Conformal Geometric Algebra and Algebraic Manipulations of Geometric Invariants

Geometric invariance is an important approach in computer vision and graphics.When a new invariant is found,an important problem is to find its "geometric" relationship (relationship with geometric meaning) with basic invariants.The discovery of this relationship is mainly based on algebraic manipulations of invariants.
We show how the basic,advanced and rational invariants in conformal geometric algebra (CGA) appear naturally in geometric problems,how the y are manipulated algebraically,and how to obtain the sufficient and necessary conditions and the complete form of geometric the orems by means of invariants manipulation. Automated geometric the orem proving,as a byproduct of the completion of geometric the orems,is further developed into automated quantitative description of geometric relations. The recovery of the geometric meaning of this quantitative description leads to a natural extension of the geometric the orem.Computing the geometric relationship among geometric invariants is a direct application of the se techniques.