Course Overview
This course focuses on creating systems for three-dimensional modeling and simulation. The discipline applies to multiple fields including CAD, CAM, CAE, robotics, computer vision, and graphics.
Primary Topics
The curriculum addresses four main areas:
1. Geometric and Topological Representation of 3D Objects
Understanding how to mathematically represent and store three-dimensional objects in computer systems, including data structures and topological relationships.
2. Curve and Surface Representation Techniques
Study of mathematical foundations for representing curves and surfaces, including parametric formulations, NURBS, and other advanced surface modeling techniques.
3. Geometric Algorithms and Operations
Implementation of algorithms for operations on curves, surfaces, and solids, including intersection, Boolean operations, and transformations.
4. Practical Applications
Real-world applications in engineering design, manufacturing, and simulation systems.
Advanced Research Topics
The course examines emerging research areas such as:
- Mesh Generation: Creating quality meshes for finite element analysis
- Shape Reconstruction: Reconstructing 3D models from scanned data
- Data Compression: Efficient storage and transmission of geometric data
- Feature-Based Modeling: High-level modeling using engineering features
- Data Conversion: Translating between different geometric representations
- Non-manifold Geometry: Handling complex topological structures
- Variational Surface Modeling: Optimization-based surface design
Course Format
Meeting Times: Mondays and Wednesdays, 3:30–5:20 PM Location: Scaife Hall 324
Teaching Team
Instructor: Professor Kenji Shimada
- Office: 314 Scaife Hall
- Email: shimada@cmu.edu
Course Philosophy
The course prepares students to develop sophisticated geometric modeling systems that underpin modern CAD, CAM, and simulation software, with emphasis on both theoretical foundations and practical implementation.