# Online Handwriting Recognition Method with a Non-Inertial Reference Frame Based on the Measurement of Linear Accelerations and Differential Geometry: An Alternative to Quaternions

## TL;DR

This paper introduces a new handwriting recognition method using a pencil-mounted sensor and non-inertial reference frames, avoiding the need for a flat surface.

## Contribution

A novel handwriting recognition system using linear acceleration and differential geometry instead of quaternions.

## Key findings

- The system successfully reconstructs handwriting traces using curved lines and shapes.
- The non-inertial reference frame approach provides an alternative to quaternions for orientation problems.
- The method works without requiring a specific reference surface.

## Abstract

This work describes a mathematical model for handwriting devices without a specific reference surface (SRS). The research was carried out on two hypotheses: the first considers possible circular segments that could be made during execution for the reconstruction of the trace, and the second is the combination of lines and circles. The proposed system has no flat reference surface, since the sensor is inside the pencil that describes the trace, not on the surface as in tablets or cell phones. An inertial sensor was used for the measurements, in this case, a commercial Micro-Electro Mechanical sensor of linear acceleration. The tracking device is an IMU sensor and a processing card that allows inertial measurements of the pen during on-the-fly tracing. It is essential to highlight that the system has a non-inertial reference frame. Comparing the two proposed models shows that it is possible to construct shapes from curved lines and that the patterns obtained are similar to what is recognized; this method provides an alternative to quaternion calculus for poorly specified orientation problems.