A new algorithm for creating slope lines with no intersections

This study develops a new algorithm to create any kinds of slope lines with no intersections automatically. It gives enough evidence to support that the real-intersection and the complementary theorem proposed in this research are sufficient conditions of the generation of slope lines without any intersections. This method can dynamically draw any kind of normal-based slopes, scarps, escarpments, steep rock hills or embankments. The efficiency of the algorithm is tested by using three experiments.