Signed Distance Field / Function

A function over space giving each point's distance to the nearest object surface, signed to distinguish inside from outside.

A signed distance field is a function defined over space: given any point, it returns the distance to the nearest object surface, with a sign distinguishing whether the point is inside or outside the object (robotics and graphics usually take positive outside and negative inside, though some mathematical literature uses the opposite convention); the object's surface is exactly where the function equals 0. Its gradient has magnitude 1 everywhere, and points in the direction that moves away from the surface fastest. These two properties make it useful throughout embodied AI: a simulator can query it directly for penetration depth and contact normals during collision detection; motion planning uses it to compute how far a robot is from an obstacle and which way to steer to avoid it; and 3D reconstruction and neural implicit representations often represent an object's surface as an SDF. Note that the same abbreviation SDFormat refers to Gazebo's scene-description file format, an unrelated thing.

ExampleWhen planning an arm's trajectory, first build a signed distance field for the table and obstacles, then query the SDF value at sampled points on each link; if it's below a safety margin, push the trajectory away along the gradient direction — this is how optimization-based planners like CHOMP avoid obstacles.

Also called

SDF, Signed Distance Function

Related

Truncated Signed Distance Function · Euclidean Signed Distance Field · Collision Detection · Collision Checking · Covariant Hamiltonian Optimization for Motion Planning · Implicit vs. Explicit 3D Representation

Sources

Wikipedia - Signed distance function