creative technology / new media

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print / present

argument(s) -- math

Q: What are the mathematics requirements for creative technology?

A:

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).

Nevertheless, to some extent, at least on an introductory level, topics that should be addressed are [1]:

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

It seems worthwhile to proceed from isometries in euclidean geometry, to transformations in linear algebra, via an introduction of coordinate systems.

Q: And more specifically for animation and visualisation?

A:

In summary:

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

It must be emphasized that students will generally start from an intuitive idea of a phenomenon, for which they should be able to find a more or less adequate formalism or model that embodies this intuition. In practice this might mean that they merely adapt an existing animation or visalization to fit their needs.

Q: Any special wishes for game development?

A:

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

Evidently, these may be considered a generalization of the issues treated for animation and information visualisation, extended to 3D space. However, the natural phenomena are more complex, and the computational requirements may be considered to be significantly higher.

Q: What about the (he)art of mathematics?

A:

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.

Topics from mathematics that provide a useful background include [1]:

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

Q: Would that be all?

A:

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?

In addition, some students may even express an interest for geometrical algebra [5]. Apart from being somewhat offstream, it may also be observed that these topics require perhaps a more computational than mathematical approach.

statement(s)

line(s) -- theme(s) / coffee / grind(s) / thesis /

_ .. / ... / / theme(s) / create / common(s) / art(s) / space(s) / _ / .

a mathematician is a device for turning coffee into theorems

...

blind(s) judge(s) control(s) brain(s) craft(s) closure(s)

...

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

/ science(s) / role(s) / digital(s) / flow(s) / mechanic(s)

math(s) -- resource(s) / perspective(s) / method(s) / graph(s)

_ .. / ... / common(s) / idea(s) / change(s) / topic(s) / _ / .

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

tool(s) / classic(s) / statement(s) / opinion(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]

/ flow(s) / dynamic(s) / particle(s) / game(s) / screen(s) / cycle(s)

math(s) -- media / perspective(s) / resource(s) / theme(s) /

_ .. / ... / common(s) / idea(s) / change(s) / topic(s) / _ / .

(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)

/ requirement(s) / formula(s) / game(s) / resource(s) / X / cycle(s)

reference(s) -- math

kindle

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)

tutorial(s) -- math

* _ .. -- @ media / scribble / utopia / design / fun ? [:/] _

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

experiment knowledge illusion scratch engine craft maze run ar x

* - play / story / search / flow(s) / topic(s) / cage(s) # ! @ Æ

[] readme new(s) workshop(s) project(s) CA1 CA2 CA3 CA4 CA5 course(s) - creative exploration(s) / serious games / ethic(s) - resource(s) _

# @

argument(s) -- math

Q: What are the mathematics requirements for creative technology?

A:

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Q: And more specifically for animation and visualisation?

A:

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Q: Any special wishes for game development?

A:

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Q: What about the (he)art of mathematics?

A:

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Q: Would that be all?

A:

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statement(s)

line(s) -- theme(s) / coffee / grind(s) / thesis /

_ .. / ... / / theme(s) / create / common(s) / art(s) / space(s) / _ / .

/ science(s) / role(s) / digital(s) / flow(s) / mechanic(s)

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math(s) -- resource(s) / perspective(s) / method(s) / graph(s)

_ .. / ... / common(s) / idea(s) / change(s) / topic(s) / _ / .

tool(s) / classic(s) / statement(s) / opinion(s)

/ flow(s) / dynamic(s) / particle(s) / game(s) / screen(s) / cycle(s)

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math(s) -- media / perspective(s) / resource(s) / theme(s) /

_ .. / ... / common(s) / idea(s) / change(s) / topic(s) / _ / .

/ requirement(s) / formula(s) / game(s) / resource(s) / X / cycle(s)

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reference(s) -- math

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tutorial(s) -- math

* _ .. -- @ media / scribble / utopia / design / fun ? [:/] _

* - play / story / search / flow(s) / topic(s) / cage(s) # ! @ Æ

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