Fitting 3D circles to scattered points

Following a comment at update-to-glob_to_loc3-and-loc_to_glob3-functions, I have modified the Python code at the linked site, so it can be run from Excel, via xlwings.  The spreadsheet described below, and the associated Python code, can be download from:

The original code and background information can be found at: Fitting a Circle to Cluster of 3D Points.  The code performs the following functions:

  • Generates points along a circular arc, then applies a random 3D offset to these points, to generate a cloud of points close to the original curve.
  • Finds the best fit circle passing through these points.
  • Generates graphs of the points, and the best fit circles, using Matplotlib.

To simplify the process as far as possible, I have converted the code to two user-defined functions (UDFs) that can be called from Excel, using xlwings, to generate the cloud of points, and to return the coordinates of a series of points along the best fit circle, or along an arc extending over the range of the data.  This data is then plotted in Excel, using xy charts.

Typical spreadsheet input and output are shown in the screen shots below:

The Points_by_ang function generates points along an arc of the specified circle, with random 3D offsets of magnitude determined by the k factor.  The input data in the example is the same as is hard coded in the original Python code.  The Fit_circ3D functions returns 3D coordinates along the best fit arc or circle (or alternatively other results, as defined by the “out” value).  Note that if the number of generated points is changed from 100, the range must be adjusted in the fit_Circ3D function, so that all of the input data range contains real numbers, not #N/A# or blank cells.

The best fit circles, projected to the XY, XZ and YZ planes, are shown below:

The Matplotlib results from the original code are very similar:

Changing the input data, the graphs automatically re-draw to show the new results:

To use different input points (either generated from another source, or real survey data) simply paste the data anywhere in the spreadsheet, and adjust the “3DPoints” range in the Fit_circ3D function, and the chart data ranges for the input data.

To use the spreadsheet:

  • If necessary, install Python, Numpy, and xlwings.  All the necessary packages are included in the default Anaconda Python installation.
  • Copy 3DCirc.xlsm and to any convenient directory.
  • Run 3DCirc.xlsm, and if necessary enable macros.


This entry was posted in Coordinate Geometry, Excel, Link to Python, Maths, Newton, NumPy and SciPy, UDFs, VBA, xlwings and tagged , , , , , , , . Bookmark the permalink.

One Response to Fitting 3D circles to scattered points

  1. Pingback: More Python rotation functions | Newton Excel Bach, not (just) an Excel Blog

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