  Most existing approaches for point cloud normal estimation aim to locally fit
a geometric surface and calculate the normal from the fitted surface. Recently,
learning-based methods have adopted a routine of predicting point-wise weights
to solve the weighted least-squares surface fitting problem. Despite achieving
remarkable progress, these methods overlook the approximation error of the
fitting problem, resulting in a less accurate fitted surface. In this paper, we
first carry out in-depth analysis of the approximation error in the surface
fitting problem. Then, in order to bridge the gap between estimated and precise
surface normals, we present two basic design principles: 1) applies the
$Z$-direction Transform to rotate local patches for a better surface fitting
with a lower approximation error; 2) models the error of the normal estimation
as a learnable term. We implement these two principles using deep neural
networks, and integrate them with the state-of-the-art (SOTA) normal estimation
methods in a plug-and-play manner. Extensive experiments verify our approaches
bring benefits to point cloud normal estimation and push the frontier of
state-of-the-art performance on both synthetic and real-world datasets.
