3DVinci SketchUp Projects-of-the-Month January 2010 1

Intersecting Cylinders in Google SketchUpA math professor named Debra Borkovitz, who went through in the books our GeomeTricks series, created some YouTube videos on geometry using SketchUp. The one shown below is the one that inspired this project.

This project will show how to create two intersecting cylinders, and get the solid that is created where they meet. Then you’ll try the same thing with three cylinders.

This is a great project for geometry students, or anyone who thinks 3D math is cool!

For this project, it helps to have some basic knowledge of Google SketchUp (though detailed instructions are provided). In particular, it’s important to know how to zoom, orbit, and pan the view. If you need more information on how to get started, and a description of some basic tools, please read 3DVinci’s Getting Started Guide (PDF). PC users: go to http://www.3dvinci.net/SketchUp_Intro_PC.pdf.Mac users: go to http://www.3dvinci.net/SketchUp_Intro_MAC.pdf.

Intersecting Cylinders in Google SketchUp

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Step 1: Create Two Intersecting Cylinders1. Open Google SketchUp. If your file contains a person standing on the ground near the origin, click the Eraser

tool and erase him / her.

2. Activate the Circle tool, and click the origin to place the center point. For the circumference, click anywhere along the green or red axis.

3. Activate Push/Pull, click the circle, and pull it up to create a cylinder.

Intersecting Cylinders in Google SketchUp

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4. The center of the cylinder needs to be more or less near the origin. So orbit to see the bottom of the cylinder, and use Push/Pull to pull it down, using approximately the same distance you pulled it up in the previous step (this distance does not have to be exact).

5. The origin needs to be visible, so from the main menu choose View / Face Style / X-ray, which makes all faces translucent.

6. The cylinder will be rotate-copied, but first the entire cylinder needs to be selected. So press Ctrl+A or Cmd+A, which selects everything in the model.

Intersecting Cylinders in Google SketchUp

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7. Click the Rotate tool (or press the shortcut key Q).

8. Face the front of the cylinder by choosing Camera / Standard Views / Front. When you move the protractor around in blank space, it should be green because it is lying in the red-blue plane.

9. Press and hold the Shift key, which locks the protractor in its green orientation. Keeping Shift pressed, click the origin to place the protractor on it.

10. Press the Ctrl key (PC) or Option key (Mac) to make a copy. (You don’t have to hold the Ctrl / Option key - just tap it once.) Then click anywhere to start the rotation, and move the mouse to pull out the rotated copy.

Intersecting Cylinders in Google SketchUp

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11. Keep moving the mouse until you see 90 degrees appear in the Angle field in the lower right corner of the SketchUp window. If you can’t get 90 to appear, just type it (don’t click in the Angle field, just type and the number will appear) and press Enter.

12. Choose View / Face Style / X-ray again to bring back the opaque faces.

Step 2: Get the Intersection Solid1. To paint the cylinders, click the Paint Bucket tool.

Intersecting Cylinders in Google SketchUp

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2. In the Materials window (Windows) or Colors window (Mac), find a collection of colors you like.

3. To paint one entire cylinder, choose a color, press and hold the Ctrl or Option key, and click any face of the cylinder. This paints the both flat ends plus the round face. Then choose another color and do the same for the other cylinder.

4. Now we’ll peek inside the cylinders to see if we can figure out what the intersection solid looks like. Start by using Push/Pull to bring all four cylinder ends closer to the center.

Intersecting Cylinders in Google SketchUp

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5. Then erase some of the flat ends (right-click on each circular face and choose Erase). The intersection solid will include some of the round faces from the cylinders inside.

6. To create intersection edges, use Ctrl+A or Cmd+A again to select everything. Then right-click on any selected face and choose Intersect / Intersect with Model. (Intersect Selected will also work.)

Now there are edges along the edges where the cylinders overlap.

7. Now activate the Eraser tool and click the four circles at the ends of the cylinders. The shape below is the solid intersection.

Intersecting Cylinders in Google SketchUp

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Step 3: Three CylindersNow that you know how to intersect two cylinders, we’ll try the same thing with three: one cylinder in each of the standard planes. Getting the intersection solid requires just a bit more work this time.

1. As before, create a cylinder by pulling up a circle and then down, and create a 90-degree copy of it while in Front view. This time, leaving the copied cylinder selected.

2. Switch to Top view (Camera / Standard Views / Top), and this time press Shift to lock the protractor to the blue direction while in blank space.

Intersecting Cylinders in Google SketchUp

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3. Make a 90-degree copy of the selected cylinder.

4. Turn off X-ray view and paint the three cylinders with three colors.

5. Use Intersect with Model to get the intersection edges.

Intersecting Cylinders in Google SketchUp

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6. Erase the edges of the three cylinders. This time there are a still few more pieces that need to be erased.

7. To make erasing edges easier, choose View / Hidden Geometry. This displays each small, individual edge that needs to be erased, such as the ones shown below.

8. This is how the intersection solid looks after the abov edges are erased. When hidden geometry it turned off, you should have a smooth face.

Intersecting Cylinders in Google SketchUp

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9. Keep going with hidden geometry turned on, and erase the rest of the extra edges. Don’t worry if you end up losing some small faces.

10. To replace any missing faces, just use the Line tool to trace over edges. Don’t trace over an edge that should be hidden; trace over one of the “permanent” edges along the sides. After painting and turning off hidden edges again, here’s the solid you should get:

If you try this project with your children or students, and have a fantastic intersection model you’d like to share, please let me know! I will be happy to blog about it, and/or feature it on our online forum for SketchUp and education. Contact me at bonnie@3dvinci.net. Thanks!

And if you enjoy SketchUp for 3D geometry, you’ll love 3DVinci’s GeomeTricks books. The link to these is: http://www.3dvinci.net/ccp0-catshow/GM.html. The two books shown below comprise the 3D Solids series, which show how to make all sorts of amazing solid models.