translation vector sentence in Hindi
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- If the translation vector of a glide plane operation is itself an element of the translation group, then the corresponding glide plane symmetry reduces to a combination of reflection symmetry and translational symmetry.
- The translational symmetry is given by oblique translation vectors from one point on a true reflection line to two points on the next, supporting a rhombus with the true reflection line as one of the diagonals.
- Combining two equal glide plane operations gives a pure translation with a translation vector that is twice that of the glide plane operation, so the even powers of the glide plane operation form a translation group.
- Performing the two operations in sequence, i . e . first the rotation and then the translation ( with translation vector given in the already rotated coordinate system ), gives a combined rotation and translation matrix
- The simplest representation would be to represent the map as a transformation matrix and a translation vector ( n ^ 2 + n real values ), but I'd like each value to have a single clearly defined function.
- The " primitive translation vectors " 1 } }, 2 } }, 3 } } span a lattice cell of smallest volume for a particular three-dimensional lattice, and are used to define a crystal translation vector
- The " primitive translation vectors " 1 } }, 2 } }, 3 } } span a lattice cell of smallest volume for a particular three-dimensional lattice, and are used to define a crystal translation vector
- As it does so, the object's motion will be described by two vectors : a translation vector, and a rotation vector "'? "', which is an areal velocity vector : the Darboux vector.
- In the remaining two cases symmetry description is with respect to centred cells that are larger than the primitive cell, and hence have internal repetition; the directions of their sides is different from those of the translation vectors spanning a primitive cell.
- The same applies for a change of angle between translation vectors, provided that it does not add or remove any symmetry ( this is only the case if there are no mirrors and no glide reflections, and rotational symmetry is at most of order 2 ).
- A final remark relates to the fact that if the essential matrix is determined from corresponding image coordinate, which often is the case when 3D points are determined in this way, the translation vector \ mathbf { t } is known only up to an unknown positive scaling.
- In the case of symmetry groups in the plane, additional parameters are the direction of the translation vector, and, for the frieze groups with horizontal line reflection, glide reflection, or 180?rotation ( groups 3 7 ), the position of the reflection axis or rotation point in the direction perpendicular to the translation vector.
- In the case of symmetry groups in the plane, additional parameters are the direction of the translation vector, and, for the frieze groups with horizontal line reflection, glide reflection, or 180?rotation ( groups 3 7 ), the position of the reflection axis or rotation point in the direction perpendicular to the translation vector.
- For each of the types " D " 1, " D " 2, and " D " 4 the distinction between the 3, 4, and 2 wallpaper groups, respectively, is determined by the translation vector associated with each reflection in the group : since isometries are in the same coset regardless of translational components, a reflection and a glide reflection with the same mirror are in the same coset.
- Where \ textbf { a } ^ * and \ textbf { b } ^ * are the primitive translation vectors of the 2D reciprocal lattice of the surface and \ textbf { k } ^ { | | }, \ textbf { k } _ 0 ^ { | | } denote the component of respectively the reflected and incident wave vector parallel to the sample surface . \ textbf { a } ^ * and \ textbf { b } ^ * are related to the real space surface lattice in the following way:
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