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How to 3D print your Christmas tree with minimal waste

16 December 2014

Just in time for Christmas, a Canadian researcher shows us how to 3D print a christmas tree using a special algorithm that minimises material waste.

Simon Fraser University computing science professor Richard Zhang knows how to print a 3D Christmas tree efficiently and with zero material waste, using what he claims is the world’s first algorithm for automatically decomposing a 3D object into what are called 'pyramidal' parts.

Zhang, a computer graphics expert specialising in geometric modelling and processing, developed the algorithm with PhD candidate Ruizhen Hu, an international student from Zhejiang University in China.

A pyramidal part has a flat base with the remainder of the shape forming upwards over the base with no overhangs, much like a pyramid. A pyramidal shape is optimal for 3D printing because it incurs no material waste and saves print time.

Christmas trees aside, the algorithm could become a big deal in the world of 3D printing, where it offers interesting potential for the design of moulds.

In 3D printing, the printer deposits melted plastic layer by layer in a bottom-up fashion. If the shape has an overhang, such as a tree branch, extra material has to be printed beneath it as support.

This extra plastic is waste material and must be removed, which can be time consuming and difficult. And removing waste material that supports an object’s hollow interior or tiny fragile parts, like the star atop a Christmas tree, can be almost impossible without causing breakage.

"Coming up with a practical algorithm to decompose 3D objects into the smallest possible number of pyramidal parts was quite a challenge,” says Zhang. “Importantly, it is impractical for most real-world objects to be broken into exactly pyramidal parts since this would result in too many parts. Ruizhen came up with a really clever way of transforming the problem to obtain an effective solution.”

The new algorithm partitions the object into a small number of nearly pyramidal parts that can be 3D-printed with little or no material waste. These printed parts can then be glued together to form the finished object. The Christmas tree, for example, is divided in half for fabrication, and then glued together. In moulding and casting, the ideas are similar.

“If the moulded or cast parts are pyramidal, then removing the mould or cast after fabrication would not result in any breakage,” Zhang adds.

In keeping with the Christmas theme, he suggests chocolatiers might use the algorithm to design chocolate moulds for Christmas trees or reindeer.

Assuming you won't actually be 3D printing Christmas trees in the run-up to the holidays, all of us at DPA nonetheless wish all of you a very enjoyable and peaceful Christmas and a happy New Year!

Les Hunt

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