CSG

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.

 

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 Þ

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

ASSIGNMENT: 3D DOODLE

In this assignment, you will draw, save, and post 3-dimensional doodle(s) in a CSG applet. For this assignment, and future assignments, you will need the Java VM Plug-In from java.com to download applets. The Java VM Plug-In, also called Java Runtime Environment (JRE), takes less than 5 minutes to download and install via fast internet access, and less than one hour via 56K access. You may, however, already have the JRE installed. So don't do it if you can see Indira's CSG Applet.

Indira's CSG applet is similar to software the Pixar folks use when they design their characters, but much simpler. (Some of you may be familiar with similar software—such as AutoCad.) 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.

In the example above, I used this Operation String:

((L1 I N1) M S1) U C1

which means:

((CYLINDER1 & CONE1) — SPHERE1) + CUBE1

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:

I then enlarged my doodle (scaled it up), and rotated it to a view I liked. I copied and saved my doodle using Hoversnap. 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. And lastly, I uploaded and inserted both of my 3D doodles on this page in a comment. Then I labeled them— just as I previously uploaded my other doodles.

You receive 2 points for each of the 3 operations + – &, plus 1 point 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 copy the operation string for each. Also, you do not need to post more than one view of your doodle(s).

Post your 3D doodles in a comment on this page after you have created them;
then copy and save them with Hoversnap.
Copy and Insert your 3D doodles the same way you did your previous doodles.
Do NOT post any huge images on any of our wiki pages, (bigger than 15K),
or I will delete them until you have learned to crop out their empty spaces.
Make your images fit inside the comment window.
Label each doodle with its corresponding Operator String.

Warning! Don't let this assignment obsess you. Before you know it, hours may go by, and I don't want you to neglect the other assignments coming this week. 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 CSG Applet.
Click here for a CSG Video Demo.

OTHER SET NOTATIONS

Throughout this course, you will use set operations extensively. 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 popular standard notations:

UNION           +   v   |     È  

INTERSECTION    ·   ^   &     Ç  

NEGATION        —   ~   !     Ø    

REMINDER: HOW TO SAVE YOUR DOODLES USING HOVERSNAP

1. Draw your 3D doodle in the Java CSG applet
2. Rotate your doodle till you like it
3. Use HoverSnap to capture your doodle from the screen to your PC
4. Repeat steps 2 thru 4 for a different view
5. Attach your GIF images to the PIX page
6. Insert your images in a comment on this page
7. Label your doodles with YOUR Operation String

Comments:

From wHolt - 1/26/06 2:20 PM [Edit] [Delete]

— negation                     & intersection                     + union

sphere – cone                sphere & cone                   sphere + cone 

files/Pix/wHolt-minus.gif  files/Pix/wHolt-interection.gif  files/Pix/wHolt-union.gif