Dec 11, 2014 | By Simon

In most cases, if you were to 3D print a plastic christmas tree using an FDM method, the end result wouldn't look too much like an actual tree; it would probably more closely resemble a box residing underneath the christmas tree.

Aiming to eliminate the need for these 'boxed' support structures when 3D printing a model such as the aforementioned christmas tree, **Simon Fraser University** Computer Science professor Richard Zhang and PhD candidate Ruizhen Hu have developed a new method for automatically decomposing a 3D object into pyramidal parts.

The method, which employs an algorithm developed by Hu, generates 3D objects into pyramidal parts that feature a flat base and build upwards into a pyramid-like shape...ultimately using the subsequent layers of material to support itself without the need for excess support material.

The result is a system that can break apart a 3D object into pyramidal parts that, while there is some post-print assembly required, reduces material usage and can drastically speed up print times.

Operating as a formula that breaks apart 3D objects into pyramidal structures, the algorithm intelligently divides an object into components that can be printed from their widest side to their narrowest side...essentially using the parts themselves as their own support structures.

According to Hu's **published research paper** on the project, "The goal of exact pyramidal decomposition is to find a decomposition of a 2D or 3D shape with the minimum number of pyramidal parts. This is known to be a hard problem. Fekete and Mitchell [2001] proved that both the 3D version of the problem and the 2D version on polygons with holes are NP-hard. It was suspected that on simple polygons, the problem might be polynomial."

As for the construction of the algorithm itself, Hu adds:

"Given an input shape S, we start by a uniform point sampling of its interior, then progressively build increasingly larger atomic solid primitives towards candidate pyramidal parts. Accordingly, our analysis starts locally and becomes more global as the clustering progresses."

Certainly, finding the absolute ideal decomposition of a 3D shape into pyramidal parts doesn't come easy...and neither does explaining it. What better example to give with the holidays approaching than with a festive holiday tree?

Here is the algorithm illustrated visually in the context of a christmas tree:

As seen in the Christmas tree print that Zhang holds in his left hand below, the model was broken into four components using the decomposition method starting with the tree trunk and culminating with the top body. Each of these sections were divided by the algorithm and programmed to begin printing at their widest part and finishing at their narrowest (hence the name *pyramidal*). These printed parts can then be glued together to form the original and intended 3D shape. The Christmas tree, for example, is divided in half for fabrication, and then glued together. When compared to the tree model in his left hand, it is clear just how powerful this algorithm is moving into the next generation of rapid prototyping techniques and practices.

*Photographs of some physically printed and fabricated 3D models. In each photo, from left to right, we show printed whole model, printed parts with bases lay on the ground, and the 3D model produced by gluing the parts which have been hand-painted in color. Support material is noticeable as it is printed at a lower density. Also note support material interior to some shapes, e.g., the SIGA model, which would be hard to remove.*

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

Zhangs adds that this method could prove to be an invaluable solution for those looking to use their 3D prints for casting and mold making...including molds used by chocolatiers responsible for creating some sweet boxed delights for us to put under our own christmas trees.

As for where Zhang and Hu are headed with the concept in the future, they want to simplify the decomposition process so that shapes are more easily broken down for ease-of-use:

"We would like to look into the interesting problem of "pyramidalization", which seeks a minimal way to modify a given shape to maximally reduce the size of its pyramidal decomposition, so that the shape becomes more printable, moldable, and castable."

Posted in 3D Printing Technology

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What an awesome workaround

Bogdan wrote at 12/12/2014 2:02:28 AM:

Very interesting solution, it may work for decorative 3D Printed Objects !