Providing a simplified model of real terrain has applications to route planning for robotic vehicles and military maneuvers. This thesis explores planar-patch surface modeling to represent terrain in a simple and effective way. In planar-patch surface modeling the terrain is subdivided into a set of planar subregions. The homogeneity of the gradient within a planar subregion simplifies calculating the cost of traversing the region, thus simplifying route planning. The author has explored three main strategies to model the surface: joint top-down and bottom-up, strict bottom-up, and presmoothing bottom-up approaches. Results of the algorithms are shown graphically by using the APL and Grafstat packages, verifying their correctness and accuracy.