A parametric model for oriented, navigable surfaces in virtual environments

ABSTRACT

This paper introduces a parametric model of oriented, navigable surfaces in virtual environments. An oriented, navigable surface in 3D space is modeled as a ribbon which has a central axis and can be twisted around the central axis. The axis is represented with a cubic spline curve and is approximately arc-length parameterized. The profile of the ribbon along the axis is described by a slant function. With the representation of the ribbon axis and the ribbon profile, a point on the ribbon surface can be expressed as a function of two parameters: the arc length along the axis and the offset from the axis. The parametric model of a ribbon naturally forms a local ribbon coordinate system which provides a frame of reference for behavior code. In order to provide an uniform, continuous frame of reference for an agent to navigate through connected ribbons, we unite the ribbons to form a ribbon called a path.

REFERENCES

• 1: Artz, B. 1995. An analytical road segment terrain database for driving simulation. In Proceedings of 1995 Driving Simulation Conference, 274--284.
• 2: Atkinson, K. 2002. Modelling a road using spline interpolation. Tech. rep., Reports on Computational Mathematics #145, Department of Mathematics, The University of Iowa.
• 3: Carles, O., and Espie, S. 1999. Database generation system for road applications. In Proceedings of 1999 Driving Simulation Conference, 87--103.
• 4: Stephane Donikian, VUEMS: A Virtual Urban Environment Modeling System, Proceedings of the 1997 Conference on Computer Graphics International, p.84, June 23-27, 1997
• 5: Evans, D. F. 1995. High-fidelity Roadway Modeling for Real-time Driving Simulation. Master's thesis, The University of Iowa.
• 6: Rida T. Farouki , Takis Sakkalis, Real rational curves are not “unit speed”, Computer Aided Geometric Design, v.8 n.2, p.151-157, May 1991 [doi>10.1016/0167-8396(91)90040-I]
• 7: Francis J. Hill, Computer Graphics Using OpenGL, Prentice Hall PTR, Upper Saddle River, NJ, 2000
• 8: Koutaki, G., and Uchimura, K. 2004. Automatic road extraction based on cross detection in suburb. Computer Graphics International (April), 337--344.
• 9: Papelis, Y., and Bahauddin, S. 1995. Logical modeling of roadway environment to support real-time simulation of autonomous traffic. In Proceedings of First Workshop on Simulation and Interaction in Virtual Environments, 62--71.
• 10: Plumert, J. M., Kearney, J. K., and Cremer, J. F. 2004. Children's perception of gap affordances: Bicycling across traffic-filled intersections in an immersive virtual environment. Child Development 75, 4, 1243--1253.
• 11: Wang, H., Kearney, J. K., and Atkinson, K. 2002. Arclength parameterized spline curve for real-time simulation. In Proceedings of 5th international conference on Curves and Surfaces, 387--396.
• 12: Wang, H., Kearney, J. K., and Atkinson, K. 2002. Robust and efficient computation of the closest point on a spline curve. In Proceedings of 5th international conference on Curves and Surfaces, 397--406.
• 13: Hongling Wang , Joseph K. Kearney , James Cremer, Steering Behaviors for Autonomous Vehicles in Virtual Environments, Proceedings of the 2005 IEEE Conference 2005 on Virtual Reality, p.155-162, March 12-16, 2005 [doi>10.1109/VR.2005.69]
• 14: Hongling Wang , Joseph K. Kearney, Efficient roadway modeling and behavior control for real-time simulation, University of Iowa, Iowa City, IA, 2005
• 15: Peter Willemsen , Joseph K. Kearney , Hongling Wang, Ribbon Networks for Modeling Navigable Paths of Autonomous Agents in Virtual Urban Environments, Proceedings of the IEEE Virtual Reality 2003, p.79, March 22-26, 2003
• 16: Peter Jason Willemsen , Joseph K. Kearney, Behavior and scenario modeling for real-time virtual environments, 2000

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.6 SIMULATION AND MODELING
      I.6.3 Applications

Additional Classification:
  K. Computing Milieux
  K.7 THE COMPUTING PROFESSION
      K.7.m Miscellaneous

Keywords:
navigation, surface modeling, virtual environments