Mesh Navigation Through Jumping

Abstract

The motion planning problem has been applied to a wide variety of fields and contexts. However, very few solutions to this problem combine multiple modes of motion. This report explores the motion planning problem in a three-dimensional environment where the character can not only walk on all available surfaces, but also jump between different surfaces. We take a more fundamental approach than much of the practically oriented work in the field. Starting from a set of physics-based axioms, we establish the definitions of minimal and optimal jumps between any two points. By extending these concepts to three-dimensional line segments, we define the jump link minimal velocity and jump link minimal arc length, which are two concrete heuristics for connectivity and optimality. Combined with special case definitions for projected edges, this allows us to provide a practical implementation of a jump link. We then provide notes on the results’ usage in practice. The usage of jump links in a path planning algorithm is left for future work.