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Binary angular measurement (BAM) [1] (and the binary angular measurement system, BAMS [2]) is a measure of angles using binary numbers and fixed-point arithmetic, in which a full turn is represented by the value 1. The unit of angular measure used in those methods may be called binary radian (brad) or binary degree.
It can also be described as the shortest path distance in a rotation graph, a graph that has a vertex for each binary tree on a given left-to-right sequence of nodes and an edge for each rotation between two trees. [2] This rotation graph is exactly the graph of vertices and edges of an associahedron. [3]
In a binary search tree, a right rotation is the movement of a node, X, down to the right. This rotation assumes that X has a left child (or subtree). X's left child, R, becomes X's parent node and R's right child becomes X's new left child. This rotation is done to balance the tree; specifically when the left subtree of node X has a ...
Sailors have traditionally divided a turn into 32 compass points, which implicitly have an angular separation of 1/32 turn. The binary degree, also known as the binary radian (or brad), is 1 / 256 turn. [21] The binary degree is used in computing so that an angle can be represented to the maximum possible precision in a single byte.
A rotation in the plane can be formed by composing a pair of reflections. First reflect a point P to its image P′ on the other side of line L 1. Then reflect P′ to its image P′′ on the other side of line L 2. If lines L 1 and L 2 make an angle θ with one another, then points P and P′′ will make an angle 2θ around point O, the ...
Some say that the direction of rotation reflects the direction that a node is moving upon rotation (a left child rotating into its parent's location is a right rotation) while others say that the direction of rotation reflects which subtree is rotating (a left subtree rotating into its parent's location is a left rotation, the opposite of the ...
A point P has coordinates (x, y) with respect to the original system and coordinates (x′, y′) with respect to the new system. [1] In the new coordinate system, the point P will appear to have been rotated in the opposite direction, that is, clockwise through the angle . A rotation of axes in more than two dimensions is defined similarly.
CORDIC (coordinate rotation digital computer), Volder's algorithm, Digit-by-digit method, Circular CORDIC (Jack E. Volder), [1] [2] Linear CORDIC, Hyperbolic CORDIC (John Stephen Walther), [3] [4] and Generalized Hyperbolic CORDIC (GH CORDIC) (Yuanyong Luo et al.), [5] [6] is a simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots ...