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Implement the remaining methods of "ellipsoid" class in "GenEllipsoid" class #46
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@pgagarinov Can you give me a small hint to generalize intersection algorithm of finite ellipsoid and hyper-plane described here (and implemented into elltoolboxcore+ellipsoid) on generalized case with infinite eigenvalues, please? |
The same goes for polar() method |
Regarding polar - please have a look at #42 (comment) and talk to Alex Timchenko. Regarding the intersection - the hint is that you need to use a definition of generalized ellipsoid (see comments for issue #46). Obviously an intersection of hyperplane and generalized ellipsoid is a generalized ellipsoid GE=E+L. So you need to find its E and L components separately. Start with a pen, a sheet of paper and a few simple 3-dimensional examples: unlimited cylinder, 2-dimensional ellipsoid in 3d space, 1-dimensional ellipsoid in 3d space. In each of the above examples figure out who an intersection looks like. This should help you with the formulas for n-dimensional case. |
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This includes polar, hpintersect and a few others - see issue #42 for more details
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