Fall term
Fall term
Section 101
1:30-2:30 M W F
Buchanan A205
In the course this fall, as in previous years, I will show how mathematics and computers can be used together to produce graphics of mathematical interest. The primary programming language to be used is PostScript. It is ideal for this purpose because its imaging model uses affine geometry in a crucial manner. Towards the end of the course, elementary 3D graphics including perspective, and perhaps something about the regular solids, will be discussed. New this year: I will also allow work in Java, and will arrange weekly tutorials for those interested in it.
Towards the end of the term, students will have to propose and carry out their own projects. You can even look at a previous year's projects.
Students will be
given accounts in the Mathematics Department undergraduate
computer laboratory, and will also be able to
run GhostScript or GhostView
on PC-compatible machines or Macintoshes elsewhere.
The documentation below is in both PostScript
and PDF formats.
For reading PostScript you can use
GhostView & GhostScript if you do not
have another PostScript file browser.
For PDF files
Acrobat Reader is available from Adobe.
We have PostScript help on our local help facility If you would like to know something that isn't there, ask about it.
Chapter 2 - Elementary coordinate geometry
Chapter 3 - Evolution of a simple program
Chapter 4 - Drawing lines: conditionals and coordinates
Chapter 5 - Drawing polygons: loops in PostScript
Chapter 6 - Curves
Chapter 7 - Automatic curve drawing
Chapter 8 - Rigid transformations
Chapter 9 - Drawing in 3D
A rotated square:
The source
The picture
A program of two pages:
The source
The picture
A procedure to draw the visible parts of a line on a page
in any user coordinate system:
The source
A sample picture
The simple version of mkpath.inc
The 3d matrix manipulation file matrix3d.inc
Projection and perspective procedures as well as routines to construct surfaces are in draw3d.inc
Notes on a new version of mkpath.inc.
A better error handler than the default one that comes with Ghostscript. It is the same as the one made by Adobe, except that one line of optional output has been suppressed, in order to make it more convenient. To use this program, put (ehandler.ps) run at the beginning of a program.
Euclid's proof of I.47
The picture
Source
Remarks on solutions for the second homework
Approximating the graph of
cos(t) with Bezier curves. The picture has two pages, the
second at four times the scale
of the first. Note the different graphs drawn with different
numbers of Bezier curves: green = 2, blue = 4, black = 8.
(Of course this fine point makes the code very difficult to read.)
The picture
Simplified source
The psplot package:
gzipped (Unix)
zipped (Windows)
The tutorial applets
Pythagoras' Theorem