We study an extension of the problem of construction of a triangle from the feet of its internal angle bisectors. Given a triangle ABC, we give a conic construction of points P which are the incenter or excenters of their own anticevian triangles with respect to ABC. If the given triangle contains a right angle, a very simple ruler-and-compass construction is possible. We also examine the case ...

In this note we present an application of a new tool (the Gröbner cover method, to discuss parametric polynomial systems of quations) in the realm of automatic discovery of theorems in elementary geometry. Namely, we describe, through a relevant example, ow the Gröbner cover algorithm is particularly well suited to obtain the missing hypotheses for a given geometric statement to hold rue. We de...

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.

Symbolic computation of NURBS plays an important role in many areas of NURBSbased geometric computation and design. However, any nontrivial symbolic computation, especially when rational B-splines are involved, would typically result in B-splines with high degrees. In this paper we develop degree reduction strategies for NURBS symbolic computation on curves. The specific topics we consider incl...

This paper presents a generalization of the notion of circumcenter as the intersection of perpendicular bisectors. We define Generalized Perpendicular Bisectors between two regions as an area where each point is the center of at least one circle crossing both regions. This allows us to determine all the possible discrete circle centers that cross a given set of pixels. The possible radii can th...

This paper studies algebraic and geometric properties of curve–curve, curve– surface, and surface–surface bisectors. The computation is in general difficult since the bisector is determined by solving a system of nonlinear equations. Geometric considerations will help us to determine several distinguished curve and surface pairs which possess elementary computable bisectors. Emphasis is on lowd...

This paper deals with the determination of skeletons and conditional bisectors in discrete binary images using the Euclidean metrics. The algorithm, derived from [18], proceeds in two steps: rst, the Centers of the Euclidean Maximal Discs (CMD) included in the set to skeletonize are characterized and robustly identi ed. Second, a refront propagation is simulated starting from the set boundaries...