Signed distance function

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a> and its applications, the signed distance function or signed distance field (SDF) is the <a href="/facts/Orthogonal_distance/P0aEswE4">orthogonal distance</a> of a given point x to the <a href="/facts/Boundary_(topology)/WgdH18kp">boundary</a> of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> Ω in a <a href="/facts/Metric_space/gnBBRXtc">metric space</a> (such as the surface of a geometric shape), with the <a href="/facts/Sign_(mathematics)/z0xollg1">sign</a> determined by whether or not x is in the <a href="/facts/Interior_(topology)/5sxGnQfY">interior</a> of Ω. The <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> has positive values at points x inside Ω, it decreases in value as x approaches the boundary of Ω where the signed distance function is zero, and it takes negative values outside of Ω. However, the alternative convention is also sometimes taken instead (i.e., negative inside Ω and positive outside). The concept also sometimes goes by the name oriented distance function/field.

Signed distance function open-in-new

Signed distance function