ECS 178 INTRODUCTION TO GEOMETRIC
MODELING (4) I
Lecture: 3 hours
Discussion: 1 hour
Prerequisites: Course ECS
175
Grading: Letter; projects (50%), midterm (20%), final
(30%)
Catalog Description:
Interactive graphics techniques for defining and manipulating
geometrical shapes used in computer animation, car body design, aircraft
design, and architectural design.
Expanded Course Description:
- Basic Theory of Curves and Surfaces
- Mathematical representation of shapes
- Parametric representation of curves and surfaces
- Evaluation of geometrical characteristics
- Interpolation Methods
- Lagrange and Hermite interpolation
- B) Ferguson and Coons surface patches
- Theory of Splines
- Spline functions
- Natural splines
- Generation of spline curves and surfaces
- Approximation Methods for Curves and Surfaces
- Bernstein-Bezier Approximation
- B-spline curves and surfaces
- Rational polynomial curves and surfaces
- NURBS (Non Uniform Rational B-splines)
- Generalized Surface Schemes
- Generalized surface schemes (e.g. triangular patches)
- Surface interrogation
- Scattered data interpolation
- Applications of Geometric Modeling
- Grid generation applications
- Computer graphics applications
- Scientific visualization applications
Textbook:
G. Farin, Curves and Surfaces for CAGD: A Practical Guide, Morgan
Kaufman, 2002
Computer Usage:
The three to five programming projects that are assigned in this
course are meant to be used as modules of an interactive curve and surface
modeling system.
- Curve Modeling Techniques
The student has to implement various curve interpolation and approximation
techniques that allow the interactive specification of three-dimentional
curves (e.g. Bezier, B-spline, rational curves).
- Surface Modeling Techniques
The student has to implement various surface interpolation and approximation
techniques that allow the interactive specification of three-dimentional
surfaces (e.g. Bezier, B-spline, rational surfaces).
- Simple, 3D Modeling System
The curve and surface modules are to be integrated into a single system
that allows the user to interactively design and store simple, 3D geometries.
The projects are to be done in a graphics workstation environment.
Engineering Design Statement:
The main purpose of this course is to have to use the theoretical insight
gained through the lectures for development of a simple, interactive
system that allows the modeling of curves and surfaces. The student will
be allowed to fully utilize graphics libraries supported by the individual
workstation chosen for the projects, the main goal is the design and
implementation of user-friendly interfaces and techniques needed for
the easy definition and manipulation of geometries in three dimensions.
ABET Category Content:
Engineering Science: 2 units
Engineering Design: 2 units
Goals:
Students will:
- Learn about different parametric curve and surface schemes.
- Understand the (dis) advantages of different geometry representations.
- Gain practical experience by implementing several CAGD techniques and
developing user interfaces.
- Obtain ability to apply CAGD methods to practical applications.
Student Outcomes:
- An ability to apply knowledge of mathematics, science, and engineering
- An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability
- An ability to identify, formulate, and solve engineering problems
- The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental, and societal context
- A recognition of the need for, and an ability to engage in life-long learning
- A knowledge of contemporary issues
- An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice
Instructors: B.
Hamann, K. Joy, N. Max
Prepared by: B. Hamann, K. Joy (Feb 1997)
Overlap Statement:
This course does not duplicate any existing course.
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