  Point cloud analysis is challenging due to its unique characteristics of
unorderness, sparsity and irregularity. Prior works attempt to capture local
relationships by convolution operations or attention mechanisms, exploiting
geometric information from coordinates implicitly. These methods, however, are
insufficient to describe the explicit local geometry, e.g., curvature and
orientation. In this paper, we propose On-the-fly Point Feature Representation
(OPFR), which captures abundant geometric information explicitly through Curve
Feature Generator module. This is inspired by Point Feature Histogram (PFH)
from computer vision community. However, the utilization of vanilla PFH
encounters great difficulties when applied to large datasets and dense point
clouds, as it demands considerable time for feature generation. In contrast, we
introduce the Local Reference Constructor module, which approximates the local
coordinate systems based on triangle sets. Owing to this, our OPFR only
requires extra 1.56ms for inference (65x faster than vanilla PFH) and 0.012M
more parameters, and it can serve as a versatile plug-and-play module for
various backbones, particularly MLP-based and Transformer-based backbones
examined in this study. Additionally, we introduce the novel Hierarchical
Sampling module aimed at enhancing the quality of triangle sets, thereby
ensuring robustness of the obtained geometric features. Our proposed method
improves overall accuracy (OA) on ModelNet40 from 90.7% to 94.5% (+3.8%) for
classification, and OA on S3DIS Area-5 from 86.4% to 90.0% (+3.6%) for semantic
segmentation, respectively, building upon PointNet++ backbone. When integrated
with Point Transformer backbone, we achieve state-of-the-art results on both
tasks: 94.8% OA on ModelNet40 and 91.7% OA on S3DIS Area-5.
