Toronto, Dec 16 (IANS): Using an algorithm for automatically decomposing a three dimensional object into what are called pyramidal parts, researchers have revealed how to print a 3D Christmas tree efficiently and with zero material waste.

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.

"Coming up with a practical algorithm to decompose 3D objects into the smallest possible number of pyramidal parts was quite a challenge," said Richard Zhang, professor at Simon Fraser University in Canada.

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 a waste material and must be removed, which can be time consuming and difficult.

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.

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.

The study was published in the journal ACM Transaction on Graphics.