  Qualifying the discrepancy between 3D geometric models, which could be
represented with either point clouds or triangle meshes, is a pivotal issue
with board applications. Existing methods mainly focus on directly establishing
the correspondence between two models and then aggregating point-wise distance
between corresponding points, resulting in them being either inefficient or
ineffective. In this paper, we propose DirDist, an efficient, effective,
robust, and differentiable distance metric for 3D geometry data. Specifically,
we construct DirDist based on the proposed implicit representation of 3D
models, namely directional distance field (DDF), which defines the directional
distances of 3D points to a model to capture its local surface geometry. We
then transfer the discrepancy between two 3D geometric models as the
discrepancy between their DDFs defined on an identical domain, naturally
establishing model correspondence. To demonstrate the advantage of our DirDist,
we explore various distance metric-driven 3D geometric modeling tasks,
including template surface fitting, rigid registration, non-rigid registration,
scene flow estimation and human pose optimization. Extensive experiments show
that our DirDist achieves significantly higher accuracy under all tasks. As a
generic distance metric, DirDist has the potential to advance the field of 3D
geometric modeling. The source code is available at
\url{https://github.com/rsy6318/DirDist}.
