
Distance from points to an ellipse 1.0 File ID: 81545 


 Distance from points to an ellipse 1.0 License: Shareware File Size: 10.0 KB Downloads: 6
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Distance from points to an ellipse 1.0 Description 

Description: This is a modified version of an iterative algorithm published by D. Eberly. Internet publication: "Distance from a point to an ellipse in 2D" (2004) Geometric Tools, LLC, www.geometrictools.com Book publication: "3D Game Engine Design", 2nd edition. Morgan Kaufmann Publishers, San Francisco, CA, 2007. (see Section 14.13.1)
Usage: [RSS, XYproj] = Residuals_ellipse(XY,ParG) Input: XY(n,2) is the array of coordinates of n points x(i)=XY(i,1), y(i)=XY(i,2) ParG is a vector 5x1 of the ellipse parameters ParG = [Center(1:2), Axes(1:2), Angle]' Center  the coordinates of the ellipse's center Axes  the axes (major, minor) Angle  the angle of tilt of the ellipse
Output: RSS is the Residual Sum of Squares (the sum of squares of the distances) XYproj is the array of coordinates of projections(nearest points on the ellipse)
This algorithm is proven to converge and reaches an accuracy of 78 significant digit. It takes 45 iterations per point, on average. 
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