WHAT IS IT? ----------- This model maps turtles between cartesian and spherical 3-dimensional coordinates. To create a sphere the program randomly generates turtles about the shell of a sphere in spherical coordinates. To render the sphere in the StarLogoT graphics window it translates the turtles from spherical to cartesian 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 setup-sphere button to generate turtles randomly about the surface of a sphere. Click the go (forever) button to run the model. To generate a square click the setup-square button and click the go button. NUM-TURTLES determines the number of turtles that are used to generate the various geometries THETA-VEL determines the speed at which the turtles are rotated. (Rotating turtles in the rotate-turtles procedure is implemented simply by incrementing each turtle's theta variable by theta-vel! ROTATING turtles 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 blue white and turtles further away (negative) appear blue black. THINGS TO TRY ------------- Try moving the theta-vel slider as the model is running. This will provide real time feedback to your adjustments. EXTENDING THE MODEL ------------------- Create a procedure to transpose turtle coordinates. Remember that it is easier to transpose in cartesian coordinates. Try animating the phi variable. Conceptually why does this not make sense? Adjust the setup-square procedure to generate a hollow square. Adjust the setup-square procedure to generate a rectangle. Create a procedure to generate new 3D geometries. STARLOGOT FEATURES ------------------- Notice the use of scale-color to show the depth of turtles along the y axis.