Cylindrical Coordinates

Cylindrical coordinates specify a point in 3-D with a mix of polar coordinates and cartesian. Polar coordinates use a distance and angle measure to locate points in 2-D. Cylindrical coordinates use an additional distance measure to locate points in 3-D. For this example r and f are two polar coordinates and y is the third. We can translate from cylindrical to 3-D cartesian coordinates using r and f to determine x and z and using y as it is given.
Here is a patch that lets you play with 3-D cylindrical coordinates. The code is in the comments section. Since it uses cartesian coordinates we translate from cylindrical to cartesian as we send messages to OpenGL.

Polar Coordinates

The polar coordinate system is another way of keeping track of points on the plane. Instead of using Descartes' x and y coordinates to determine the position of a point we use r and q. The polar coordinate system is based on a line drawn from the origin of coordinates to the point. The length of this line is r. The angle between the line and the x-axis is q.
The mathematical relationship between cartesian and polar coordinates goes as follows.

x = r cos(q)
y = r sin(q)

The objects cartopol and poltocar convert between cartesian and polar coordinates. The angle is measured in radians. The code is in the comments section.
Lots of very exciting mathematics surrounds this relationship between polar and cartesian coordiantes by way of exponentials and complex numbers. One such jewel is Euler's formula.

Coordinates in OpenGL

Here is a patch that lets you play with a 3-D Cartesian coordinate system using OpenGL.
OpenGL uses Cartesian coordinates x, y, z for placement of objects, light source, viewpoint and focus point. The code is in the comments section.

Cartesian Coordinates

Coordinate systems allow us to refer to points in space using numbers. There are different kinds of coordinate systems and they can have different numbers of dimensions. A very familiar coordinate system is the 2-D Cartesian coordinate system.
In this coordinate system two numbers, x and y, specify a point in a plane. The name Cartesian comes from Descartes who is said to have "invented" the system while laying in bed sick and watching a fly crawl across the tiled ceiling.

The above 2-D Cartesian system can be expanded into a 3-D cartesian if we simply add a third dimension, z. As x determines the left/right position and y determines the up/down position the additional coordinate z determines the back/forth position.

Convolution

Convolution is one of the jewels of Fourier analysis.
It is the Fourier transform of the multiplication operator and useful in physics and signal processing.The integral equation for using the quantum mechanical propagator K reduces to a convolution if it depends only on relative differences in space and time. K=K(x-x',t-t')Here is a patch using convolution with a drifting time series and a set of different kernel functions. The output time series is the convolution of the input time series and the kernel function. Click on all of the different kernel functions to see how they change the output signal.
We are colonizing a field. Source code in comments section.

Player Participate

Gondry's film and installation at Deitch Projects, Be Kind Rewind, presents a refreshing view of culture, putting value on process and participation over product and profit. Making computer games out of ourselves, our movement vocabularies and the environments we inhabit, follows this same philosophy.

“I don’t intend nor have the pretension to teach how to make films. Quite the contrary. I intend to prove that people can enjoy their time without being part of the commercial system and serving it. Ultimately, I am hoping to create a network of creativity and communication that is guaranteed to be free and independent from any commercial institution.”-Michel Gondry

nice moves: Cavin Moore
nice music: Real Nice by Should Have Thought of That

Think Tank

Discourse is a dance. Sometimes it feels fun, sometimes dangerous. Here is the artifact from friday's think tank. We can learn from the content and form of such improvisations, improving our communications by getting rid of the bad style and keeping the good.

Click To Play

Gravity Fields

To use the force you must learn the force. Gravity is Newton's force.
Simulation is a great way to learn about gravity. So is dancing.
This is a simple physics engine for simulating a particle in a central force field. The code is in the comments section. Here is an example of what you can do with it.

Action Words

Austinian theory tells us that words don't simply describe, they can also do. In How To Do Things With Words Austin describes ways in which language is used to perform actions. For example, challenging a fiend to battle must be done explicitly and out in the open. In fact, the challenge only manifests once it has been stated. When it comes to promises, demands, vows and dedications, saying is doing.

Action heros often use performative utterances to power up. Specific language must be used in order for their super powers to manifest. The Wonder Twins must vocally "activate" before they can morph. To awaken the Eye of Thundera and assemble his team, Lion-O must yell "Thunder, Thunder, Thundercats... Ho!".

Similarly Prince Adam does not stroll around as a Master of the Universe. Only by lifting his sword and announcing "By the Power of Grayskull! I have the Power!" does Adam make himself He-Man.

The assembly of Voltron also requires these types of illocutionary acts. As the five heros incorporate their mechanical lions into a single super robot the leader calls out "Form feet and legs! Form arms and torso! And, I'll form the head!"

Here is a collection of performative utterances from the cartoon anthology Force Five. This language is mostly used for activating weaponry. Deciding what kind of cyborg super robot we will become requires a decision of what language we will use to activate our latent potentialities. Come to class on Friday ready to assemble bodies using performative speech acts.

Voltes