Together with a rotation matrix, R, a translation vector, t, yields a relation between two equivalent positions in a crystal, given by Rx+ t = x'. Please see the link.
In 2 dimensional space it is a translation vector which is a 2x1 column vector.
To find the image of the point X(3, 5) along the translation vector (-4, 6), you simply add the components of the translation vector to the coordinates of point X. This results in the new coordinates: (3 + (-4)) and (5 + 6), which simplifies to (-1, 11). Therefore, the image of X(3, 5) along the translation vector (-4, 6) is (-1, 11).
It is a translation on the Cartesian plane
The vector (6, -2)T
6
In crystallography, the k vector represents the direction and magnitude of a wave in a crystal lattice. It is important because it helps determine the arrangement of atoms in the crystal structure. The k vector is related to the periodicity of the crystal lattice, influencing properties such as diffraction patterns and electronic band structures.
Glide reflection
a translation
Translation along a vector involves moving an object in a specific direction by a specified distance based on the properties of the vector. This operation involves shifting the object without rotating or changing its orientation, following the direction and magnitude of the vector.
In 2 dimensional space it is a translation vector which is a 2x1 column vector.
In a translation, a vector defines the direction and distance that an object moves from its original position. It consists of two components: the horizontal and vertical displacements. By applying this vector to each point of the object, all points are shifted uniformly, resulting in a new position of the object without altering its shape or orientation. Thus, the vector essentially guides the entire translation process.
To find the image of the point X(3, 5) along the translation vector (-4, 6), you simply add the components of the translation vector to the coordinates of point X. This results in the new coordinates: (3 + (-4)) and (5 + 6), which simplifies to (-1, 11). Therefore, the image of X(3, 5) along the translation vector (-4, 6) is (-1, 11).
2 stacked
It is a translation on the Cartesian plane
George Huntington Williams has written: 'Modern petrography' -- subject(s): Petrology 'Elements of crystallography for students of chemistry physics and mineralogy' -- subject(s): Crystallography 'Elements of crystallography' -- subject(s): Crystallography 'Elements of crystallography' -- subject(s): Crystallography
Crystallography Reviews was created in 1987.
An affine transformation is a linear transformation between vector spaces, followed by a translation.