November 5, 2014

Stereographic projection of line art

Filed under: Blender, Freestyle — blenderyard @ 2:54 PM

I came across an interesting blog post describing how to create lampshades using backward stereographic projection from 2D input images.  Following the detailed instructions given by the blog author, I had a few hours of fun math programming exercise in Matlab to reproduce the same visual result.  As an input 2D image I chose a variation of a Japanese traditional line art pattern called Seigaiha (青海波), here created using Freestyle in Blender.


The input image underwent a series of raster/vector image processing including black/white component labeling, contour simplification, and 2D mesh generation to obtain 3D mesh data of a spherical lampshade as a result of backward stereographic projection described in the reference document.  The 3D geometry data was then imported to Blender and rendered with Cycles.  The screen capture below shows a view port render of the imported mesh data (with the Solidify modifier applied to give physical thickness).


A top-view render below with a stronger point lamp shows a clear shadow pattern of the lampshade that nicely matches the input Seigaiha texture image.




  1. Hey, thanks for the link, and nice to see you got this working! Did you use the same method?

    Comment by jasmcole — November 6, 2014 @ 6:45 PM

    • Yes, and your description of the method was very enough to reproduce it as it was from scratch on my side, namely in Matlab using the dpsimplify and Mesh2d library as well as Blender for visualization of the projection results. It was fun to fill the missing gaps in-between the steps you’ve described so that I could obtain the working Matlab code. The whole process looked like a nicely presented puzzle. Thanks anyway for your blog post!

      Comment by blenderyard — November 7, 2014 @ 5:18 PM

  2. Very Nice Tamito good job! I cannot get the matlab code working yet. Do you want to give me a hand? If yes, please send me an email 🙂

    Comment by Naufal Lyijynen — December 28, 2015 @ 3:34 PM

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