CSPICE_PJELPL orthogonally projects an ellipse onto a plane.
Given:
elin a structure describing a SPICE ellipse.
[1,1] = size(elin); struct = class(elin)
The structure has the fields:
center: [3x1 double]
semiMajor: [3x1 double]
semiMinor: [3x1 double]
plane a structure describing a SPICE plane.
[1,1] = size(plane); struct = class(plane)
The structure has the fields:
normal: [3x1 double]
constant: [1x1 double]
are, respectively, a SPICE ellipse and a SPICE plane. The
geometric ellipse represented by 'elin' is to be orthogonally
projected onto the geometric plane represented by 'plane'.
the call:
elout = cspice_pjelpl( elin, plane )
returns:
elout the SPICE ellipse that represents the geometric
ellipse resulting from orthogonally projecting the ellipse
represented by 'elin' onto the plane represented by 'plane'.
[1,1] = size(elout); struct = class(elout)
Any numerical results shown for this example may differ between
platforms as the results depend on the SPICE kernels used as input
and the machine specific arithmetic implementation.
%
% Assign the values for plane/ellipse definition
% vectors.
%
center = [ 1, 1, 1 ]';
vect1 = [ 2, 0, 0 ]';
vect2 = [ 0, 1, 1 ]';
normal = [ 0, 0, 1 ]';
%
% Create a plane using a constant value of 0...
%
plane = cspice_nvc2pl( normal, 0 );
%
% ...and an ellipse.
%
elin = cspice_cgv2el( center, vect1, vect2 );
%
% Project the ellipse onto the plane.
%
elout = cspice_pjelpl( elin, plane );
%
% Output the ellipse in the plane.
%
fprintf( 'Center : %f %f %f\n', elout.center )
fprintf( 'Semiminor: %f %f %f\n', elout.semiMinor )
fprintf( 'Semimajor: %f %f %f\n', elout.semiMajor )
MATLAB outputs:
Center : 1.000000 1.000000 0.000000
Semiminor: 0.000000 1.000000 0.000000
Semimajor: 2.000000 0.000000 0.000000
Projecting an ellipse orthogonally onto a plane can be thought of
finding the points on the plane that are `under' or `over' the
ellipse, with the `up' direction considered to be perpendicular
to the plane. More mathematically, the orthogonal projection is
the set of points Y in the plane such that for some point X in
the ellipse, the vector Y  X is perpendicular to the plane.
The orthogonal projection of an ellipse onto a plane yields
another ellipse.
For important details concerning this module's function, please refer to
the CSPICE routine pjelpl_c.
MICE.REQ
ELLIPSES.REQ
PLANES.REQ
Mice Version 1.0.0, 11JUN2013, EDW (JPL)
project ellipse onto plane
