Circularapproximate

Circularapproximate is a term used in computational geometry and computer vision to denote a family of methods for deriving a circular representation from a set of data points. The goal is to compute a circle with a center (x0, y0) and a radius r that best approximates the observed points under a chosen error metric. Variants of circularapproximate may emphasize robustness to noise, computational efficiency, or adherence to geometric constraints such as tangency to a boundary or alignment with a known axis.

Typical workflows begin with a rough estimate of the circle parameters, followed by iterative refinement that reduces the chosen objective function. Algorithms fall into several families, including algebraic circle fits, which are fast but may be biased by point distribution, and geometric fits, which optimize actual radial distances and tend to be more accurate. Robust variants, such as RANSAC, mitigate outliers, while the Hough transform performs a global search for circular shapes in noisy data. Some implementations enforce curvature constraints or use weighted residuals to handle uneven sampling.

Applications span object recognition, quality control in manufacturing, robotics localization, and analysis of lidar or sonar data where circular features such as wheels, coins, or pipes are expected.

Limitations include sensitivity to outliers, degeneracy with arc segments or multiple circles, and the trade-off between speed and accuracy. Related topics include circle fitting, arc approximation, and methods for fitting other conic sections.