If you haven't yet bought a Christmas tree yet, you may have left it a bit late. But don't despair: there's still time to print one. And a new 3D printer algorithm that claims to provide super-efficient 3D printing of Christmas trees with zero material waste may be just the ticket. Using a system of printing entitled "Approximate Pyramidal Shape Decomposition," the algorithm also promises a way to produce accurate molds for casting chocolate Santas and reindeer too.

Computer science professor Richard Zhang from Simon Fraser University, in conjunction with visiting PhD candidate Ruizhen Hu from Zhejiang University, China, lay claim to having developed the world’s first algorithm for decomposing a 3D object into what are known as pyramidal parts.

Pyramidal parts look just like they sound; they have a flat base and triangular sides that rise up to meet at a point, resulting in a shape with no overhanging parts. This shape is apparently the optimal building block for 3D printing because it wastes no material in its creation and also saves print time.

In practice, this all makes a difference in the way a 3D part is printed. This is because in conventional 3D printing, the printer creates each layer from deposited melted plastic from the bottom-up. This means that any shape that has overhanging parts, such as the tree branch in our Christmas tree example, must also have printed all of the supporting material for that part. After all the printing is finished, all of the supporting plastic then has to be cut away, which is both a waste of time and material.

In addition, taking away all of the material required for support of hollow or delicate parts can also result in breakage or loss of the part, further wasting material, time, and money. This all means that a 3D printing method that creates objects without additional support also has to create structures that are self-supporting as they are laid down, which is where pyramidal printing comes to the fore.

"Coming up with a practical algorithm to decompose 3D objects into the smallest possible number of pyramidal parts was quite a challenge," revealed Professor Zhang. In practice, however, not all objects can be broken down into pyramidal components, and the researchers are well aware of this fact.

"Importantly, it is impractical for most real-world objects to be broken into exactly pyramidal parts since this would result in too many parts," said Zhang. "Ruizhen came up with a really clever way of transforming the problem to obtain an effective solution."

In essence, they simply divided the object to be printed into two halves and then glued them together after they were made. The team points out that the algorithm-produced parts are superior in efficiency to waste proportions over human-chosen material removal by some 67.7 percent.

While not perfect, in tested situations where no human user was able to obtain the optimal part count with certain shapes, the algorithm was close to perfect every time.

Apart from 3D printing directly-created objects, the algorithm also provides a possible improvement in the areas of mold making and casting. Because molds are often required to have quite substantial supporting structures for thin or fragile elements of an object, removing them after casting may result in broken parts. According to the researchers, pyramidal construction would remove the need for such support elements.

"If the molded or cast parts are pyramidal, then removing the mold or cast after fabrication would not result in any breakage," said Zhang.

Which, of course, would be great news for preserving the antlers on molded chocolate reindeer or protecting the fine detail on a cast confectionery Santa.

No announcement has been made to any commercial release of the algorithm and software, but a good deal of modelling information for replicating the 3D process can be obtained from the research paper presented to the SIGGRAPH Asia 2014 conference.

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