Intersection numbers: A development of formulas for degree and genus relevant to computer-aided geometric design

Scope and method of study. This paper presents calculations of implicit degree of triangular and tensor product surfaces and genus of the curve of intersection of two triangular or tensor product surfaces. In CAGD robust surface intersection algorithms are a current topic of investigation and the underlying theory of degree and genus is crucial to that investigation. The purpose of this paper is to make those topics more accessible to scholars outside of the area of algebraic geometry.; Findings and conclusions. The formulas for the implicit degree are given for general triangular and tensor product surfaces with any number and variety of base points. These formulas are developed completely in this paper using few outside sources. The theory of intersection numbers for divisors on certain 1 and 2-dimensional manifolds is used to develop these formulas. The formulas for the genus of the curve of intersection for general rational surfaces are also given in the case where the surfaces have simple base points.