Intersection points of curves are the basic elements for many algorithms in the CAD/CAM area. In most circumstances, the key property of an intersection point is the behavior of the curves in a neighborhood of that intersection point. This paper presents the classification of intersection points from the differential geometric point of view in terms of the movement of particles along curves. The movement is evaluated in the neighborhood of an intersection point under the constraint that the particle moves along one curve with respect to the other. Applications of this classification and an universal algorithm for boolean operations on areas enclosed by continuous, simple curves show the advantages of this classification for todays CAD/CAM problems.