This program can render solids of revolution, as well as export them so that they can be 3D printed.
This program supports three methods for volumes of revolution: Disc, Washer, and Shell.
Choose to rotate around the x axis or the y axis. Note: only solids of revolution that revolve about the y axis can be exported.
Resolution is the amount of cylinders per unit used to render the solid of revolution. The more cylinders used to render the solid of revolution, the better the estimation of the volume of revolution is.
The boxes labeled “from” and “to” represent the bounds of integration. For the disc and washer methods, the bounds of integration are along the axis of revolution. For the shell method, the bounds of integration are distances from the axis of revolution.
Equations have to be written in a particular way in order to correctly generate a solid of revolution. Instead of using mathematical notation, code notation must be used.
You can write the variable of integration, denoted by the function symbol in the text box. The variable of integration is different depending on the axis of revolution. You cannot write any variables that are not the variable of integration.
How to write the functions
The function must be written using code notation. Here are some examples, assuming that the variable of integration is x:
Math Notation -> Code Notation
x+5 -> x+5
x-5 -> x-5
2x -> 2*x
x/2 -> x/2
x^2 -> pow(x, 2)
ln(x) -> log(x)
e^x -> exp(x)
|x| -> abs(x)
sin(x) -> sin(x)
cos(x) -> cos(x)
sqrt(x) -> sqrt(x)
pi -> PI
When writing the functions, remember to use parentheses to make the order of operations correct.
The volume box will show the current estimate of the volume of revolution, based on the volumes of the rendered cylinders. The more cylinders (higher resolution) used to render the solid of revolution, the better the estimation of the volume of revolution is.
The color of the rendered solid of revolution can be freely changed. Note: that this has no effect on exporting or the color of any 3D prints.
The title bar is the name of the solid of revolution. If it is not left empty, the solid of revolution is added to the history queue on the right.
Use wasd to rotate the camera around the generated solid.
Use c to pull the camera further away and f to push it closer.
Use the arrow keys to move the camera up, down, left, or right. This also moves the point the camera rotates around, so I don’t necessarily recommend it.
Press r to reset the camera to its default settings.
The program tries its best to show the entire solid in frame when you press generate, but it doesn’t always succeed.
You can only export solids that revolve about the y axis.
The history queue shows all of the solids of revolution that have been generated during the current session, provided they were given a title when they were generated.
Double clicking on an item of the history queue will load the associated solid of revolution.
You can clear the history queue using the clear button at the bottom right of the queue.
Clicking the Export STL button will create a .stl file of the currently selected solid in the history queue. The name of the file will be the title of the solid.
This button works best for exporting solids generated with the disc method, and it usually works with solids generated with the washer method, too. It is not recommended to use this button to export solids generated with the shell method, especially if they have any amount of concavity.
Printing files exported with the Export STL button
Begin by sending the .stl file onto the computer with the 3D printing software.
Once the .stl file is on the computer with the 3D printing software, import it into the 3D printing software.
If there is a warning symbol next to the name of the print (this will almost certainly occur while using PrusaSlicer/Slic3r), right click it to repair the .stl file before printing it.
Since the .stl files are generated sideways, you will need to rotate them properly before printing. They are also generated with millimeter units, so resizing may be necessary.
If slicing your .stl file fills in a hole that it shouldn’t, use the Export Advanced button and follow those instructions instead. This is most likely due to your solid having concavity.
Press slice and begin the print.
Clicking the Export Advanced button will create a .zip archive of the currently selected solid in the history queue. The name of the archive will be the title of the solid. Within the archive, there will be a .stl file for each of the individual cylinders used to generate the solid.
This button is designed to export solids generated with the shell method, especially if they have any amount of concavity. It is most likely not necessary to use the button to export solids generated with the shell or washer method, but it would probably work.
Printing files exported with the Export Advanced button
Begin by sending the .zip archive to the computer with the 3D printing software.
Once the .zip archive is on the computer with the 3D printing software, extract the contents using 7zip. For some reason, the regular file explorer refuses to interact with these archives properly.
Open blender. Click file > import > STL (.stl). Select all of the files that were extracted from the .zip archive and press Import STL.
The files will be imported sideways. To fix this, press r, then x, and rotate all of the files at once until they are oriented correctly. If the files get deselected, you can reselected all of them by pressing a. Note: blender must be in Object Mode for this to work. If you aren’t in Object Mode, try pressing tab (it swaps between Object Mode and Edit Mode).
Press n to open the menu on the side of main viewer, and click on the panel labeled 3D-Print. Open the export section.
Select the destination location for your new .stl file, make sure the format is STL, then click Export. You can now close blender.
Import your new .stl file into the 3D printing software.
If there is a warning symbol next to the name of the print (this will almost certainly occur while using PrusaSlicer/Slic3r), right click it to repair the .stl file before printing it.
Since the .stl files are generated with millimeter units, resizing may be necessary.
Press slice and begin the print.
This project can’t be run on macOS, due to incompatibility between Godot 4 and macOS