Artistic Rendering of Curves via Lattice Paths

Anton Bakker and Tom Verhoeff
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 447–450 Short Papers


We present a general technique to transform arbitrary 3D curves into more artistic solid curves. The transformation first aligns the curve to the lattice; next, it transforms the curve into a lattice path with straight line segments; finally, it rounds this path into a smooth curve again. We also show an elegant way of thickening the curve. There are various parameters to play with, such as lattice alignment, the type of lattice, and cell size of the lattice. We implemented this technique in Rhinoceros with Grasshopper, and show some examples based on closed curves.