Implicits and Fields

nTopology’s approach to modeling geometry is based on the implicit field technology, which makes it possible to reliably perform modeling operations without ever breaking the geometry. It enables increased design complexity and automation without adding much to the file size. To take advantage of this powerful technology, we need to understand the world of implicits and learn to work with them.

Since implicit geometries are very closely tied with fields, let’s start by understanding what a field is. If we think about weather information such as temperature, humidity, and wind speed, these are continuous and everywhere. If we probe the values at different locations, we can sample the temperature or humidity at those points. This is a field. Similarly, fields can also represent different types of data, such as stress, velocity, or distance. All this can be used alone or combined together to enhance our implicit geometry for optimal performance.

What drives the geometry in nTopology is the distance field, where at every point in all directions in the infinite 3D space, there is a distance value that describes how far away that point is from the boundary of the geometry. These values are the outputs of the mathematical equation that describes that geometry, and we use the term implicit to mean that the values of this distance field are negative where it is inside a solid body and positive where it is outside of this body. So, an implicit field is defined as a scalar field that describes a shape by the non-positive value of a field, and an implicit body is simply defined as a three-dimensional geometry represented by an implicit field.

There’s a tool inside the software for visualizing and probing the values of the field of every implicit body. This is called the Field Viewer. It allows us to see the section view of the field at a plane, like a window that lets us look into what is continuous in the 3D space. The two different color gradients distinguish the positive and the negative areas. Simple elements like planes and points have simple fields associated with them as well. For example, along the plane, the value of the field is zero. To one side of the plane, the values are entirely positive, and to the other side, the values are entirely negative.