The new algorithm to replicate natural tessellation patterns

The new algorithm to replicate natural tessellation patterns
© iStock/vovashevchuk

Researchers have created and applied a new algorithm which simplifies the replication of natural tessellation patterns on surface meshes computationally.

The new algorithm replicates natural tessellation patterns on surface meshes using a new approach to modelling.

What are natural tessellation patterns?

A tessellation pattern is made up of geometric shapes tightly arranged to cover a surface without overlapping each other.

Examples of natural tessellation patterns can be seen on the pattern of a giraffe fur, a tortoise shell, and honeycomb.

The lead author of the work and researcher at Max Planck Institute for Informatics in Saarbrücken, Germany, Rhaleb Zayer, said: “When we look at how natural tessellation occurs in nature, the individual cells grow simultaneously, and each individual cell does not necessarily know who are its neighboring cells nor their location or coordinates.”

Cells represent the tiles that make up complex natural tessellation patterns. Zayer explained: “To capture this behavior, we need to adopt an intrinsic view of the problem and depart from the widely adopted extrinsic perspective which requires full knowledge of all individual cell interactions and locations.”

How to imitate nature

There has previously been an assumption that region boundaries in the pattern need to be separate by lines. However, the researcher have now simplified the replication of natural tessellation patterns on surface meshes by disregarding this assumption and developing a method that models the partition as a set of smooth functions layered over the surface.

The method relies mainly on modern numerical computing, multiplication and addition (known as basic sparse linear algebra kernels).

Applications of the algorithm

The authors demonstrated the results of the new algorithm using large-scale test cases beyond the capabilities of state-of-the-art. For example, they applied it to the 3D Model of the famous pilot Amelia Earhart’s flight suit, which is highly detailed and encompasses ten million facets.

Amelia Earhart’s Flight Suit with 10 000 seeds, the resulting cells are visualized in different colors. A close-up of the cell distribution (top row) and the underlying mesh (middle and bottom rows) reveals small scale geometric complexity (pocket fold, button fold) that can successfully be processed with a computationally- and memory efficient approach.) © SIGGRAPH ASIA

In future work, Zayer and his team hope to add the function of interactively editing tessellations using their framework. Potential applications of tis include 3D printing applications and modelling, for designers and architects.

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