Distance function

In mathematics, a distance function is a function that maps points within a space onto a distance.

Metric Spaces

A metric space is a set for which distances between all members of the set are defined. A metric space is defined by a metric, also called a distance function, that defines a distance between each pair of elements of the set. In this case, the distance function maps two points onto a non-negative real number, which is 0 if both points are identical.

Function Representation

A geometric shape can be represented by a signed distance function, which maps each point in space onto the signed distance from that point to the shape's closest boundary point. Points on the boundary are mapped to 0. There are two conventions used, one where distances inside the shape are positive, and outside the shape are negative, and the other convention is the opposite of this. This representation of geometric shapes is called function representation (FRep or F-Rep).