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Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation ).
Vertex distance is the distance between the back surface of a corrective lens, i.e. glasses (spectacles) or contact lenses, and the front of the cornea. Increasing or decreasing the vertex distance changes the optical properties of the system, by moving the focal point forward or backward, effectively changing the power of the lens relative to ...
The circle defined by this slice will be very small, corresponding to the small angle of the rotation. As the rotation angles become larger, the slice moves in the negative z direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the ...
Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane). This is the convention followed in this article.
The angle θ and axis unit vector e define a rotation, concisely represented by the rotation vector θe.. In mathematics, the axis–angle representation parameterizes a rotation in a three-dimensional Euclidean space by two quantities: a unit vector e indicating the direction of an axis of rotation, and an angle of rotation θ describing the magnitude and sense (e.g., clockwise) of the ...
In a simple rotation of the 24-cell in a hexagonal plane, each vertex in the plane rotates first along an edge to an adjacent vertex 60 degrees away. But in an isoclinic rotation in two completely orthogonal planes one of which is a great hexagon, [ax] each vertex rotates first to a vertex two edge lengths away (√ 3 and 120° distant). The ...
A peripheral vertex in a graph of diameter d is one whose eccentricity is d —that is, a vertex whose distance from its furthest vertex is equal to the diameter. Formally, v is peripheral if ϵ(v) = d. A pseudo-peripheral vertex v has the property that, for any vertex u, if u is as far away from v as possible, then v is as far away from u as
They constitute a mixed axes of rotation system, where the first angle moves the line of nodes around the external axis z, the second rotates around the line of nodes N and the third one is an intrinsic rotation around Z, an axis fixed in the body that moves. The static definition implies that: α (precession) represents a rotation around the z ...