Digital geometry

Digital geometry is a fascinating area of study that focuses on discrete sets of points, often used to create models or images of objects in two or three dimensions. When we talk about digitizing, we mean replacing an object with a set of specific points that represent it. The images we see on TV screens, computer displays, or in newspapers are all examples of digital images.

This field is very important in computer graphics and image analysis. One of its main goals is to build accurate and efficient digital representations of objects. This can be done in different ways, such as using special algorithms like Bresenham's line algorithm or by processing real digital images.

Digital geometry also studies the properties of these point sets, like their shape and structure. It looks at how to change these digital objects into simpler or altered forms while keeping their basic characteristics. Another key part is figuring out the real-world properties of objects, such as their size or shape, from their digital images. The study also includes digital curves, surfaces, and special mathematical functions used in this space.

Digital space

A 2D digital space is like a grid that only has points at whole number positions. We can think of a picture as a function on this grid.

Digital connectivity describes how points in this space can be connected. For example, in a 2D grid, points can be connected in 4 ways (up, down, left, right) or in 8 ways (including the diagonals). These connections help us understand the shape and structure in digital images.