a modal/duality modality

Delaunay Triangulating Robert Delaunay’s Eiffel Tower Paintings

Boris Delaunay was a Russian mountain climber and geometer who created the Delaunay triangulation, a way to triangulate a set of points such that “skinny” triangles are avoided as much as possible.

Robert Delaunay was a French abstract impressionist and cubist known for his unique use of color theory to depict the great symbol of French turn-of-the-century modernism, the Eiffel Tower.

I manually marked points at each intersection of color and line of two paintings, Delaunay triangulated them with Jonathan Shewchuk’s Triangle program, and colored each triangle with the color at the centroid in the original painting.

The Red Tower (La tour rouge) - Robert Delaunay, 1911 The Red Tower, Delaunay Triangulated—2017
La tour rouge—Robert Delaunay, 1911 and its Delaunay Triangulation, 2017 [source]

La Tour Eiffel - Robert Delaunay, 1922 La Tour Eiffel, Delaunay Triangulated—2017
La tour Eiffel—Robert Delaunay, 1922 and its Delaunay Triangulation, 2017 [source]

Discussion Questions

Future Work

Future work could include triangulating other artwork, 3D triangulating cubist sculpture, using the average of all enclosed colors rather than the centroid for assigning colors to polygons, and experimenting with constrained Delaunay triangulations with constraints marking the boundary of certain objects in the painting.

Process and Source Code

First, use the trailokya annotator to manually place points on an image of your choosing. Color field and cubist works are good choices to start with. You’ll end up with something like

A demonstration of the
    trailokya annotator

Then, copy the list of points and save it in a file points.json. For this next part, you will need Jupyter Python Notebook, numpy, matplotlib, and Pillow installed. You will also need to download and make Triangle, a Delaunay triangulator.

Download the trailokya.ipynb notebook and place it in the same directory as points.json and image.jpg from before. Run through the cells, making adjustments as desired, and executing the Triangle program when prompted. The last cell will write a file image-triangulated.png in the same directory.

You can also preview the notebook first. Below is the scatterplot of the points for La tour Eiffel.