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In this algorithm, one recursively draws a line to split the vertices into two sets. The Delaunay triangulation is computed for each set, and then the two sets are merged along the splitting line. Using some clever tricks, the merge operation can be done in time O( n ) , so the total running time is O( n log n ) .
Each block begins with a line containing four floating-point values, the freestream Mach number, the freestream angle of attack, the freestream Reynolds number, and the time. The rest of the block contains the values iterated over i , j , k , m (block index), and the outermost n , which counts through 5 sections, the density, the 3 components ...
Let X be an affine space over a field k, and V be its associated vector space. An affine transformation is a bijection f from X onto itself that is an affine map; this means that a linear map g from V to V is well defined by the equation () = (); here, as usual, the subtraction of two points denotes the free vector from the second point to the first one, and "well-defined" means that ...
A two-line element set (TLE, or more rarely 2LE) or three-line element set (3LE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the epoch. Using a suitable prediction formula, the state (position and velocity) at any point in the past or future can be estimated to some accuracy.
In any geometry, the set of points on a line are said to be collinear. In Euclidean geometry this relation is intuitively visualized by points lying in a row on a "straight line". However, in most geometries (including Euclidean) a line is typically a primitive (undefined) object type , so such visualizations will not necessarily be appropriate.
State vectors are defined with respect to some frame of reference, usually but not always an inertial reference frame. One of the more popular reference frames for the state vectors of bodies moving near Earth is the Earth-centered inertial (ECI) system defined as follows: [1]: 23 The origin is Earth's center of mass;
By extension, this can be used to transform all three basis vectors to compute a rotation matrix in SO(3), the group of all rotation matrices, from an axis–angle representation. In terms of Lie theory, the Rodrigues' formula provides an algorithm to compute the exponential map from the Lie algebra so(3) to its Lie group SO(3).
The projective linear group of n-space = (+) has (n + 1) 2 − 1 dimensions (because it is (,) = ((+,)), projectivization removing one dimension), but in other dimensions the projective linear group is only 2-transitive – because three collinear points must be mapped to three collinear points (which is not a restriction in the projective line ...