Computational Geometry

Computational Geometry is a branch of computer science and mathematics that focuses on the design and analysis of efficient algorithms for solving problems stated in terms of geometry. It provides the fundamental methods for processing and manipulating geometric objects such as points, lines, polygons, and polyhedra, addressing core tasks like constructing convex hulls, partitioning space with Voronoi diagrams, detecting intersections, and performing efficient spatial queries.

1. Introduction to Computational Geometry
   1. Core Problems and Motivations
      1. Geometric Computation in Science and Engineering
      2. Applications in Computer Graphics
      3. Applications in Robotics and Path Planning
      4. Applications in Geographic Information Systems
      5. Applications in Computer Vision
      6. Applications in VLSI Design
      7. Applications in Molecular Biology
   2. Historical Context
      1. Early Developments in Geometry Algorithms
      2. Milestones in Computational Geometry
      3. Key Figures and Contributions
      4. Evolution of the Field
   3. Fundamental Challenges
      1. Numerical Precision Issues
      2. Degeneracy Handling
      3. Algorithmic Efficiency
      4. Robustness Requirements