Abstract: A method and apparatus for intelligently tutoring a student to improve math or other skills is provided. The method and apparatus present groups of problems to a student in a sequential manner, and award points to the student when the student enters a correct response. Statistics regarding the student's performance are recorded and may be viewed in a variety of selectable formats so that parents, teachers, and other interested parties can track the students progress. The student's performance is analyzed, and the level of difficulty of problems being presented is controlled in order to challenge a student to improve educational skills, without over or under burdening the student.

Abstract: A method of modeling and rendering a three-dimensional complex surface using a triangle mesh is disclosed. The method can reduce memory requirement and rendering time by using local height maps and by assigning neighborhood coordinates to any point on a surface near the triangle mesh assigned to that surface. Barycentric coordinates are used to identify points in a triangular polygon to work with height data in the local height map associated with that triangular polygon. The local height maps allow collision detection of a ray with the three-dimensional surface. Lipshitz constants associated with the three-dimensional surfaces are used to find a point on the next ray closest to the three-dimensional surface to jump to, making the search for such collision points efficient.