The Art of Science: The Not-Quite-3D Christmas Tree

The tree in the center was printed with a traditional 3D printing algorithm, while the others were made with the new pyramid technique

Little plastic Christmas trees don’t really count as art, but the science and math behind this one is pretty interesting, so we’ll let the deeper questions of aesthetics and meaning slide just this once.

Computer Science researcher Richard Zhang of Canada’s Simon Fraser University printed the tree as a demonstration of a newly developed 3D printing algorithm that has potential applications far beyond seasonal tchotchkes.

Michael Byrne at Motherboard explains:

“Zhang is solving a real-life problem: saving waste. Printing an object with overhanging parts, like a tree branch, requires the deposition of extra material below to support the top part through the printing process. At the end, this material is cut away and trashed. The answer, according to Zhang, is in using pyramidal components.”

“Decomposing a complex shape into simpler primitives is one of the most fundamental geometry problems,” Zhang and his team write in a recent paper. “The main motivation is that most computation and manipulation tasks can be more efficiently executed when the shapes are simple.”

And pyramids offer an elegant solution, because, Zhang says, pyramids are 2.5D.  (I’ll give you a second to collect your brain cells from the floor)

Byrne explains:  “Two-and-a-half dimensions is a concept used in machining (and computer graphics, with a different meaning) to describe an object with no overhangs. It only has a top, and can be viewed as a projection of 2D flatness into the third dimension.”

There’s lots more info about the science and math behind the printable pyramids in Byrne’s article and in Zhang’s paper.