Thickening a Polygon Mesh for Rapid Prototyping (3D Printing)

Most shapes can now be rendered physically via 3D CAD/CAM, but the output of most 3D parametric surface plots is not buildable by 3D printers in the original raw form. This Demonstration shows the operations for generating surfaces parallel to the parametric surface, then identifying the polygon edges at the open boundary of the surface and stitching the front and reverse surface copies together with a row of polygons to form a closed polyhedral surface. The result may be exported for 3D printing.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


Polygon surfaces exported for rapid prototyping undergo a verification step to ensure that they are buildable. The object presented for 3D printing must be a closed, strictly manifold triangle mesh. This means that each edge connects exactly two polygons. Rapid prototyping machines construct replicas of 3D CAD models by laminating successive horizontal slices of the object from bottom to top. The object must produce a closed outline at every horizontal slice.
[1] I. Peterson, "Plastic Math," Science News, 140(5), 1991, pp. 72–73.
[2] M. Burns, Automated Fabrication: Improving Productivity in Manufacturing, Englewood Cliffs, NJ: Prentice Hall, 1993.
[3] A. Glassner, "Maintaining Winged-Edge Models," Graphics Gems II (J. Arvo, ed.), San Diego: Academic Press, 1991 pp. 191–201.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+