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I'm a 73-year-old engineer struggling with numerically implementing a math problem.

I am working on a kinematic linkage project that generates motion paths (as long sequences of x,y coordinates) of the end points of linkages and dumps the data into a comma-delimited file to be imported into Excel for analysis.

The analysis involves moving along the linkage motion path data taking three consecutive data points and calculating the radius (curvature) and circle center point (x,y) coordinates. This all needs to be automated in Excel calculations for hundreds of triads of points.

It's not a difficult problem to do on paper with the usual equations on a single data set, but this gets really excessively complicated as Excel equations.

Excel is very limited with determinants, so that approach is out.

I'm thinking that the most straightforward approach would be to find the intersection of the two perpendicular bisector lines of the two secant lines created by the three consecutive data points.

Or, is there a better way of computationally solving this?

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  • $\begingroup$ Pick two edges, find their midpoints, write the equations of the lines through midpoints and perpendicular to the corresponding edge (this is easy). These lines intersect at the center of the circle you seek. where these lines intersect. To find the coordinates of the center you need to solve a linear systems of two equations in two variables. The solution has explicit and simple formula. The radius is then easy to determine. $\endgroup$
    – Liviu Nicolaescu
    Commented Nov 14, 2019 at 19:55
  • $\begingroup$ Also, this is a good question, but for a different forum. If you are actually going to write a computer program or routine to do this repeatedly, you might ask on a forum dedicated to software performance. Gerhard "MathOverflow Is For Something Different" Paseman, 2019.11.14. $\endgroup$
    – Gerhard Paseman
    Commented Nov 14, 2019 at 20:04

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