## Graffitized knot renders (2024)

This video piece is an experiment with a process that I call **graffitization**: the process of transforming geometry/images in a manner that evokes graffiti art.

In this case, the source geometry is a “Billiard knot”, a mathematical knot given by the closed trajectory of a ball that bounces within the edges of a rectangle. More complex graffiti pieces oftent consist of many intertwined loops, so a knot seems like a good starting point to capture this kind of structure.

The system starts with a polygonal representation of a billiard knot made of thick strokes, which is progressively deformed so that the strokes cover the area of an input text image and follow a set of predefined orientations. This optimization procedure is driven by a differentiable rasterizer , which allows to propagate differences in image space to the parameters that determine the stroke shape and layout. Finally these strokes are outlined so that they appear layered with randomized crossings.

The resulting outline is finally used to guide Stable Diffusion with a ControlNet. The output animations are generated by interpolating different initial noise latents for the diffusion process. I find it fun and fascinating that using ControlNet enables results that are similar to high quality 3d rendering, while the input is completely 2d.

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