3D Printing and Illustrating Mathematics

Transcription

1 3D Printing and Illustrating Mathematics Elizabeth Denne dennee/math_vis.html Washington & Lee University Women s Intellectual Network Research Symposium, UVA September 15, 2018.

2 Outline Introduction Designing models Calculus II 3D design and printing tips More examples

3 Introduction to Topology Fall 2014

4 Introduction Designing models Calculus II 3D design and printing tips Summer 2015 More examples

5 Taping Shape Exhibit Spring 2016 Rueben H. Fleet Science Center, San Diego California.

6 Introduction Designing models Calculus II 3D design and printing tips More examples 3D printing technologies Additive manufacture: many thin layers are joined to create solid object. 1. Fused deposition modeling [Ultimaker, uprint, Makerbot] 2. Stereolithography [FormLabs] 3. Selective laser melting [Shapeways]

7 What can be 3D printed? 3D design basics Any volume with a closed surface as its boundary. Surface: faces, vertices, edges, no holes. In practice: 1. Think about model you want to create. 2. Model it in Mathematica (maybe). 3. Import into, or design model entirely in 3D design software. 4. Export.stl file. 5. Open file in 3D printer s software, choose size, scale, supports, print quality, etc, producing a print file. 6. File is then printed by 3D printer (or not).

8 What can be 3D printed? 3D design basics Any volume with a closed surface as its boundary. Surface: faces, vertices, edges, no holes. In practice: 1. Think about model you want to create. 2. Model it in Mathematica (maybe). 3. Import into, or design model entirely in 3D design software. 4. Export.stl file. 5. Open file in 3D printer s software, choose size, scale, supports, print quality, etc, producing a print file. 6. File is then printed by 3D printer (or not).

9 3D design basics Expect failure! Iterative process. 3D design of model is flawed. Printing supports not in the right place. Object is too small, too thin. 3D printer fails. Software: Mathematica, Maple (both $). TinkerCAD, OpenSCAD (both free). Cinema4D ($), Rhinoceros ($), Blender (free). Meshlab, TopMod, Grasshopper, others.

10 Resources Math & 3D printing people Laura Taalman (JMU) Henry Segerman (UOklahoma) David Bachman (Pitzer) dbachman/ Jason Cantarella (UGA) Platforms Thingiverse: Shapeways:

11 3D printing in the classroom 1. Make manipulatives and visualizations. Volumes by slices, quadratic surfaces, etc 2. Students design and 3D print objects. How much course time is dedicated to this? Use 3D printing as an add-on project. Build a course around 3D printing. Do you need a 3D printer? Buy own printer. Requires, money, space, maintenance, but fast(ish) turnaround time. Use an online service (eg. Shapeways.com). No startup cost but more expensive per print, higher quality, more design freedom.

12 Set up at W&L IQ (Integrative and Quantitative) Center in Science Center. Stereo 3D lab, Physical/Mechanical Lab, Computer Visualization Lab. Microscopes, high speed cameras, and other toys. 3D printing: FormLabs Form 1+ printer. ProJect 260-3D Systems. Ultimaker 3, uprint SE, Series 1 Pro, Makerbot 2X. Secret weapon: Dave Pfaff.

13 Introduction Designing models Calculus II 3D design and printing tips Volumes by slices More examples

14 Class Project Calculus II students were asked to: work in groups of 2-3 people, learn the basics of Cinema 4D, use Cinema 4D to model the slices of two different volumes for 3D printing, create a technical report summarizing their results. Tips: one class spent on learning the program, two classes spent on the math, 3D design, and writing. IQ center printed the models the class made.

15 Cinema 4D

16 C4D menus Top menu: Undo, Redo, Live Selection. Then Tools which allow objects to be moved, scaled and rotated. Side menu: Make Editable, Model Mode. Then Point, Edge and Polygon Modes. Object Creation buttons

17 Add cylinder Left click on Cube. Select Cylinder.

18 Add cylinder

19 Edit cylinder Attribute Manager: Change Radius to 5cm. Change Height to 1 cm. Zoom in.

20 Edit cylinder Object Manager: Delete Phong Tag (two small brown circles). Actual cylinder.

21 Edit cylinder Attribute Manager: Change Rotation Segments to something between 60 and 120. Actual cylinder.

22 Edit cylinder Coordinate Manager: Shift cylinder up 0.5cm (to lie flat on xz-plane). Click on Make Editable button.

23 Finished cylinder

24 Add cylinders

25 Join cylinders together Select all the cylinders. Go to Mesh Conversion Connect Objects + Delete.

26 Completed cylinder

27 What s inside View of middle and top slice from inside model. Horizontal wall still present. Use a different technique to join (overlapping) cylinders to prevent this (uses the Boole tool and union).

28 Design and Printing tips Check normal vectors, and optimize. Think about the number of approximating segments. No gaps or overlapping parts of the design. Objects must be thick enough to print! More supports, or a different orientation may work better.

29 A tough print We had many fails before we figured out how to print the frame!

30 Introduction Designing models Calculus II 3D design and printing tips Schwarz P surface and frame... More examples

31 Multivariable Calculus Some were designed in Mathematica, then imported into Cinema4D. Add equations. Find appropriate font. Thicken equations. Use Bend tool and Boole tool to add equations.

32 Teaching Integrals

33 Yet more...

34 Topological Objects

35 Knots Laura Taalman s collection of trefoil knots.

36 Thank you Dave Pfaff & the IQ center at W&L. Emily Jaekle ( 16) & Ryan McDonnell ( 17). My Fall 2014 Introduction to Topology class. My Fall 2016 Calculus II classes.