We all know that skeletal structures form the foundation of many natural and manmade items. They provide support and stability and may be found in anything from plants and animals to structures and numerous architectural uses.

Voronoi diagrams are an effective tool for investigating the link between form and function in bone structure. You may construct a broad variety of bone forms and sizes by altering the parameters used to generate the Voronoi chart. This makes Voronoi diagrams an ideal tool for studying the link between form and function in bone construction.

Voronoi charts, as a pathfinding and data visualization tool, are effective for partitioning space into regions depending on their distance from a certain point. There are many strategies for calculating Voronoi diagrams, but they all follow the same fundamental premise. First, a collection of points is chosen as Voronoi sites. These locations might be similarly spaced, randomly distributed, or depending on other factors. The surrounding area is then partitioned into cells for each site, with each cell representing the space closest to that site.

Each Voronoi site is represented by a cell in the final diagram. One crucial aspect of Voronoi diagrams is that they are distance-based rather than area-based. So, the size of a cell may not always reflect the actual size of the region it stands for.

*Bone Structure Voronoi*

**How Voronoi Diagrams Can Help Us Understand Bone Structure? **

By employing Voronoi diagrams, a more comprehensive comprehension of the correlation between form and utility in the development of bones can be attained. We may construct a variety of bone forms and sizes by altering the parameters used to build the figure. The utilization of Voronoi diagrams proves to be an exceptional instrument in the exploration of the correlation between structure and utility in the development of bones.

In the process of crafting a Voronoi diagram, one may manipulate three pivotal attributes: the quantity of points, the spacing between points, and the configuration of the points. By manipulating these factors, a plethora of bone shapes and dimensions can be produced.

#### APPLICATION OF VORONOI

In this section, we use **Voronoi diagrams** to analyze the framework of the skeletal system. We are going to study the ways in which skeletal structures are affected by factors such as population number, scale factor, and scale border conditions. Because we are familiar with these logical processes, we are able to incorporate these shapes into the design of buildings.

**Initial Setup**

Create a Point Population in a Boundary.

Make a Voronoi diagram out of the points.

Scaling the Voronoi cells to extract the edges.

Creating a mesh from the edges, then using Catmull-Clark subdivision to smooth the geometry.

Defining a crop boundary to remove edge geometries.

**Parameters**

Point Count

Scale Boundary

Member Scale Factor

Outer Scale factor

#### PARAMETRIC FACTORS

Specifically focusing on the parametric elements that influence the Voronoi diagram, such as scale factor, point count, and scale border. Understanding how these elements impact the Voronoi diagram allows us to utilize this tool more successfully.

Voronoi diagrams have a wide range of applications, from telecommunications to geography. To utilize this tool properly, however, you must first grasp how the parametric elements of scale factor, point count, and scale border impact the resultant diagram.

###### Scale Factor

**Definition:**

The scale factor indicates the degree of magnification or reduction applied to the original Voronoi diagram. In other words, it controls how big or small each zone is. With a bigger scale factor, areas will be larger, whereas with a lesser scale factor, regions will be smaller.

This variable is proportional to the number of points separating two locations in the subset. If we raise the scale factor, for instance, we likewise increase the distance between individual points. The Voronoi diagram's regions will grow as a result. When the opposite is done, reducing the scale factor shortens the distance between locations. This will result in smaller areas on the Voronoi diagram.

**Benefits:**
In recent years, scale factor has emerged as a critical consideration in building design, particularly for Voronoi structures. The scale factor has many applications in the design of Voronoi structures. First, it provides a more precise depiction of cellular size. This is because the scale factor allows for a more faithful representation of the cells in the final structure by adjusting their size. Second, a more consistent cell size can be achieved by adjusting the scale factor. That's because we can make all the cells the same size by adjusting the scale factor.

###### Point Count

**Definition:**

The point count is a count of how many points are in the subset. This element will have a direct impact on the number of regions in the Voronoi diagram. More points in the subset will result in more areas in the diagram. Fewer points in the subset equals fewer areas in the diagram.

The more points that are utilized, the more accurate the diagram will be. However, utilizing additional points will make the diagram more complicated and harder to understand. As a result, while selecting the point count, it is critical to strike a balance between accuracy and interpretability.

**Benefits:**
Point count is utilized in Voronoi architecture for a variety of reasons. For starters, it is quite easy to adopt. Second, it is rather rapid, particularly when compared to other approaches for calculating point counts. Finally, as previously said, it is often precise enough for a wide range of applications. One disadvantage of employing point count is that it might be skewed if the points are not distributed consistently. In reality, however, this is generally not an issue since the points are often created by a random process.

###### Scale Boundary

**Definition:**

The scale boundary indicates how near the points in the subset may be to the plane's edges. This element will have an immediate impact on the geometry of the regions in the Voronoi diagram. Points closer to the plane's boundaries will produce areas with a more irregular form. Points farther away from the plane's edges will produce more regular-shaped sections.

The scale boundary is also the greatest distance between any two data points. The size of the Voronoi cells is determined by this distance. If the scale border is big, the cells will also be huge. If the scale border is tiny, the cells will be small as well. As a result, the scale border in the Voronoi diagram may be utilized to adjust the amount of detail.

**Benefits:**
A crucial component of Voronoi architecture is the scale boundary. It aids in regulating the degree of detail seen in the finished output. In urban planning, voronoi architecture is often employed. This is due to the potential for more effective space use. It may also aid in making an area seem more organized.

In conclusion, Voronoi diagrams are an effective tool for investigating the link between form and function in bone structure. It is possible to construct a broad variety of bone forms and sizes by altering the parameters used to build the Voronoi chart. As a result, Voronoi diagrams are an excellent tool for investigating the relationship between form and function in bone structure.

Numerous parametric elements may alter the morphology of a bone structure. Understanding how these components interact allows us to better adjust the form of the bone structure to our architectural demands.

Ar. Neil John Bersabe

**Lead Architect**

John Michael Jalandra

**Content Writer**

**BER****SAB****ARC Design Studio 2022**

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