getBorders.m File Reference

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Functions
function	getBorders (in gramian, in center, in zval, in npnt)
	Return a matrix of MATLAB doubles of shape [npnt, 2 * nell] (or [npnt, 3 * nell] if the input zval is present) containing the 2D (or 3D) coordinates of a set of points on the boundary of a set of 2D ellipsoids whose Gramian matrices and centers are specified as input argument. More...

Function Documentation

getBorders()

function getBorders	(	in	gramian,
		in	center,
		in	zval,
		in	npnt
	)

Return a matrix of MATLAB doubles of shape [npnt, 2 * nell] (or [npnt, 3 * nell] if the input zval is present) containing the 2D (or 3D) coordinates of a set of points on the boundary of a set of 2D ellipsoids whose Gramian matrices and centers are specified as input argument.

Here nell refers to the number of ellipsoids which is equal to 2 * max(1, size(gramian, 3), size(center, 2)).

Parameters

[in]	gramian	: The input matrix of MATLAB doubles of shape [2, 2, nell] containing the Gramian matrices of the nell 2D ellipsoids whose boundary points are to be returned. (optional, default = eye(2, 2, 1))
[in]	center	: The input matrix of MATLAB doubles of shape [2, nell] containing the 2D coordinates of the centers of the nell 2D ellipsoids whose boundary points are to be returned. (optional, default = zeros(2, 1))
[in]	zval	: The input scalar (or matrix of shape [npnt, nell] of) MATLAB double(s) containing the z-axis coordinates of the points on the borders of the nell 2D ellipsoids. If present, the specified value(s) will occupy the [1 : 2 : 3 * nell] columns of the output bcrd. This argument is present for the sake of convenience and better performance of the algorithm to avoid further reallocations. (optional. If not present or empty, it will not be present in the output.)
[in]	npnt	: The input scalar MATLAB whole number containing the number of points to return on the boundary of the target 2D ellipsoid. (optional, default = 50)

Returns

bcrd : The output matrix of MATLAB doubles of shape [npnt, 2 * nell] (or [npnt, 3 * nell] if the input argument zval is present) containing the coordinates of a set of npnt points on the boundary of the target 2D ellipsoid.

Possible calling interfaces ⛓

pm.geom.ell2.getBorders()
pm.geom.ell2.getBorders(gramian)
pm.geom.ell2.getBorders(gramian, center)
pm.geom.ell2.getBorders(gramian, center, zval)
pm.geom.ell2.getBorders(gramian, center, zval, npnt)

Warning

The condition npnt == size(zval, 1) must hold for the corresponding input arguments.

Example usage ⛓

cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.
addpath('../../../../'); % Add the ParaMonte library root directory to the search path.
 
figure("color", "white"); hold on; box on;
bcrd = pm.geom.ell2.getBorders();
h = plot(bcrd(:, 1), bcrd(:, 2), '-');
pm.vis.figure.savefig("getBorders.2d.png", "-m3");
 
npnt = 50;
figure("color", "white"); hold on; box on; view(3);
bcrd = pm.geom.ell2.getBorders([], [], repmat([1 : 20], npnt, 1));
for iell = 1 : 2 : size(bcrd, 2) / 3
    icol = (iell - 1) * 3 + 1;
    plot3(bcrd(:, icol), bcrd(:, icol + 1), bcrd(:, icol + 2), '-');
end
pm.vis.figure.savefig("getBorders.3d.png", "-m3");

Visualization of the example output ⛓

Final Remarks ⛓

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Copyright

Computational Data Science Lab

Author:

Joshua Alexander Osborne, May 21 2024, 5:33 PM, University of Texas at Arlington
Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin