School of Mathematics School of Mathematics
Course 376 - Numerical Simulation of Physical Systems, Computer Aided Design 2000-01 ( JS & SS Mathematics )
Lecturer: Dr. Mike Peardon, Prof. F. Neelamkavil

Requirements/prerequisites: Some knowledge of Ordinary Differential Equations, and of Newton's Laws.

Duration: 9+11 Weeks

Number of lectures per week:
Assessment:
End-of-year Examination: The 342 and 3D4 sections are assessed separately. The overall result is the average of the results for the two sections.

Description:

Ths course consists of 342 (for Michaelmas Term) plus 3D4 for the second semester.

Course 342 --- Practical computational simulations.

# Course 342 - Practical computational simulations.

### 2000-01

Description:

The course provides a practical introduction to some numerical techniques for simulating physical systems.

• The C compiler: Using the C compiler, command line arguments, file input/output, structures, linking to libraries.

• Matrix methods: inversion, eigenvalues and eigenvectors.

• Finite difference methods: solving ODEs and PDEs.

Textbooks:
• UNIX in a Nutshell, Robbins. O'Reilly Publishing. ISBN: 1-56592-427-4.
• Practical C Programming, 3rd Edition, Oualline. O'Reilly Publishing. ISBN: 1-56592-306-5.
• Numerical Recipes in C, Press, Teukolsky, Vetterling and Flannery. Cambridge. ISBN: 0-521-43108-5. Online: http://www.nr.com/

Course 3D4 --- Computer-aided design

# Course 3D4 - Computer-aided design

### 2000-01

Description:

Design is considered to be an interactive process involving specification, synthesis, presentation, analysis, evaluation and modification. Computers are central to engineering and the design of complex machines, structures and processes relies upon modern high speed computers. Computer-Aided Design(CAD) is concerned with the provision and use of a number of carefully chosen computer-based tools and techniques intended to facilitate and possibly automate the work of the designer.

The objective of this course (3D4 followed by 4D4 next year) is to equip the students with the fundamental understanding of the major elements of CAD and related areas including design, computer graphics, geometric modelling, simulation, robotics and computer vision. The course concentrates on the bridge between theory and its practice and is a good preparation for a career that may span several specialisms.

Design process and the role of CAD
Importance of Computer Graphics

Vector and Raster Graphics
Input and output devices
New graphics technologies

Device independence
Input and output functions
Standards (Graphics, data exchanges, communications)
Graphics and Graphical User Interfaces (GUI)

4. VISUALISATION-AIDS
Raster algorithms
2D transformations (Scaling, translation, rotations), Homogeneous transformations
Composite transformations, Shearing, Reflection Window to View port transformations
Line and polygon clipping

Introduction to 3D viewing operations
Projections, View volumes and clipping in 3D
Visual realism (hidden line/surface removal, shading, etc)
Engineering applications

5. GEOMETRIC MODELLING
Parametric/non-parametric representations
Generation of curves (Splines, Bezier, NURBS, etc)
Generation of surfaces (Bezier, B-Spline, etc)

6. THREE DIMENSIONAL GRAPHICS
• The 3D pipeline
Transformations in 3D
Viewing and Projection

Phong Illumination Model