Contents

## About this app

In this app, you can experience Voronoi and Delaunay diagrams that are used in the field of computer graphics and simulation in 2D, 3D and spherical. In addition, by applying various algorithms to the generated diagrams, you can transform them, make holes, and create ivy-like patterns.

## How to use

### 2. Choose the dimension.

### 3. Choose the type.

### 4. Choose an operation to apply.

### Appx1. Set the number of vertices.

### Appx2. Regenerate diagram.

### Appx3. Fade out polygons

## 3 Diagrams you can Experience

### 1. Voronoi diagram.

It is often used in fracture simulation scenes because it can generate beautiful fragments. Even in nature, such patterns appear on bubbles and skeletons of microorganisms. This diagrams is a partition of a plane into regions based on closest point. In this app, it is generated by connecting the circumcenter of the Delaunay diagram.

### 2. Delaunay diagram.

Delaunay diagram triangulated so that each triangle is close to a regular triangle. It is often used in the field of computer graphics because it is a suitable triangle for calculation. In this app, it is generated by projecting a convex hull of the higher dimension. Click here for the video.

### 3. Convex hull

It is a shape that neatly wraps a set of points without dents. It is often used in physics engines because it is a shape suitable for calculation. This is the basis of the Delaunay diagram. Actually, what is called a spherical Delaunay diagram in this app is the same as a 3D convex hull. This app uses a Quickhull algorithm that can be extended to higher dimensions because projects a 4D convex hull to generate a 3D Delaunay diagram.

## 5 Algorithms you can apply

### Voronoi Relaxation

By moving the point to the centroid of the generated Voronoi diagram, the point can be spread evenly with a few calculations. This is called Voronoi Relaxation.

### A* Algorithm

If you continue to find the shortest path of any two points using the A * algorithm, you will get an ivy-like pattern.

### Constrained Delaunay Diagram

The Delaunay diagram can be constrained to pass through a given edge, which is called the Constrained Delaunay Triangulation. This algorithm can be used to create Delaunay diagrams of any shape.

### Polygon Offset

You can use Polygon Offset to shrink the polygon around where you tap to create an animation that breaks apart and disappears. Polygon offset is an algorithm that is also used in contouring.

### Boolean Operation

Boolean operations, commonly used in the field of 3D modeling, allow you to calculate the intersection of a 3D Voronoi diagram and any solid. By doing so, you can make beautiful fragments from any solid.

*Note. This algorithm removed from the app because not working well with a smartphone at this time.