# BESPOKE TALK Series: Differentiating Bone Structure with Voronoi Studies

We all know that skeletal structures are the basis of numerous natural and artificial objects. They offer support and stability and can be found in everything from plants and animals to buildings and various architecture applications.

Voronoi diagrams are a powerful tool to investigate the relationship between shape and function in bone structure. By modifying the parameters used to generate the Voronoi chart, you can create a wide range of bone shapes and sizes. This makes Voronoi diagrams a perfect tool to study the relationship between shape and function in bone structure.

As a tool for pathfinding and data visualization, Voronoi charts are useful for dividing space into areas based on their distance from a particular point. There are some different algorithms for the calculation of Voronoi diagrams, but they all follow the same basic principle. First, a set of points is selected as Voronoi locations. These sites can be equally spaced, randomly spread, or based on other criteria. Then, for each site, the surrounding space is divided into cells, each cell being the space nearest to this site.

The resulting diagram is a set of cells, each cell corresponding to an individual Voronoi site. The important point to note on the Voronoi diagrams is that they are based on distance, not region. This means that the size of a cell may not correspond to the size of the zone it represents.

*Bone Structure Voronoi*

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

Voronoi diagrams can help us understand the relationship between form and function in bone structure. By varying the parameters used to generate the diagram, we can create a wide range of bone shapes and sizes. This makes Voronoi diagrams an ideal tool for studying the relationship between form and function in bone structure. There are three primary parameters that can be varied when generating a Voronoi diagram: the number of points, the distance between points, and the shape of the points. By varying these parameters, we can create a wide range of bone shapes and sizes.

#### 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

Focusing on the parametric factors that affect the Voronoi diagram, specifically in terms of scale factor, point count, and scale boundary. By understanding how these factors influence the Voronoi diagram, we can more effectively use this tool to our advantage.

There are many applications for Voronoi diagrams, ranging from telecommunications to geography. However, in order to use this tool effectively, it is important to understand how the parametric factors of scale factor, point count, and scale boundary affect the resulting diagram.

###### Scale Factor

**Definition:**

The scale factor is a measure of how much the Voronoi diagram is scaled up or down. In other words, it determines the size of the regions in the diagram. A larger scale factor will result in larger regions, while a smaller scale factor will result in smaller regions.

This factor is directly related to the distance between points in the subset. For example, if the scale factor is increased, the distance between points will also increase. This will cause the regions in the Voronoi diagram to become larger. Conversely, if the scale factor is decreased, the distance between points will also decrease. This will cause the regions in the Voronoi diagram to become smaller.

**Benefits:**
In recent years, the scale factor has become an increasingly important factor in architecture, especially in the design of Voronoi structures. There are a number of benefits to using the scale factor in the design of Voronoi structures. First, it allows for a more accurate representation of the size of the cells. This is because the scale factor can be used to adjust the size of the cells so that they are more accurately represented in the final structure. Second, the scale factor can be used to create a more uniform cell size. This is because the scale factor can be used to ensure that all of the cells are the same size.

###### Point Count

**Definition:**

The point count is a measure of how many points are in the subset. This factor will directly affect the number of regions in the Voronoi diagram. More points in the subset will result in more regions in the diagram. Fewer points in the subset will result in fewer regions in the diagram. The more points that are used, the more accurate the diagram will be. However, using more points will also make the diagram more complex and difficult to interpret. Therefore, it is important to strike a balance between accuracy and interpretability when choosing the point count.

**Benefits:**
There are a few reasons why point count is used in Voronoi architecture. First, it is relatively simple to implement. Second, it is relatively fast, especially compared to other methods that might be used for estimating point counts. Finally, it is often accurate enough for many applications, as mentioned previously. One potential drawback of using point count is that it can be biased if the points are not uniformly distributed. However, this is usually not a problem in practice, as the points are typically generated by a random process.

###### Scale Boundary

**Definition:**

The scale boundary is a measure of how close the points in the subset can be to the edges of the plane. This factor will directly affect the shape of the regions in the Voronoi diagram. Points that are closer to the edges of the plane will result in regions with a more irregular shape. Points that are further from the edges of the plane will result in regions with a more regular shape. The scale boundary is also the largest distance between any two points in the data set. This distance is used to determine the size of the Voronoi cells. If the scale boundary is large, then the cells will be large as well. Conversely, if the scale boundary is small, then the cells will be small. Therefore, the scale boundary can be used to control the level of detail in the Voronoi diagram.

**Benefits:**
The scale boundary is an important aspect of Voronoi architecture. It helps to control the level of detail that is seen in the final product. Voronoi architecture is often used in urban planning. This is because it can help to create a more efficient use of space. It can also help to create a more ordered space.

In conclusion, Voronoi diagrams are a powerful tool for exploring the relationship between shape and function in bone structure. By modifying the settings used to generate the Voronoi chart, it is possible to create a wide range of bone shapes and sizes. This makes Voronoi diagrams an ideal tool to study the relation between shape and function in bone structure.

The shape of a bone structure may be influenced by numerous parametric factors. By understanding how these factors work, we are better able to tailor the shape of the bone structure to our architectural needs.

Ar. Neil John Bersabe

**Lead Architect**

John Michael Jalandra

**Content Writer**

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