# Fast and numerically stable circle fit

arXiv: https://arxiv.org/abs/1505.03795 · HTML: https://mlsanity.com/paper/1505.03795/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2015.

## Built on by (most cited first, 2 of 2)

- [Deep Algebraic Fitting for Multiple Circle Primitives Extraction from Raw Point Clouds](https://mlsanity.com/paper/2204.00920/) (2022)
- [Optimised Least Squares Approach for Accurate Polygon and Ellipse Fitting](https://mlsanity.com/paper/2307.06528/) (2023)

## Abstract (arXiv)

We develop a new algorithm for fitting circles that does not have drawbacks commonly found in existing circle fits. Our fit achieves ultimate accuracy (to machine precision), avoids divergence, and is numerically stable even when fitting circles get arbitrary large. Lastly, our algorithm takes less than 10 iterations to converge, on average.