Fitting 3D circles to scattered points

Posted on 11/02/2018 by dougaj4

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:

3DCirc.zip

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 3DCirc.py to any convenient directory.
  • Run 3DCirc.xlsm, and if necessary enable macros.

 

Posted in Coordinate Geometry, Excel, Link to Python, Maths, Newton, NumPy and SciPy, UDFs, VBA, xlwings | Tagged , , , , , , , | 7 Comments

Cubic splines with jagged data

Posted on 07/02/2018 by dougaj4

A cubic spline provides a good approximation to a smooth curve, and alternative versions are available for free download (see Daily Download 22: Splines and Curves, Update to AL-Spline-Matrix, and xlwSciPy 1.09 – update for xlwings 0.10 and Scipy 0.18.1), but if a curve has a sharp change of direction a single cubic spline will deviate significantly from the required values near the change.  An example of curves where this is a problem is a reinforced concrete moment-curvature diagram, which has sharp changes of slope at the cracking moment, and also at the reinforcement yield point.

To deal with curves of this sort, I have added an MSplineA user defined function (UDF) to the CSpline2 spreadsheet, which may be downloaded (including open-source code) from:

CSpline2.zip

This function allows a curve to be divided into any number of segments, each of which may be either linear or cubic splines.  Input and output details, and a typical example are shown in the screen shots below:

Required input ranges are the X and Y values of the input data, a list of spline segments, listing the last node number of each segment, the spline type to be applied (1 = linear or 3 = cubic), and end curve or slope details for cubic splines, and the X values where interpolation is required:

Output for this example is shown below:

Looking more closely at the region near the cracking moments it can be seen that the MSplineA function has given a good approximation to the input values, whereas a single cubic spline deviates significantly:

Posted in Arrays, Beam Bending, Concrete, Curve fitting, Excel, Newton, UDFs, VBA | Tagged , , , , , , | 2 Comments

More on building bridges, not walls

Posted on 03/02/2018 by dougaj4

In June last year I posted a link to a Jeremy Corbyn speech on the topic of building bridges, not walls.

Here are a couple of (more poetic) links on the same topic.

The first is from Anaïs Mitchell.  This song was written over 10 years ago, as part of the folk opera Hadestown, and the word are those of Hades, Lord of the Underworld:

An interesting interview with Anaïs Mitchell from 2016:

The singer-songwriter Anaïs Mitchell grew up on a sheep farm in semirural Vermont to a soundtrack of folk ballads and protest music. As a child, she believed that “if you could just write a song good enough, you could change the world.”

That belief has never quite left her. She is testing it in her first musical, the theatrically frisky and musically daring “Hadestown,” a version of the Orpheus myth retold in the American vernacular, which just opened at New York Theater Workshop.

…

One of Mr. Page’s songs will send a shiver for anyone following the presidential election: “Why We Build the Wall.” Though Ms. Mitchell wrote it a decade a ago, the song has taken on the uncanny echo of Donald J. Trump’s remarks on the campaign trail. Ms. Mitchell is unsurprised. “Political leaders will always invoke that image when it serves them,” she said, “because it appeals at a visceral level to people who feel scared.”

Ms. Mitchell is not scared, and she plans to keep writing — for the concert stage and the theatrical one. The Orpheus-like part of her insists on it. “Whether or not you can change the world with a song, you’ve still got to write the song,” she said. “You still have to try.”

Full interview at The New York TimesNew York Times.

The second is from Melanie Safka, singing “Close To it All” at a live performance in 1971:

Posted in Bach | Tagged , , | 1 Comment

Building Houses in Cambodia

Posted on 30/01/2018 by dougaj4

Driving through the Phnom Penh traffic …
01Phnom Penh Traffic1

02Phnom Penh Traffic2

and crossing the Mekong River …

bty

bdr

Brings us to the Raw Impact construction site  ..

bty

Where we have 4 days to complete 2 houses:

bty

bty

bty

bdr

bty

bdr

On day 4, with one house complete and one nearly there …

bty

We hand over to two Cambodian families to start a new life …

bdr

Posted in Bach, Newton | Tagged , , | 2 Comments

Two forks in the Celtic path

Posted on 14/01/2018 by dougaj4

Re-visiting the Steeleye Span version of Tam Lin lead me to two very different musical groups that I had not heard of before:

Anaïs Mitchell is an American singer-songwriter and musician, here performing another version of Tam Lin with Jefferson Hamer:

More on Anaïs Mitchell at Orpheus for the age of Trump: Anaïs Mitchell on her folk opera Hadestown.

The Melbourne Scottish Fiddle Club is an amateur group that explores the lively sounds of Scottish music, with repertoire that both acknowledges and reinvents traditional roots:

Posted in Bach | Tagged , , , , | Leave a comment