Geometry for Computer Applications
Math 431 Fall 2018
Topics from projective geometry and transformation geometry,
emphasizing the two-dimensional representation of three-dimensional objects
and objects moving about in the plane and space.
The emphasis will be on formulas and algorithms of immediate
use in computer graphics, vision and robotics.
Official Course Number:
MATH 431 (Section 0101) (3 credits)
9:30 -- 10:45, Hornbake 0125
(wmg AT math.umd.edu)
3106 Math Building
(cdaly69 AT math.umd.edu)
(Linear Algebra) or MATH341 (with minimum grade C-).
Math 241 (Multivariable Calculus) and MATH246 (Differential Equations)
would also be useful.
Examinations and grading:
There will be one midterm and one final exam
(possibly replaced with final projects).
Biweekly problem sets will be assigned.
The final grade will include all assigned material as well as class
Although attendance is not mandatory,
it will be counted as class participation in determining the final grades.
There will be no required text for the course,
but I will follow the course notes,
which are evolving as I continue to develop the course.
Several other recommended references include:
Vince's recommended book is a general-purpose
reference. The last sections of Lay's book give a good
exposition of some of the basic linear algebra we discuss
at the beginning. Please let me know if you know of some
other useful books on the subject. (The literature is vast.)
Materials will be distributed and posted as they are written.
- Mathematics for Computer Graphics, Fourth Edition,
by John Vince,
Springer Undergraduate Topics in Computer Science,
- Linear Algebra and its applications, Fourth edition,
by David C. Lay, Addison Wesley, ISBN 13:978-0-321-38517-8
(1994, 1997, 2006, 2012)
- Practical Linear Algebra: A Geometry Toolbox,
by Gerald Farin and Dianne Hansford,
CRC Press, ISBN 978-1-4665-7956-9 (2014)
- Applied Geometry for Computer Graphics and CAD,
Second Edition, by Duncan Marsh, Springer Undergraduate Mathematics Series,
ISBN 2-85433-801-6 (1999,2005)
Nigel Hitchin's course notes,
available from his
An Invitation to 3D Vision: From Images to Geometric Models,
by Jana Kosecka, Yi Ma, S. Shankar Sastry, Stefano Soatto,
Springer Interdisciplinary Applied Mathematics 26,
ISBN 978-0-387-21779-6 (2004).''
- Projective geometry, both real and complex
- Conic sections and quadric surfaces
- How topology makes data types complicated
- Geometric transformations
- One-parameter groups and matrix exponentials
- Complex numbers and quaternions
- Representing lines in 3-space by Plucker coordinates