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# Distance from points to an ellipse 1.0

Date Added: July 30, 2013  |  Visits: 192

This is a modified version of an iterative algorithm published byD. Eberly.Internet publication: "Distance from a point to an ellipse in 2D" (2004) Geometric Tools, LLC, www.geometrictools.comBook 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 7-8 significant digit. It takes 4-5 iterations per point, on average.

 Requirements: No special requirements Platforms: Matlab Keyword: Angle,  Center,  Dxyi,  Ellipse,  Major,  Minor Users rating: 0/10