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Rotation formalisms are focused on proper (orientation-preserving) motions of the Euclidean space with one fixed point, that a rotation refers to.Although physical motions with a fixed point are an important case (such as ones described in the center-of-mass frame, or motions of a joint), this approach creates a knowledge about all motions.
Railroad reverse ("S") curve. In civil engineering, a reverse curve (or "S" curve) is a section of the horizontal alignment of a highway or rail route in which a curve to the left or right is followed immediately by a curve in the opposite direction.
The examples in this article apply to active rotations of vectors counterclockwise in a right-handed coordinate system (y counterclockwise from x) by pre-multiplication (the rotation matrix R applied on the left of the column vector v to be rotated).
3D visualization of a sphere and a rotation about an Euler axis (^) by an angle of In 3-dimensional space, according to Euler's rotation theorem, any rotation or sequence of rotations of a rigid body or coordinate system about a fixed point is equivalent to a single rotation by a given angle about a fixed axis (called the Euler axis) that runs through the fixed point. [6]
Alignment of 27 avian influenza hemagglutinin protein sequences colored by residue conservation (top) and residue properties (bottom) Multiple sequence alignment is an extension of pairwise alignment to incorporate more than two sequences at a time. Multiple alignment methods try to align all of the sequences in a given query set.
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
Binary Alignment Map (BAM) is the comprehensive raw data of genome sequencing; [1] it consists of the lossless, compressed binary representation of the Sequence Alignment Map-files. [ 2 ] [ 3 ] BAM is the compressed binary representation of SAM (Sequence Alignment Map), a compact and index-able representation of nucleotide sequence alignments ...
For example, to study the equations of ellipses and hyperbolas, the foci are usually located on one of the axes and are situated symmetrically with respect to the origin. If the curve (hyperbola, parabola , ellipse, etc.) is not situated conveniently with respect to the axes, the coordinate system should be changed to place the curve at a ...