cspice_saelgv |
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## AbstractCSPICE_SAELGV calculates the semi-axis vectors of an ellipse generated by two arbitrary three-dimensional vectors. ## I/OGiven: vec1, vec2 the two vectors defining an ellipse (the generating vectors). [3,1] = size(vec1); double = class(vec1) [3,1] = size(vec2); double = class(vec2) The ellipse is the set of points center + cos(theta) vec1 + sin(theta) vec2 where theta ranges over the interval (-pi, pi] and center is an arbitrary point at which the ellipse is centered. An ellipse's semi-axes are independent of its center, so the vector center shown above is not an input to this routine. 'vec1' and 'vec2' need not be linearly independent; degenerate input ellipses are allowed. the call: [ smajor, sminor ] = ## ExamplesAny 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. % % Define two arbitrary, linearly independent, vectors. % vec1 = [ 1; 1; 1 ]; vec2 = [ 1; -1; 1 ]; % % Calculate the semi-major and semi-minor axes of an % ellipse generated by the two vectors. % [ smajor, sminor] = ## ParticularsWe note here that two linearly independent but not necessarily orthogonal vectors vec1 and vec2 can define an ellipse centered at the origin: the ellipse is the set of points in 3-space center + cos(theta) vec1 + sin(theta) vec2 where theta is in the interval (-pi, pi] and center is an arbitrary point at which the ellipse is centered. This routine finds vectors that constitute semi-axes of an ellipse that is defined, except for the location of its center, by vec1 and vec2. The semi-major axis is a vector of largest possible magnitude in the set cos(theta) vec1 + sin(theta) vec2 There are two such vectors; they are additive inverses of each other. The semi-minor axis is an analogous vector of smallest possible magnitude. The semi-major and semi-minor axes are orthogonal to each other. If smajor and sminor are choices of semi-major and semi-minor axes, then the input ellipse can also be represented as the set of points center + cos(theta) smajor + sin(theta) sminor where theta is in the interval (-pi, pi]. The capability of finding the axes of an ellipse is useful in finding the image of an ellipse under a linear transformation. Finding this image is useful for determining the orthogonal and gnomonic projections of an ellipse, and also for finding the limb and terminator of an ellipsoidal body. ## Required ReadingFor important details concerning this module's function, please refer to the CSPICE routine saelgv_c. MICE.REQ ELLIPSES.REQ ## Version-Mice Version 1.0.1, 23-MAR-2015, EDW (JPL) Edited I/O section to conform to NAIF standard for Mice documentation. -Mice Version 1.0.0, 07-MAY-2008, EDW (JPL) ## Index_Entriessemi-axes of ellipse from generating vectors |

Wed Apr 5 18:00:34 2017