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This instructable was created at TechShop San Jose (www.TechShop.ws)
Step 1: Form Development
The first curve manipulates the length and scale, in an exponential function. The second curve manipulates the shape of the swell, in a sine function.
The number sliders then divide that form into helical strips, and subdivide those strips into planar surfaces.
"Sides" changes the number of strips, "U div" changes the number of subdivisions or facets, and "Offset Holes" changes the size of the triangular holes in the facets.
Step 2: Interlocking Tabs
"Tab Depth" extends the tabs outward from the lamp, "Tab Width" changes the shape of the tab from rectangular to trapezoidal, and "Tab Angle" changes the width of the base of the tab.
Step 3: Baking and Unrolling
Select your baked strip and click the join button (ctrl+J) to make sure all your surfaces are joined, then select Surface>Unroll Developable Surface from the Rhino dropdown menu. Select your strip, and make sure Explode=No, the hit enter.
You now have a flattened strip ready to prepare for cutting.
Step 4: Optimizing for Laser Cutting
You can go ahead and hide your baked strip (the lightbulb button) to make it easier to see your lines. You will now have solid cut lines and dashed fold lines.
Now back at the main functions at the beginning of the definition, the "Dashes" slider will change the number of dashes on your fold lines.
Once you are happy with your dashes, find the last "Group" function at the end of the definition and bake it.
There you have it. One strip ready to cut!
Step 5: Laser Cutting
If you end up using the same material I did on the same kind of laser cutter, you can use my notes on the power settings to get yourself to a good starting point.
Remember to cut the same amount of strips as the "Sides" setting used in the Grasshopper definition.
Step 6: Folding
Now you can begin to fold your tabs outwards so they face the outside when it is asembled.
Step 7: Assembly
The last strip can be difficult to attach, but it is worth the effort.
Step 8: Finished!
Be sure to take a look at the Illustrator file with 3 designs ready to cut.