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Mathematical graphics
The MSRI Summer School - Reed College, July 13 - July 26, 2003
Lectures on PostScript (Bill Casselman)
NOTE: In order to view PostScript files in your browser,
you will have to configure your browser's
application so as to invoke ghostview as the application to read them:
<path-to-ghostview>/ghostview %s
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References
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Lectures
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Exercises
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Monday's exercises (.pdf)
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Monday's solutions
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Tuesday's exercises (.pdf)
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Tuesday's solutions
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Exercise 1 (src)
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Exercise 1
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Exercise 2 (src)
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Exercise 2. This is potentially
a very difficult problem, since the size of the grid
has to depend on a and b. And you don't want to
draw a huge
number of disks. The best solution comes from
the reduction theory of Karl Friedrich Gauss!
But this solution ignores the difficulties.
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Exercise 3 (src)
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Exercise 3. This constructs the Bézier curves
according to the formula for parametrized curves. This assigns the
control points with a parameter of 3.14159 .../6 = 0.5236. The one used by Java2D
is about 0.552, and looks more like a circle.
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Exercise 4 should be clear from the examples in the lecture.
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Exercise 5 (src)
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Exercise 5
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No solution provided for Exercise 6.
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Wednesday's exercises (.pdf)
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Wednesday's solutions
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Thursday's exercises (.pdf)
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Thursday's solutions
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Exercise 1. The simplest way to construct a regular tetrahedron
is by using four corners of a cube. Then scale it. Another way is
to deduce from an argument about centres of gravity that if the top is
(0,0,1) then the base is at z=-1/3. Again, it will need scaling to get
edges of length 1.
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Place an imaginary plane between the two tetrahedra.
Draw first the one on the opposite side of this plane
from the (inverse-transformed or virtual eye). This is the first use
of the technique of binary space partitioning.
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