  Implicit representations of geometry, such as occupancy fields or signed
distance fields (SDF), have recently re-gained popularity in encoding 3D solid
shape in a functional form. In this work, we introduce medial fields: a field
function derived from the medial axis transform (MAT) that makes available
information about the underlying 3D geometry that is immediately useful for a
number of downstream tasks. In particular, the medial field encodes the local
thickness of a 3D shape, and enables O(1) projection of a query point onto the
medial axis. To construct the medial field we require nothing but the SDF of
the shape itself, thus allowing its straightforward incorporation in any
application that relies on signed distance fields. Working in unison with the
O(1) surface projection supported by the SDF, the medial field opens the door
for an entirely new set of efficient, shape-aware operations on implicit
representations. We present three such applications, including a modification
to sphere tracing that renders implicit representations with better convergence
properties, a fast construction method for memory-efficient rigid-body
collision proxies, and an efficient approximation of ambient occlusion that
remains stable with respect to viewpoint variations.
