An Algorithm for Extracting the Geometric Parameters of a Right Circular Cone From the Coefficients of Its Algebraic Equation

Abstract

A right circular cone is an important geometric primitive that is used in many applications. The geometric parameters of the cone are the coordinates of its vertex, the direction of its axis, and the semi-angle of its vertex. These geometric parameters do not appear explicitly in the cone's algebraic equation which is widely used because of its simplicity. So, in this paper an algorithm is introduced to extract the cone's geometric parameters from the coefficients of its algebraic equation. A solid theoretical frame work is given through three propositions. The algorithm is tested on an eleven cases and proves reliability and simplicity. The algorithm can also detect non right circular cone cases.