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This depends, even from a *new media* perspective,
whether the focus is on
animation, information visualisation,
game development or even more general on
an artful application of mathematics
in for example web design or interactive installation(s).

- points, vectors, planes & isometries
- linear (matrix & vector) algebra
- combinatorial and numerical algorithms

In summary:

- graph theory
- basic calculus, newtonian physics
- particle systems in 2D space

Yes, in particular the mathematics needed for
*game physics*, *dynamic lighting* and
*visual effects* [2]:

- game physics -- motion, speed, collision detection
- dynamics lighting -- normal, reflections & refractions
- natural phenomena -- waves, perturbations, explosions

There are nowadays many tools, including
the *processing.org* software, to produce
*generative art*, or more general visual patterns.
Artists speak of such methods as using
*algorithms as a paintbrush*.
However, where the methods are often used in a naive way,
is seems desirably to create algorithms that are
to some extend well-founded in mathematical theory.

- basic topology, iterated functions
- quaternions & rotations
- fractals, mandelbrot & julia sets
- lindenmayer systems -- online tutorial

Very likely, most students will find the topics treated
thus far already quite difficult.
However if we look at the area of *visual computing*,
which issues such as image processing, triangulation
and rasterization,
additional topics need to be covered, such as [3,4]:

- delaunay triangulation, voronoi diagrams
- convolution filters
- and what else?

a mathematician is a device for turning coffee into theorems

/ Erdos / idea(s) / joke(s) / perspective(s) ?

scenario(s) / a (wide) variety of perspective(s)

- we eat problems for breakfast [VU/olympiade]
- we study pattern(s) & structure(s) [UvA/mathematics]
- we grind ... coffee / game(s) for ... boy(s)/girl(s)?
- we ... love story ...? [UT/.CREATE]

- (casual) game(s) -- toss paper(s) / crayon physic(s) / color(s)
- graphic effect(s) -- tunnel / example(s) / convolution(s)
- animation(s) -- blob(s) / example(s) / eye(s) / particle(s)
- student tutorial(s) -- physics / linear math / animation(s)
- physics engine(s) -- PhysX / unity example(s) / resource(s)
- sound synthesis -- basic(s) / fm tool(s) / music pad / drum box
- generative art(s) -- nano webber / stripe(s) / bulb(s)

- Mathematics of Digital Images: Creation, Compression, Restoration, Recognition (Hardcover) by S. G. Hoggar -- (amazon)
- Mathematics for 3D Game Programming and Computer Graphics, Second Edition (Game Development Series) (Hardcover) by Eric Lengyel -- (amazon)
- Visual Computing: Geometry, Graphics, And Vision by Frank Nielsen -- (amazon)
- Geometry and Topology for Mesh Generation (Cambridge Monographs on Applied and Computational Mathematics) (Paperback) by Herbert Edelsbrunner -- amazon)
- Geometric Algebra for Computer Science -- An Object-Oriented Approach by Leo Dorst, Daniel Fontijne, Stephen Mann -- (online)

- algorithm(s) -- www.geometryalgorithms.com/algorithms.htm
- integration -- www.gaffer.org/game-physics/integration-basics
- character physics -- www.teknikus.dk/tj/gdc2001.htm
- lindenmayer -- www.biologie.uni-hamburg.de/b-online/e28_3/lsys.html
- fractal(s) -- www.people.nnov.ru/fractal

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