Quadric Surfaces with Maple

Contributed by
Kristen Schreck

Subject: Multivariable Calculus

Each student will generate a different quadric surface with Maple.  Students will present their surface, along with a description and illustration of its properties and traces, to the class.

Duration: one week

This project introduces students to the modeling component of 3D printing using the mathematics software program, Maple, to plot several quadric surfaces in both implicit form and parameterized form.  Students will learn how to export their Maple code as an STL file which can be uploaded to Cura to create a 3D print.  During this process, students will discover that some quadric surfaces can be readily printed from the STL file exported from Maple, while, for other surfaces, they will need to use some ingenuity (which may possibly involve other modeling programs) to 3D print the surface.

Students are assigned quadric surfaces from the table given in this lesson. Some quadric surfaces are given in implicit form, others are parameterized by u and v.
  • In Maple, use the implictplot3d and plot3d commands to plot your assigned surfaces. Identify the name of each surface in your Maple worksheet.  For reference, see the Maple Worksheet on Quadric Surfaces and the Maple file.

  • Create an STL file in Maple for two of your assigned surfaces.  

    Note:  You will need to use the plot3d command to generate the STL file in Maple. This means, for those surfaces defined implicitly, you will need to find a uv parameterization.

  • Obtain a 3D print of two of the quadric surfaces given in your list.

    Note: In order to print your surface, it will need to have a flat base or some type of support. This is where you will need to use some ingenuity and creativity.


Final Product:

  • The completed Maple worksheet showing the code, names, 3D plots, and “export to STL” commands for each of your quadric Surfaces.

  • Two 3D printed quadric surfaces.  Include photos and/or video taken during the printing process and of the final surfaces.

  • Write a set of detailed step-by-step instructions for printing your quadric surfaces beginning with plotting the surface in Maple all the way to 3D printing using the Ultimaker 2+.  Assume that your readers will be 3D printing a surface of this type for the very first time. Include screen shots of Maple, Cura, and photos of your surface as examples to illustrate the various steps in your instructions.  Provide any useful tips that you have discovered along the way.

  • If you successfully print your quadric surfaces and provide clear instructions, the instructor will be post your work on YouMagine.

Examples of Student’s 3D Printed Surfaces:


Schreck 3
Schreck 4



Grading Rubric:

CriteriaInstructor CommentsPoints Earned
Completed Maple worksheet
Two 3D printed quadric surfaces
Photos/video during printing process and of final 3D printed surfaces
Clear and detailed written instructions (with photos) for plotting and creating a 3D print of a quadric surface

Summary of Printing Instructions:

  1. In Maple:

    • Use plot3d and the plottools[export] commands to export the Maple code for each of your quadric surface as an STL file
    • Choose currentdir( ) with filename mysurface.stl

      to export your file to the current working directory (shown in the status bar at the bottom right of the Maple window)

  2. In Cura:

    • After opening your STL file, click on the object and select Scale to resize your object
    • In Setup choose Simple and Hollow if your surface has a hole
    • In Advanced settings under Profile choose Fast Print
    • Depending on your surface, under Shell set Top/Bottom Thickness = 0.0 mm
    • Under Platform Adhesion choose Brim or Raft
    • If necessary, Enable Support and choose Support Pattern
    • In View Mode choose Layers to calculate the printing time
    • Save your STL file to the SD card as a G-code file

  3. Using the Ultimaker 2+ Printer:

    • Insert the SD card
    • Choose Material for the filament type (PLA)
    • Choose Print and select the file to be printed
    • Note:  Be very careful!  The printer will take some time to heat up. The nozzle will reach temperatures over 200°C and the build plate will be hotter than 100°C.  Do not touch the nozzle or the build plate at any time during the printing process.