Is the data from accelerometer and/or gyroscope sufficient enough to construct a path of movement (on a plain canvas)?
The environment is indoors, so usage of GPS data is out of question.
I've though about this topic more than once. AFAIK, there are some studies showing results using accelerometers/gyros but the calculations are complex, and to be possible it depends on the processing power / memory you have available in your project. I've then found posts about something called subpos and I see it as an alternative, you can read something here: https://hackaday.io/project/4872-subpos-positioning-system The basic idea is to have some beacons and then calculate position using wifi signals. I think that a combination of the two conceps (subpos + sensors) could be useful in a practical approach.
You can found more info in this question: Indoor Positioning System based on Gyroscope and Accelerometer