Pimp your IKEA LAMPAN with Inkscape

You can easily pimp your IKEA LAMPAN by adding a paper cutting inside:

The Math

First we have to do some math. The lampshade is a geometric shape, a truncated cone.

The pattern is part of a circular ring, i.e. a circular sector from which a second sector is cut out:

The theorem of Pythagoras gives m = √h²+(R-r)² and from the theorem of rays we get the equation R/r = M/(M-m). Thus: M = m-R/(R-r) applies. The sketch also shows: 2R-π = 2M-π-(α/α) and from this follows α = 2π-R/M - that is 360-R/M degrees.

With this information you can create something like this in Inkscape:

Bending a rectangular

You can now start editing. But I like it more to work on an rectangular shape. Therefore I'll add some helping lines.

I insert an additional node on the left and on the right:

Then I create a centre line as helper for the next steps and use the extension "Draw Handles":

I changed the colour to grey to make the handles more visible:

Now I can start to design lampshade as a rectangle. The height must be m and the wight R. (And I changed the colours again.)

To bend the rectangular object you have to select the object, go to "Path -> Path Effects...":

Click on the "+" and then select "Bend":

Now click on the "Edit on Canvas":

And move endpoints from the green line to the centre points of the blue object:

Now move the handles to the endpoints of the orange lines:

You can make the path effect permanent by clicking on "Path-> Object to Path" in the menu. Now it's save to remove all of the helping objects and print it out. Even cooler and less work is it to use a laser cutter. If you don't have one search for a fablab or hacker space in your town.