This work introduces the notion of computational hypertime, or the simulation and visualization of hypothetical environments possessing multidimensional time. An overview of hypertime is provided,including an intuitive visualization paradigm and a discussion of the failure of common simulation techniques when extended to include multidimensional time. A condition for differential equations describing hypertime motion to be amenable to standard time-iterative simulation techniques is provided,but is not satisfied by any known model of physics. An alternate simulation algorithm involving iterative refinement of entire equations of motion is presented,with an example implementation to solve elastic collisions in hypertime. An artificial intelligence algorithm for navigating crowds in any arbitrary nD/mT environment is discussed,and an implementation is provided using collision cones and stochastic global optimization techniques. Possible models of hypertime energy and other open questions are discussed. Both algorithms are described and show favorable results, meeting all design criteria and running at interactive speeds on common desktop computer systems.
College and Department
Physical and Mathematical Sciences; Computer Science
BYU ScholarsArchive Citation
Tychonievich, Luther A., "Simulation and Visualization of Environments with Multidimensional Time" (2008). Theses and Dissertations. 1326.
hypertime, multidimensional, time, simulation, visualization, program, algorithm, stochastic, distance, energy, momentum, elastic, collision, AI, artificial intelligence, obstacle, crowd, maneuver, maneuvering board, collision cone, velocity obstacle