CircleFit API

Circle

Represents a fitted circle characterized by position (center position of the fitted circle) and radius of the fitted circle. The field points refers to the data the model is fit to. Points are stored as a matrix (number of points, number of dimensions).

To get the coefficients one can use StatsBase.coef and coefficient names are provided by StatsBase.coefnames

Currently only in 2D.

convert the parametric form of z+Bx+Cy+D -> (x-a)²+(y-b)²-r²

Gradient weighted algebraic fit

• x: vector of x coordinates
• y: vector of y coordiantes
• p0: starting values for the fit parameters(position x, position y , radius)
• kwargs are passed to LsqFit.levenberg_marquardt

return (position x, position y , radius)

convert the parametric form of z+Bx+Cy+D <- (x-a)²+(y-b)²-r²

algorithm(model::Circle)

Gets the algorithm used for the model fitting.

Takes in points in 3D space and outputs a fitted circle in 3D based on a method in Conformal Geometric Algebra (CGA).

Input is points in 3D euclidean space with each row being a point, and each column is the xyz coordinate.
The ouput is: centrum, radius, normal_vector
where circle_cga is the CGA representation of the fitted circle, in the IPNS representation!

This method is solved by calculating the stacked matrix: M_stacked, which is solved with SVD.

Example usage:
>>> centrum, radius, normal_vector, circle_cga = circlefitCGA3D(points)

Fit a circle to the points provided as arrays of x and y coordinates

This method uses Kåsa's method The result is a GeometryBasics::Circle

parameterize(a::Float64, b::Float64, r::Float64)
parameterize(c::Circle)

Parameterizes a circle with center a, b and radius r into x, y values (mainly for plotting purposes).

Fit a circle by using the method of Pratt

https://doi.org/10.1201/EBK1439835906

https://people.cas.uab.edu/~mosya/cl/CircleFitByPratt.cpp

https://link.springer.com/article/10.1007/s10851-005-0482-8

Fit a circle by using Taubin's method https://doi.org/10.1007/s10851-005-0482-8 Warning: not optimized

fit(::Type{Circle}, x::AbstractArray, y::AbstractArray; alg=:kasa)

Fit a circle to points provided as arrays of x and y coordinates using the algorithm specified by alg (default is :kasa). Possible algorithms include

• :kasa for Kåsa's method [1]
• :taubin for using Taubin's method [2]
• :pratt for using Pratt's method [3].
• :pratt_newton for using a more numerically stable Pratt's method [4].

Returns a Circle object