Introduction: 3D Solids Constructed From Concentric 2D Morphing Shapes

About: Artist and designer, making novel ideas tangible.
I developed this easy way to create 3D solids made from concentric 2D morphing shapes at Makerplace in San Diego, CA using their 100 watt Hurricane laser. You can cut your objects from a variety of materials, such as plywood, MDF, bamboo or acrylic. For this demonstration I'll use 1/4" thick double walled corrugated cardboard. You'll note the beauty of using concentric shapes in how little of your material is wasted.

Here's what you'll need:
• A sheet of 1/4" thick double walled corrugated cardboard. (For demonstration purposes I painted one side of my corrugated cardboard black.)
• Adobe's Illustrator or other comparable vector graphics authoring tool
• Access to a Laser cutter
• White glue and a sponge brush to apply it

Prepare the Image Files
I use Adobe's Illustrator CS4 as my vector image authoring tool. You'll want to do the equivalent in whatever tool you use.

Concentric 2D Morphing Shapes
• Create a 6.5x10" file

Step 1: Make an Oval

• Use the "Ellipse Tool" to make an oval that fill your 6.5x10" artboard

Step 2: Make a Star

• Use the "Star Tool" to make a 2" square 4 pointed star in the exact center of your artboard

Step 3: Blending Your Oval & Star

• Select All (both your star and oval) and double-click the "Blend Tool" > choose: Specified Steps >12 > OK

Step 4: Blending Magic!

Here's where the magic happens! 

• You now have a special "Blend Tool" cursor icon -- click it once on the top horizontal mid-point of the oval, then click it once on the top horizontal mid-point of the star ... and Voila! You've created 12 morphing shapes.

Step 5: Making the in Between Shapes Vector

• Select All  > Object > Expand

Step 6: Editing Shapes

• To insure each piece has enough width for assembly, delete the 3 shapes in the center and every other one moving outward until you have 6 remaining shapes.

Step 7: SAVE Files, Part 1 & 2

Save this file AS: "Concentric-2D-Morphing-Shapes_part-1-of-2"

To construct the solid object you'll need a second set of concentric shapes that offsets alternate layers of the first set. To do this simply SELECT ALL and:
• Change the width FROM 10 TO 9.7
• Change the height FROM 6.5 TO 6.2
• Save this file AS: "Concentric-2D-Morphing-Shapes_part-2-of-2"

Convert your .ai files to .plt
Adobe's Illustrator CS4 does not export a plotter .plt format, but Makerplace provides me with a copy of Corel Draw 5, which does.
• In Corel Draw 5 open the, which is saved to version 8, and simply save as .plt, or an equivalent file format that works with your laser cutter.

I have included the Adobe's Illustrator (.ai) files used for this project.

Step 8: Settings to Laser Cut Your Shapes

• Place your sheet of 1/4" thick double walled corrugated cardboard on the bed of your laser cutter and focus it for the thickness of this material
• Import your "Concentric-2D-Morphing-Shapes_part-1-of-2.plt" file
• Set your cut option. On the 100 watt laser at Makerplace, my settings were Speed: 20, Power: 90; Corner power: 55

Step 9: Laser Cut Your Shapes

• Cut and set aside.
• Repeat the above step for your "...part-2-of-2.plt" file.

Step 10: Prep for Assembly

• Place your two sets of cut shapes on your work surface backside facing up. To help with clean-up I'm using a glass surface.
• Dilute your white glue. (50% glue with 50% water)
• You will only be using the inner-most solid piece from the larger set of shapes (part-1-of-2) and you won't need to put glue on this shape, so set it aside.

Step 11: Assembly

• Brush your diluted glue onto your cardboard shapes. With so few shapes you can brush glue onto all the shapes at once. If the glue does happen to dry before you finish the assembly, you can simply reactivate it with a fresh coat of glue.
• With the glue still wet, alternately stack the outer piece of the part-2-of-2 set on top of the corresponding part-1-of-2 piece. Be careful to center each piece in place before stacking the next piece.
• When all pieces are stacked (don't forget the bottom inner-most solid piece you previously set aside) clamp or place weight on your stacked object to compress it while the glue dries.

Step 12: Voila!

That's it! When the glue has dried your 3D construction is finished. Even with such a lightweight material as corrugated cardboard, you'll be pleasantly surprised how relatively strong your assembled object is. With the combinations of shapes, sizes and proportions, the number of different 3D objects you can make with this method is endless.

Thank you Makerplace for providing the space, tools and support in developing this novel idea.
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