Processing: Creative Coding and Computational Art

Figure 13-26. Interactive Toroid sketch (polyhedron variation)
If you haven’t yet, I suggest interacting with the toroid sketch. The four arrow keys and the
keys A, S, Z, and X can all be pressed and held down. The W and H keys can only be
pressed and released. When playing with the sketch, you might try to make some of the
following forms: a bicycle inner tube, a monster truck inner tube, a picture frame, a
sawed-off pyramid, a sphere, a shell, a star, a braid, or part of a phone cord. Toggling
between shaded and wireframe view (using the W key) makes it easier to see how the
geometry is changing.
Here’s how to make a sphere: press and hold the A key until the form stops collapsing.
Make sure that you press the W key to see the wireframe. To increase the size of the
sphere, press and hold the X key. Obviously, this is not the most efficient way to generate
a sphere, but it’s interesting to see its relationship to the toroid. A more efficient way to
generate a sphere would be to create a 180-degree arc and then lathe it 360 degrees.
This sketch brings together many of the features covered earlier in this chapter. The major
challenge was combining the point coordinate data used to generate the initial polygon
with the lathing of that data around the toroid. I used two separate arrays, vertices[] and
vertices2[], to enable me to combine the data. The initial polygon (to be lathed) was
generated with the two lines of code used to plot a polygon in the xz plane:
vertices[i].x = latheRadius + sin(radians(angle))*radius;
vertices[i].z = cos(radians(angle))*radius;
If I had plotted this initial polygon, it would have displayed only a horizontal line on the
right side of the screen, since the y values are all 0 and the z dimension of the polygon
can’t be seen in the xy plane.
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