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Beginners Interactive NetLogo Dictionary

User Manuals:
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Spanish # 3D Solids If you download the NetLogo application, this model is included. You can also Try running it in NetLogo Web

## WHAT IS IT?

This model creates 3D shapes out of 2D turtles by mapping turtles between cartesian and spherical three-dimensional coordinates.

## HOW IT WORKS

To create the 3D shapes the program randomly generates turtles about the shell of the shape in either cartesian (x, y, z) or spherical (theta, phi, z) coordinates, depending on which is easier to accomplish but always stores the information converting when necessary in spherical coordinates. To render the sphere in the NetLogo view, it translates the turtles from spherical to cartesian coordinates using color to simulate depth. The positions of the turtles are always stored as spherical coordinates because they are rotated on the z-axis, and the simplest way to do so is to increase theta in spherical coordinates.

Converting from cartesian to spherical coordinates:

>x = r * cos(theta) = p * sin(phi) * cos(theta) >y = r * sin(theta) = p * sin(phi) * sin(theta) >z = p * cos(theta)

theta: angle of the turtle's projection on the x-y plane. phi: turtles angle of incidence to the z axis. p: distance of the turtle from the origin.

## HOW TO USE IT

Click the different setup-SHAPE buttons to generate different 3D shapes. The turtles are randomly distributed about the surface of the shape. Click the go (forever) button to run the model.

GO starts rotating the model.

COLOR determines the color that is used to simulate depth in generating the various shapes (uses predefined NetLogo color constants).

NUM-TURTLES determines the number of turtles that are used to generate the various shapes.

SHAPE-SIZE determines the overall size of the shape. Most often it is radius or edge length.

THETA-VELOCITY determines the speed at which the turtles are rotated.

(Rotating turtles in the rotate-turtles procedure is implemented simply by increasing each turtle's theta variable by theta-velocity! Rotating turtles (around the z-axis) is easy in spherical coordinates. However it's far easier to transpose turtles in cartesian coordinates.)

## THINGS TO NOTICE

Notice that turtles closer (positive) on the y-axis appear lighter in shade and turtles further away (negative) appear darker in shade.

## THINGS TO TRY

Try adjusting the theta-vel or render-color slider as the model is running. This will provide real time feedback to your adjustments.

## EXTENDING THE MODEL

[EASY] Adjust the `setup-square` procedure to generate a rectangle.

Create a procedure to transpose turtle coordinates. Remember that it is easier to transpose in cartesian coordinates.

Create a procedure to generate new 3D geometries.

Try animating the phi variable. Conceptually why does this not make sense?

Create a procedure to rotate the geometries on a different axis.

[VERY DIFFICULT] Create a procedure to view the geometries at ANY angle instead of the present three.

## NETLOGO FEATURES

Notice the use of `scale-color` to show the depth of turtles and thereby simulate 3D.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

Please cite the NetLogo software as: 