Implicit-implicit and parametric-implicit surface intersections in Euclidean n-space

Abstract

In this paper, we study the intersection problem of two surfaces in which at least one surface is given by its implicit equation in Euclidean n-space. We first obtain the curvatures of the transversal intersection curve of two implicit surfaces. Later, the intersection problem is studied for a parametric surface and an implicit surface in n-dimensional Euclidean space. Finally, we present examples as applications of the given methods.