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Constructive Solid Geometry

CONSTRUCTIVE SOLID GEOMETRY

WHAT IS A SET?

A SET is an unordered collection of unduplicated things. These things may be letters, numbers, or anything else we care to collect. The Pixar characters above are a set of characters each created on a computer. But each character is also a set constructed from geometric solids. These solids have names such as cone, cylinder, sphere, pyramid, prism, box, egg, and donut. Computer programs stretch and shrink them like rubber, glue them together, and even use them like a sculptor uses a chisel.

woodsolids

SET OPERATIONS
+ – &

Each character is modeled using 3 operations:

+ adds two or more solids together
– subtracts the shape of one solid from another solid
& overlaps sections of two or more solids

If you have ever played with a Mr. Potato Head, you know how these operations work.
Behold! Hasbro's Darth Tater with parts!

Perhaps you would like to make your own Mr. Potato Head �

However, you will earn no points for him...

DIRECTIONS — 3D DOODLE

In this assignment, you will draw, save, and post 3-dimensional doodles that you make in a CSG applet written by Indira Malik at Cornell University. Indira's CSG Applet is similar to software the Pixar folks use when they design their characters, but much simpler. (Some of you may have heard of other CSG software—such as AutoCad, Maya, and LightWave.) Still, it takes a while to become familiar with the CSG tools. To keep this assignment fun, all you need do is combine a set of objects using each of the 3 operations at least once. You have a set of 4 objects to begin with: a sphere, a cube, a cylinder, a cone, but you do not need to use all of them. Double click to place each one on the black canvas. If nothing happens, hit the Clear All button. The next trick is to move them close enough to each other so you can apply the 3 operations. Use the Translate buttons for this. Since you are viewing in 3D, you cannot be sure if the objects are close until you rotate the view using the XYZ axes tool in the lower right of the canvas. When you have 2 or more objects overlapping like you want them, it is time to Enter an Operation String. Try either a Union, a Difference, or an Intersection operation. This applet uses U for addition, M for minus, and I for intersection.

CSG

In the example above, I used this Operation String

((L1 I N1) M S1) U C1
This told the applet to Intersect (overlap) Cylinder1 with Cone1, Minus (subtract) Sphere1 from the intersection, and then add Cube1. If my string had been L1 I ((N1 M S1) U C1), the results would have been very different. After entering my Operation String, I hit the enter key to create a new object — Object O1. I copied the Operation String, and converted it into our notation like this:

((CYLINDER1 & CONE1) — SPHERE1) + CUBE1
I then enlarged my doodle (scaled it up), and rotated it to a view I liked. I copied and saved my doodle. Next, I went back to the applet, rotated my doodle to another viewpoint by dragging it around in the canvas, and repeated the copy and save process once more.

You receive 2 points for using each of the 3 operations + – &, plus 4 points for the correct operation string. If you find it easier to make 2 or 3 doodles that together include all 3 operations, then do so, but you must label each one with its operation string. Also, you do not need to post more than one view of your doodle(s).

This is only an introduction to what can be done with sets and set operators. In today's world, there are zillions of applications of set operations. 3-Dimensional characters are only one example.

Click here to open a new browser window with CSG Instructions.
Click here to open a new browser window with Indira's CSG Applet.

HOW TO SAVE YOUR DOODLE

Draw your 3D doodle in the Java applet
Rotate your doodle till you like it
Hit [Prt Scr] button on your keyboard
Open Paint program under Accessories
Select Paste from Edit menu [Ctrl+V]
Click on Rectangle tool
Draw a rectangle to select your doodle
Edit/Copy [Ctrl+C]
Click on Rectangle tool again
Image/Stretch [Ctrl+W] 1% by 1% to shrink image
Select Paste from Edit menu [Ctrl+V]
Invert Colors under Image menu [Ctrl+I]
File/Save As... a Monochrome Bitmap
File/Save As... a GIF image
Repeat steps 2 thru 14 for a different view
Read the Comment at the bottom of this page...
And attach your GIF images to a Comment.

OTHER SET NOTATIONS

We use + – & as notation for set operations, because we can type them easily on the keyboard; but they do not necessarily mean what they mean in arithmetic; nor are + – & the only notations for set operators. Here are some other standard popular notations you may see elsewhere:
UNION + v | U INTERSECTION � ^ & ∩ NEGATION — ~ ! ¬
Learn more about sets and set operations →