Four-Space Visualization of 4D Objects

Supervisory Committee:

• Dr. Thomas Foley
• Dr. Gregory Nielson
• Dr. Gerald Farin

Table of Contents

• Abstract
• Acknowledgements
• List of Figures

• Chapter 1: Introduction
  • 1.1: Background
  • 1.2: Previous Work
  • 1.3: Overview of This Research
  • 1.4: Contents of This Paper

• Chapter 2: Four Dimensional Geometry
  • 2.1: Vector Operations and Points in Four-Dimensional Space
  • 2.2: Rotations in Four Dimensions

• Chapter 3: Overview of Visualization in Three and Four Space
  • 3.1: Viewing in Three Space
  • 3.2: Viewing in Four Space

• Chapter 4: Wireframe Display of Four Dimensional Objects
  • 4.1: High-Level Overview of 4D to 2D Projection
  • 4.2: Description of 3D to 2D Projection
  • 4.3: Description of 4D to 3D Projection
  • 4.4: Rotations in 4D Wireframes
  • 4.5: User Interaction and Visualization Aids
  • 4.6: Example 4D Wireframe Images

• Chapter 5: Raytracing in Four Dimensions
  • 5.1: General Description of the Raytracing Algorithm
  • 5.2: Generating the Four-Dimensional Ray Grid
  • 5.3: The General Raytrace Algorithm
  • 5.4: Reflection and Refraction Rays
  • 5.5: Illumination Calculations
  • 5.6: Intersection Algorithms
    • 5.6.1: Ray-Hypersphere Intersection
    • 5.6.2: Ray-Tetrahedron Intersection
    • 5.6.3: Ray-Parallelepiped Intersection
  • 5.7: Display of 4D Raytrace Data
  • 5.8: Example Ray4 Images

• Chapter 6: Conclusion
  • 6.1: Research Conclusions
  • 6.2: Future Research Areas

• References
• Appendix A: Implementation Notes and Source Code
• A PostScript Version of This Thesis