Circumcenter of Mass and Generalized Euler Line
نویسندگان
چکیده
منابع مشابه
Circumcenter of Mass and Generalized Euler Line
We define and study a variant of the center of mass of a polygon and, more generally, of a simplicial polytope which we call the Circumcenter of Mass (CCM). The Circumcenter of Mass is an affine combination of the circumcenters of the simplices in a triangulation of a polytope, weighted by their volumes. For an inscribed polytope, CCM coincides with the circumcenter. Our motivation comes from t...
متن کاملGeneralized Perpendicular Bisector and Circumcenter
This paper presents a theoretical generalization of the circumcenter as the intersection of generalized perpendicular bisectors. We define generalized bisectors between two regions as an area where each point is the center of at least one circle crossing each of the two regions. These new notions should allow the design of new circle recognition algorithms.
متن کاملSome Remarks on the Circumcenter of Mass
In this article, we give new proofs for the existence and basic properties of the circumcenter of mass defined by Adler in 1993 and Tabachnikov and Tsukerman in 2013. We start with definitions. Definition 1 The power of a point x with respect to a sphere ω(o, R) inRd is defined as Pow(ω, x) = ‖ox‖2 − R2. Here o is the center and R is the radius of the sphere ω(o, R). Definition 2 Given a simple...
متن کاملRemarks on the circumcenter of mass
Suppose that to every non-degenerate simplex ∆ ⊂ Rn a ‘center’ C(∆) is assigned so that the following assumptions hold: (i) The map ∆ → C(∆) commutes with similarities and is invariant under the permutations of the vertices of the simplex; (ii) The map ∆ → Vol(∆)C(∆) is polynomial in the coordinates of the vertices of the simplex. Then C(∆) is an affine combination of the center of mass CM(∆) a...
متن کاملRemarks on the the circumcenter of mass
Given a homogeneous polygonal lamina P , one way to find its center of mass is as follows: triangulate P , assign to each triangle its centroid, taken with the weight equal to the area of the triangle, and find the center of mass of the resulting system of point masses. That the resulting point, CM(P ), does not depend on the triangulation, is a consequence of the Archimedes Lemma: if an object...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2014
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-014-9597-2