No abstract

The right circular cylinder (RCC) is an important geometric primitive that appears in many applications. The coefficients of the RCC's algebraic equation are called algebraic parameters. The algebraic parameters have no direct geometric meaning. The geometric parameters of RCC are a vector giving the direction of its axis, a point to fix the axis position, and a positive real number giving the radius of the cylinder. In this paper, an algorithm is introduced to extract the geometric parameters of a RCC from its algebraic parameters. The algorithm can also detect non RCC cases. Seven propositions are proved to make a solid theoretical ground for the algorithm. The algorithm is tested on five cases and produces exact results.

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.

In this paper, an algorithm is introduced to serve in two tasks. The first is to extract the geometric parameters of a right circular cylinder from the coefficients of its algebraic equation. The second is to identify right circular cylinders from other quadrics given by an algebraic equation; that is, the algorithm can be used as a cylinder/not a cylinder classification tool. The algorithm is tested on a number of cases and its powerful is proved.