MMAE545 Advanced CAD/CAM

 

Spring 2005, 2006, 2007, 2008, 2009

 

The ability to understand and process three-dimensional geometric information on the computer is essential in many application areas, such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering, robotics, computer vision, and computer graphics.

 

Course Description

This course covers the representation, creation and manipulation of three-dimensional geometric objects using computers, with focus on the mathematical and computational aspects. Major paradigms of geometric modeling are surveyed, including curves and surfaces, curved solids, and polyhedra. Methods for computing geometric properties such as curvatures and mass properties are discussed. Applications of geometric computing to computer graphics, computer-aided design and manufacturing, and robotics will be discussed.

 

Course Topics

1.      Introduction

o        Computer Graphics

o        OpenGL and C programming

2.      Curves

o       Hermit curve

                                                   i.      blending functions

                                                 ii.      matrix form

                                                iii.      basis conversion

o       Bezier curve

                                               iv.      Bernstein polynomial and its properties

                                                 v.      Bezier curve properties

                                               vi.      Differentiation

                                              vii.      matrix form

                                            viii.      basis conversion

                                               ix.      de Casteljau algorithm

o       B-spline curve

                                                 x.      recursive form of blending function

                                               xi.      Cox de Boor algorithm

                                              xii.      Differentiation

                                            xiii.      uniform B-spline, matrix form, and basis conversion

                                            xiv.      B-spline curve properties

o       Non-uniform rational B-spline (NURBS) curve

3.      Surfaces

o       Bilinear patch

o       Coons patch

o       Bi-cubic patch

o       Bezier surface

                                                     i.    properties

                                                   ii.    de Casteljau

                                                  iii.    tensor product

o       B-spline surface

                                                     i.    properties

                                                   ii.    Cox de Boor

                                                  iii.    tensor product

o       NURBS surface

                                                   i.      Representation of extruded surface

                                                 ii.      Representation of revolved surface

4.      Solids

o       Boundary representation

o       Constructive solid geometry

5.      Geometric properties

o       differential geometry (local properties)

                                                   i.      tangent and normal

                                                 ii.      1st and 2nd fundamental form

                                                iii.      normal curvature

                                               iv.      principal curvature

o       global properties

                                                 v.      mass properties

6.      Applications

o       Surface reconstruction

o       B-spline based shape optimization

o       Path generation in NC machining

                                             i.      Tool path resolution and accuracy

                                           ii.      Step length

                                          iii.      Path interval

                                         iv.      Isoparametric tool path generation

                                           v.      Cartesion plane based tool path generation

o       Slicing in rapid prototyping

 

Textbook

1         Lee, K., Principles of CAD/CAM/CAE, ISBN 0 -201-38036-6, Addison Wesley, 1999.

2         Zeid, I., Mastering CAD/CAM, ISBN 0-07-297681-0, McGrawHill, 2005.

3         CAGD Notes at UC Davis

 

References

1        Ari Requicha, Geometric Modeling: A First Course, University of Southern California.

2        M. Mäntylä, An Introduction to Solid Modeling. Rockville, Maryland: Computer Science Press, 1988

3        M. Mortenson, Geometric Modeling, 2nd edition, John Wiley, ISBN 0471129577, 1997

4        Farin, G., Hansford, D., The Essentials of CAGD, A.K. Peters, 2000.

5        Shah, J., Mantyla, M., Parametric and Feature-Based CAD/CAM, John Wiley and Sons, 1995

6        Gerald Farin, Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide. Morgan Kaufmann, 5th ed., ISBN 1-55860-737-4, 2002.

7        Jonathan Corney and Theodore Lim, 3D Modeling with ACIS, Saxe-Coburg Publications, ISBN 1-874672-14-8, 2001.

8        M. Hoffmann, Geometric and Solid Modeling: An Introduction. San Mateo, CA: Morgan Kaufmann, 1989.

9        Choi, B. K. and Jerard, R. B., Sculptured Surface Machining, Kluwer Academic Publishers, 1998.

10    Design Mentor and Computing with Geometry from Michigan Technical University

 

Assignments

There will be six homework assignments, two exams, and a final project.