Search results
Results from the WOW.Com Content Network
Solutions to the illumination problem by George W. Tokarsky (26 sides) and David Castro (24 sides) This problem was also solved for polygonal rooms by George Tokarsky in 1995 for 2 and 3 dimensions, which showed that there exists an unilluminable polygonal 26-sided room with a "dark spot" which is not illuminated from another point in the room ...
The inverse problem for earth sections is: given two points, and on the surface of the reference ellipsoid, find the length, , of the short arc of a spheroid section from to and also find the departure and arrival azimuths (angle from true north) of that curve, and . The figure to the right illustrates the notation used here.
Handling the direct problem is straightforward, because α 0 can be determined directly from the given quantities φ 1 and α 1; for a sample calculation, see Karney (2013). In the case of the inverse problem, λ 12 is given; this cannot be easily related to the equivalent spherical angle ω 12 because α 0 is unknown.
The Rytz’s axis construction is a basic method of descriptive geometry to find the axes, the semi-major axis and semi-minor axis and the vertices of an ellipse, starting from two conjugated half-diameters. If the center and the semi axis of an ellipse are determined the ellipse can be drawn using an ellipsograph or by hand (see ellipse).
For example, on a triaxial ellipsoid, the meridional eccentricity is that of the ellipse formed by a section containing both the longest and the shortest axes (one of which will be the polar axis), and the equatorial eccentricity is the eccentricity of the ellipse formed by a section through the centre, perpendicular to the polar axis (i.e. in ...
Another use of elliptical distributions is in robust statistics, in which researchers examine how statistical procedures perform on the class of elliptical distributions, to gain insight into the procedures' performance on even more general problems, [20] for example by using the limiting theory of statistics ("asymptotics").
Any ellipsoid is the image of the unit sphere under some affine transformation, and any plane is the image of some other plane under the same transformation. So, because affine transformations map circles to ellipses, the intersection of a plane with an ellipsoid is an ellipse or a single point, or is empty. [8] Obviously, spheroids contain ...
The circle and ellipse models are deliberately simplified to avoid distracting details which are not relevant to the circle–ellipse problem. An ellipse has two semi-axes called h-axis and v-axis in the code. Being an ellipse, a circle inherits these, and also has a radius property, which value is equal to that of the axes (which must, of ...