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Align the vertical middle of the image with the baseline of the text plus half the x-height of the text, so that the image is vertically centered around a lower case "x" in the text. baseline: Align the bottom of the image with the baseline of the text.
Then rotate the given axis and the point such that the axis is aligned with one of the two coordinate axes for that particular coordinate plane (x, y or z) Use one of the fundamental rotation matrices to rotate the point depending on the coordinate axis with which the rotation axis is aligned.
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b.
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 ...
For example, with a cube, this is done by first looking straight towards one face. Next, the cube is rotated ±45° about the vertical axis, followed by a rotation of approximately 35.264° (precisely arcsin 1 ⁄ √ 3 or arctan 1 ⁄ √ 2, which is related to the Magic angle) about the horizontal axis. Note that with the cube (see image) the ...
The rotation has two angles of rotation, one for each plane of rotation, through which points in the planes rotate. If these are ω 1 and ω 2 then all points not in the planes rotate through an angle between ω 1 and ω 2. Rotations in four dimensions about a fixed point have six degrees of freedom.
All other points rotate through an angle between α and β, so in a sense they together determine the amount of rotation. For a general double rotation the planes of rotation and angles are unique, and given a general rotation they can be calculated. For example a rotation of α in the xy-plane and β in the zw-plane is given by the matrix
A rotation is an in-place reversal of array elements. This method swaps two elements of an array from outside in within a range. The rotation works for an even or odd number of array elements. The reversal algorithm uses three in-place rotations to accomplish an in-place block swap: Rotate region A; Rotate region B; Rotate region AB