A method for determining an intersection between a polygon representing a boundary of a surface in an earth formation and a plane includes: receiving a polygon representing a boundary of a surface in an earth formation, the polygon having a series of straight segments with a point at each end of each of the segments; overlaying a cutting grid having grid planes over the polygon; identifying a specific pattern of two adjacent segments in the polygon by proceeding from a first segment to a second segment in a selected rotational direction; matching the specific pattern to a reference pattern; categorizing the point between the two adjacent segments as an intersection point or as a non-intersection point based on the reference pattern; the iterating the identifying, matching, and categorizing for each pair of adjacent segments in the polygon such that each point between adjacent segments in the polygon is categorized.