http://www.mapleprimes.com/maplesoftblog/88732-Fitting-Circles-To-3D-Data--An-Update en-us 2026 Maplesoft, A Division of Waterloo Maple Inc. Maplesoft Document System Thu, 11 Jun 2026 09:05:27 GMT Thu, 11 Jun 2026 09:05:27 GMT The latest comments added to the Blog Entry, Fitting Circles to 3D Data - an Update http://www.mapleprimes.com/images/mapleprimeswhite.jpg http://www.mapleprimes.com/maplesoftblog/88732-Fitting-Circles-To-3D-Data--An-Update http://www.mapleprimes.com/maplesoftblog/88732-Fitting-Circles-To-3D-Data--An-Update?ref=Feed:MaplePrimes:Fitting Circles to 3D Data - an Update:Comments#comment89116 <p>I believe the objective function f2 isn't quite right.&nbsp; That is, you don't want to minize the distance to the center, but rather the distance to the circle. Consider the simpler case of fitting a 0-dimensional circle (two points) to a set of points on a line. Specifically, assume the data consists of [-1, 1, 1]&nbsp; (the 1 is repeated).&nbsp; The best fit is clearly the two points -1 and 1 (i.e. the "circle" with unit radius centered at 0).&nbsp; Fitting to the center of mass of these points gives a nonideal result.</p> The latest comments added to the Blog Entry, Fitting Circles to 3D Data - an Update 89116 Sat, 05 Jun 2010 19:34:48 Z Joe Riel Joe Riel http://www.mapleprimes.com/maplesoftblog/88732-Fitting-Circles-To-3D-Data--An-Update?ref=Feed:MaplePrimes:Fitting Circles to 3D Data - an Update:Comments#comment89312 <p>&nbsp;The objective function f2 is the square of the distance from the center of the circle to a data point. The quantity sigma2 is the sum of squares of the deviations sqrt(f2)-r. It is sigma2 that is measuring the deviations from the circle. The function f2 is an intermediate step in this calculation.</p> <p>Consider the problem in the xy-plane. The circle would be (x-h)^2+(y-k)^2=r^2. For the data point (u,v), the comparable deviation would be of the form (u-h)^2+(v-k)^2. The geometry shows that this is the distance from the center to the data point. Comparing the square root of this to r is then a measure of how close the point is to the circle.</p> <p>For the 3D case, sigma1 is used to find the best-fit plane. Then, sigma2 is used to find the best-fit circle, in analogy with the 2D case. Fitting the points to a sphere, as was done originally, is not as effective as the process used in the updated version of this calculation, as the graphs in Figures 1 and 3 show.<!--break--></p> <p>RJL Maplesoft</p> The latest comments added to the Blog Entry, Fitting Circles to 3D Data - an Update 89312 Wed, 09 Jun 2010 00:07:33 Z rlopez rlopez