  Computer-Aided Design (CAD) model reconstruction from point clouds is an
important problem at the intersection of computer vision, graphics, and machine
learning; it saves the designer significant time when iterating on in-the-wild
objects. Recent advancements in this direction achieve relatively reliable
semantic segmentation but still struggle to produce an adequate topology of the
CAD model. In this work, we analyze the current state of the art for that
ill-posed task and identify shortcomings of existing methods. We propose a
hybrid analytic-neural reconstruction scheme that bridges the gap between
segmented point clouds and structured CAD models and can be readily combined
with different segmentation backbones. Moreover, to power the surface fitting
stage, we propose a novel implicit neural representation of freeform surfaces,
driving up the performance of our overall CAD reconstruction scheme. We
extensively evaluate our method on the popular ABC benchmark of CAD models and
set a new state-of-the-art for that dataset. Project page:
https://www.obukhov.ai/point2cad}{https://www.obukhov.ai/point2cad.
