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https://github.com/brcolow/surfmetjs

Surface Metrology in Javascript
https://github.com/brcolow/surfmetjs

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Surface Metrology in Javascript

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README 

        
Four Circles for Determining Roundness (ISO 4291:1985 (current version as of 2020)):



least squares circle (LSC)

minimum zone circle (MZC)

minimum circumscribed circle (MCC)

maximum inscribed circle (MIC)



These can all be solved as non-linear minimization problems.



# Least Squares Circle (LSC)



https://github.com/mdoube/BoneJ/blob/17ee483603afa8a7efb745512be60a29e093c94e/src/org/doube/geometry/FitCircle.java#L43



Minimize:



Σ ( (x_i - a)^2 + (y_i - b)^2 - r^2 )



where:



    Σ: summation over all data points (i = 1 to N)

    (a, b): center coordinates of the circle

    (x_i, y_i): coordinates of the i-th data point

    N: total number of data points

    r: radius of the circle



This objective function represents the sum of squared distances between each data point (x_i, y_i) and the fitted circle with center (a, b) and radius r. The minimization process aims to find the circle parameters that minimize this total squared distance, essentially providing the best fit based on minimizing these individual point-to-circle distances.



Will use Levenberg–Marquardt algorithm to solve this.



# Minimum Zone Circle (MZC)



Minimize: r



Subject to:



(x_i - a)^2 + (y_i - b)^2 <= r^2  for all data points (i = 1 to N)



where:



    r: radius of the circle

    (a, b): center coordinates of the circle

    (x_i, y_i): coordinates of the i-th data point

    N: total number of data points



This formulation minimizes the radius (r) while ensuring all data points are inside or on the circle through the squared distance constraint.



# Minimum Circumscribed Circle (MCC)



Also referred to as the "Smallest-circle problem".



See https://github.com/hbf/miniball for an example implementation.



Minimize:



 r



Subject to:



min( (x_i - a)^2 + (y_i - b)^2 ) = r^2  for at least one data point (i)



where the minimization is taken over all data points.



Here, the objective is still to minimize the radius (r). However, the constraint ensures that at least one data point lies exactly on the circle (i.e., the minimum squared distance from a data point to the center is equal to the square of the radius).



# Maximum Inscribed Circle (MIC)



Also referred to as the "Maximum empty circle problem".



Maximize:



 r



Subject to:



(x_i - a)^2 + (y_i - b)^2 >= r^2  for all data points (i = 1 to N)



This formulation maximizes the radius (r) while guaranteeing that all data points are outside or on the circle through the squared distance constraint (reversed inequality compared to MZC).



These objective functions, along with the associated constraints, are used within non-linear optimization algorithms to find the circle parameters (a, b, r) that satisfy the specific geometric conditions for each case (MZC, MCC, MIC).



## Surface Metrology



### Surface Texture Parameters

    Ft Pa Pdsm Phsc Pku Pm0 Pm2 Pm4

     Pp Ppc Pq Ps Psk Psm Pt Pv PVc

    Ra Ra1 Ra1l Ra7 Ra7l Rc Rcl Rdmd Rdmn Rdq

    Rdsk Rhsc Rk Rk+vk Rku Rm0 Rm2 Rm4 Rmax

    Rmq Rmr1 Rmr2 Rp Rpc Rpk Rpk* Rpk/k Rpk+k Rpm

    Rpm/3z Rpm7 Rpm7l Rpq Rq Rs Rsk Rsm

    Rt Rtwi Rv RVc Rvk Rvk* Rvk/k Rvm Rvo Rvq

    Ry Rz1max RzDIN RzJIS R3z

    Wa Wc Wcvx Wcvxl Wcvxm Wdq

    Weslp Weslpl Wlslp Wlslpl Wp Wpc Wpl Wpr Wq

    Ws Wseg Wsegl Wsm Wt Wtc Wv Wvda Wvdas

    Wvdc Wvdd Wvddl Wvdm Wvdmp Wvoid

    AR AW R Rx W Wte Wx

    Bearing Ratios (tpa/tpi, Pmr/Rmr): 10 Primary & 10 Roughness

    Htp Values (PHtp/RHtp): 10 Primary & 10 Roughness



### Filters



    Gaussian

    Spline Based Gaussian (with adjustable tension

    Valley Suppression (ISO 13565-1 – 1996)

    Robust Spline-Based Gaussian (based on robust regression)

    Morphological Closing Filter (circular element applied to waviness profile)

    Morphological Opening Filter (circular element applied to waviness profile)



### Form removal



    Instrument reference (mean suppression)

    Least Squares Line

    Least Squares Arc

    Fixed Radius

    Least Squares Polynomial (user specified order)

    Spline Filter (for bandpass waviness with a user specified cutoff)

    Asphere (user defined coefficients with optional radius optimization)

    Free Form (user defined coordinates with optional pre-filtering)