R2 given in a read-only array in sub-quadratic time. We show that Megiddo’s prune and search algorithm for computing the minimum radius circle enclosing the given points can be tailored to work in a read-only environment in O(n1+ ) time using O(logn) extra space, where is a positi...
متن کاملMinimum Enclosing Polytope in High Dimensions
We study the problem of covering a given set of n points in a high, d-dimensional space by the minimum enclosing polytope of a given arbitrary shape. We present algorithms that work for a large family of shapes, provided either only translations and no rotations are allowed, or only rotation about a fixed point is allowed; that is, one is allowed to only scale and translate a given shape, or sc...
متن کامل