What This Document Is
These are session notes from CS 686: Computer Graphics at the University of San Francisco. The material focuses on fundamental algorithms used in determining how and when rays intersect with geometric shapes – a core concept in ray tracing and 3D rendering. It delves into methods for calculating point inclusion within polygons, starting with simpler forms and progressing to more complex structures. The notes explore both 2D and 3D geometry, building a foundation for understanding spatial relationships within graphical scenes.
Why This Document Matters
This resource is invaluable for students learning the mathematical and computational underpinnings of computer graphics. It’s particularly helpful for those struggling to grasp how to programmatically determine if a point exists *within* a defined shape. Anyone working with ray tracing, collision detection, or geometric modeling will find the concepts discussed here essential. Reviewing these notes alongside coding assignments can significantly improve understanding and debugging skills. It’s best used as a supplement to lectures and hands-on programming exercises.
Common Limitations or Challenges
These notes present the *concepts* and *approaches* to solving these geometric problems. They do not provide fully implemented code solutions or a comprehensive library of functions. The material assumes a foundational understanding of linear algebra, particularly determinants and vector operations. While the notes build from basic shapes like triangles, applying these principles to highly complex or irregular polygons may require further study and adaptation. The notes also focus on *convex* shapes; handling concave polygons requires additional techniques not covered here.
What This Document Provides
* An exploration of algorithms for point-in-polygon testing.
* A progression from 2D polygon inclusion to 3D polyhedron inclusion.
* Discussion of how to adapt techniques for different polygon types (e.g., hexagons, octagons).
* An introduction to using Cramer’s Rule in both 2D and 3D geometric calculations.
* Conceptual groundwork for understanding how ray tracing systems determine intersections with objects.
* Connections between theoretical concepts and potential implementation in code (demonstrated through example program names).
