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\mathbf{\hat{A}} \quad = \quad \frac{B C - b_x c_x}{b_y} \\ +c_y &=& \mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})} \times \mathbf{\hat{A}} \quad = \quad \frac{\mathbf{B} \cdot \mathbf{C} - b_x c_x}{b_y} \\ c_z &=& |\mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})}|\quad = \quad \sqrt{C^2 - {c_x}^2 - {c_y}^2} \\ \end{eqnarray*} diff --git a/doc/Section_howto.html b/doc/Section_howto.html index 3630c3913b..3bac6be12a 100644 --- a/doc/Section_howto.html +++ b/doc/Section_howto.html @@ -811,22 +811,27 @@ The equivalent LAMMPS a,b,c are a linear rotation of A

where A = |A| indicates the scalar length of A. The ^ hat symbol -indicates the corresponding unit vector. beta and gamma are angles -between the vectors described below. The same rotation must also -be applied to atom positions, velocities, and any other vector quantities. -This can be done by first converting to fractional coordinates in the +indicates the corresponding unit vector. beta and gamma are angles +between the vectors described below. Note that by construction, +a, b, and c have strictly positive x, y, and z components, respectively. +If it should happen that +A, B, and C form a left-handed basis, then the above equations +are not valid for c. In this case, it is necessary +to first apply an inversion. This can be achieved +by interchanging two basis vectors or by changing the sign of one of them. +

+

For consistency, the same rotation/inversion appied to the basis vectors +must also be applied to atom positions, velocities, +and any other vector quantities. +This can be conveniently achieved by first converting to +fractional coordinates in the old basis and then converting to distance coordinates in the new basis. The transformation is given by the following equation:

-

where V is the volume of the box, X is the original vector quantity and -x is the vector in the LAMMPS basis. -

-

If it should happen that -A, B, and C form a left-handed basis, then it is necessary -to first apply an inversion in addition to rotation. This can be achieved -by interchanging two of the basis vectors or changing the sign of one of them. +

where V is the volume of the box, X is the original vector quantity and +x is the vector in the LAMMPS basis.

There is no requirement that a triclinic box be periodic in any dimension, though it typically should be in at least the 2nd dimension @@ -1237,7 +1242,7 @@ discussed below, it can be referenced via the following bracket notation, where ID in this case is the ID of a compute. The leading "c_" would be replaced by "f_" for a fix, or "v_" for a variable:

-
+
c_ID entire scalar, vector, or array
c_ID[I] one element of vector, one column of array
c_ID[I][J] one element of array @@ -1436,7 +1441,7 @@ data and scalar/vector/array data. input, that could be an element of a vector or array. Likewise a vector input could be a column of an array.

-
+
diff --git a/doc/Section_howto.txt b/doc/Section_howto.txt index 36578f0b6b..8c22a42931 100644 --- a/doc/Section_howto.txt +++ b/doc/Section_howto.txt @@ -802,22 +802,27 @@ The equivalent LAMMPS [a],[b],[c] are a linear rotation of [A], [B], and :c,image(Eqs/transform.jpg) where A = |[A]| indicates the scalar length of [A]. The ^ hat symbol -indicates the corresponding unit vector. beta and gamma are angles -between the vectors described below. The same rotation must also -be applied to atom positions, velocities, and any other vector quantities. -This can be done by first converting to fractional coordinates in the +indicates the corresponding unit vector. {beta} and {gamma} are angles +between the vectors described below. Note that by construction, +[a], [b], and [c] have strictly positive x, y, and z components, respectively. +If it should happen that +[A], [B], and [C] form a left-handed basis, then the above equations +are not valid for [c]. In this case, it is necessary +to first apply an inversion. This can be achieved +by interchanging two basis vectors or by changing the sign of one of them. + +For consistency, the same rotation/inversion applied to the basis vectors +must also be applied to atom positions, velocities, +and any other vector quantities. +This can be conveniently achieved by first converting to +fractional coordinates in the old basis and then converting to distance coordinates in the new basis. The transformation is given by the following equation: :c,image(Eqs/rotate.jpg) -where V is the volume of the box, [X] is the original vector quantity and -[x] is the vector in the LAMMPS basis. - -If it should happen that -[A], [B], and [C] form a left-handed basis, then it is necessary -to first apply an inversion in addition to rotation. This can be achieved -by interchanging two of the basis vectors or changing the sign of one of them. +where {V} is the volume of the box, [X] is the original vector quantity and +[x] is the vector in the LAMMPS basis. There is no requirement that a triclinic box be periodic in any dimension, though it typically should be in at least the 2nd dimension
Command Input Output
thermo_style custom global scalars screen, log file
dump custom per-atom vectors dump file