# How to Create a Solid of Revolution?

I would like to create a solid of revolution but do not know how to do it.

Some background:

(Solids of revolution are a topic usually covered in Calculus 100, first year university.)

A right cone can be considered a solid of revolution
created by revolving the straight line, say, y = 100 - 1.272x around the y axis.

In Sketchup, a right cone can be created easily enough.

I would now like to generalize to other curves that get revolved around the y axis. As a first step, say that instead of a straight line, I have a parabola that gets revolved: y = 100 - 1.272x^2

How do I do this in Sketchup?

Draw a parabola and close the loop to make a face. Use a circle drawn on the center line as a path for Follow Me.

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Thank-you!

A short follow-up question: How do I create a corkscrew-style arrow above the axis to indicate the revolution around the axis?

Why would it be a corkscrew? The path of rotation is circular, not helical.

-Gully

Gully has a good question.

If you want a circular arrow, you could start with the circle drawn for the Follow Me path and flesh it out to make a circle. If you want a helical arrow, you could draw a helix and use it for a Follow Me path. The Helix tool in the Curvemaker extension makes the helix easy and Enerothâ€™s Upright extruder will give you the expected results for the Follow Me operation. Both are available in the Extension Warehouse.

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Maybe something like this?

Iâ€™ve attached the component file â€¦ maybe you can import it and scale it to fit your needs?

circular_arrow.skp (73.4 KB)

It may take more than one frame to fully convey the concept of Surface of Revolution:

-Gully

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I am coming back around to this after having spent a lot of time on the math and writing. I created a parabola using the plug-in â€śjimhami42â€ť posted in another thread in these forums; However, I canâ€™t figure out how to close the loop to create a face so that the Follow Me tool can be used. How is this done?

Hi DavidB. Try drawing a line connecting the two endpoints of the parabola and it should form a single face (provided the parabola in on one plane).

As I showed in my screen shot and as SJS66 wrote above, join the ends of the parabola with a lineâ€¦

It seemed pretty straightforward.
I am using SketchUp 2015, if that is relevant.
Attached is an image of what I did.

1. Created a parabola and closed it (?) by drawing a line from one point to the other.
2. Drew a circle perpendicular to the parabola, to serve as the Follow Me path.
3. Selected the perimeter of the circle.
4. Clicked the Follow Me button.
5. Clicked on the face of the parabola.
6. Nothing happens. Is the face not being recognized as a Face? Perhaps it is not closed properly (hence my question.) In any case, I do not know what I am overlooking.

(And how do I get rid of that guy in the picture?)

Select him and hit delete.
There is no face on your parabola so it canâ€™t work, that suggests its not flat.
Can you attach the model so we can look.

The parabola is created inside a group â€¦ you will need to explode it first â€¦ then connect the ends.

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Thanks, Jim.

Your video was very helpful. I found and installed the PolyGen extension.It is a big help.

A couple more questions and then I should be done with this part of my task, and can move back into my math/writing/programming work.

At about 0:46 of the video, you select the outer surface of the paraboloid and then the mouse goes off-screen, so I canâ€™t see what was done. At 0:49 of the video, the concentric circles of the paraboloid are gone, and so is the circle that was created to use with Follow Me. What did you do there?

Also, looking ahead, I am planning to repeat this process with an exponential Solid of Revolution instead of a parabola. I am not familiar with Ruby, but I assume the natural exponential function and the natural log function can be used in PolyGen with the syntax Math.exp[u] and Math.ln[u], respectively. Is this correct?

After selecting all the faces, I used the â€śSoften Edgesâ€ť function which can also be accessed by right-clicking on the selected faces and selecting â€śSoften/Smooth Edges.â€ť Keep in mind, that this doesnâ€™t change the facets in the geometry, but renders them to look smooth. The hole at the origin is the result of the facets being too small to create. You will find many tips on scaling the geometry up 10x or 100x before creating the surface of revolution. I didnâ€™t find a Math.ln(u) function, but using Math.log(u) I get this:

Note that using Math.log(0) causes SketchUp to misbehave, so I started at 0.001 instead.

[edited] The natural logarithm function is actually Math.log(u), not Math.log2(u) as I previously stated (now corrected).

BTW, U-V Polygen was originally designed for surfaces. If you use something like the values shown below, you can create almost any parametric surface:

Thank-you very much. I think the graphics are now all finished, and I have taken my latest blog post (address in Profile) out of draft mode. A few more small edits may be done to the math, but the bulk of the post is finished.

poor Sketchup

Hi All,
Very excited to see the above. Iâ€™m a math teacher too and want kids to design a surface (region) and rotate it around an axis to form a solid. Had been working with Inventor but the program was so difficult to use and for other reasons was not ideal. Iâ€™ve had some success with the above. I (and the kids) have created their regions using UV PolyGen. Weâ€™ve had a little trouble closing the loop but not as much as with Inventor. My problem is that there is often a hole in the solid after using the Follow Me tool. One student made a Christmas tree and after Following Me around the circle there was a 1/10" hole in his tree. Others make goblets which worked well but ended up with a hole in the bowl and pieces of the stem missing. Any help would be welcome. Thanks.

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Work at a larger scale to avoid the holes.