# Intersection Arbitrary Ellipsoid and a Plane

Version 1.0.0.5 (3.72 KB) by
This function computes the intersection any Ellipsoid and a Plane,
Updated 27 Jul 2023

Arbitrary ELIPSOID and A PLANE INTERSECTION
function[Aye,Bye,qx,qy,qz]=intersection_elipsoid_plane2(elp,plane)
% Plane equation AA.x + BB.y + CC.z+ DD = 0
% Standart Ellipsoid equation (x/a)^2 + (y/b)^2 + (z/c)^2 = 1
% Arbitrary Ellipsoid equation Ax^2 + By^2 + Cz^2 +2 Dxy + 2Exz + 2Fyz + 2Gx + 2Hy + 2Iz + J = 0
% Author: Sebahattin Bektas,Ondokuz Mayis University,2015
%
% Inputs -----------------------------------------------------------------
% Plane=[AA BB CC DD] :Plane equation's coefficients 1x4
%
% for standard ellipsoid elp must be 1x3 =[a b c]
% for arbitrary ellipsoid elp must be 1x10 =[ A B C D E F G H I J]
%
% elp=[a b c]: Semi-axes of standart ellipsoid
% or
% elp=[ A B C D E F G H I J]: Arbitrary Ellipsoid coefficient
% Outputs ----------------------------------------------------------------
% Aye: Semi-major axis of intersection ellipse
% Bye: Semi-minor axis of intersection ellipse
%
% qx,qy,qz : Cartesian coordinates of intersection ellipse's center
% This source code is given for free! However, I would be grateful if you refer
% to corresponding article in any academic publication that uses
% this code or part of it.
% BEKTAS, S Orthogonal distance from an ellipsoid. Bol. Ciênc. Geod. [online]. 2014, vol.20, n.4, pp. 970-983. ISSN 1982-2170.
% BEKTAS, S Intersection of an Ellipsoid and a Plane,International Journal of Research in Engineering and Applied Sciences VOLUME 6,ISSUE 6,2016

### Cite As

Sebahattin Bektas (2024). Intersection Arbitrary Ellipsoid and a Plane (https://www.mathworks.com/matlabcentral/fileexchange/52958-intersection-arbitrary-ellipsoid-and-a-plane), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2022a
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.0.0.5

1.0.0.4

updated

1.0.0.3

expanded

1.0.0.2

updated

1.0.0.1

expanded for arbitrary ellipsoid

1.0.0.0