orth_to_frac {cry}

From orthogonal to fractional coordinates

Description

This function transforms any number of orthogonal coordinates (x,y,z), arranged as a vector or in a matrix or data frame, into the corresponding number of fractional coordinates (x_f,y_f,z_f), arranged in the same format.

1. ochoice = 1: X axis along a; Y axis normal to a, in the (a,b) plane; Z axis normal to X and Y (and therefore parallel to c*).

2. ochoice = 2: this is also called "Cambridge setting". The X axis is along a*; the Y axis lies in the (a*,b*) plane; the Z axis is, consequently, along c.

Usage

orth_to_frac(xyz, a, b, c, aa, bb, cc, ochoice = 1)

Arguments

xyz

A vector or n\times 3 matrix or data frame of orthogonal crystal coordinates.

a

A real number. One of the unit cell's side lengths, in angstroms.

b

A real number. One of the unit cell's side lengths, in angstroms.

c

A real number. One of the unit cell's side lengths, in angstroms.

aa

A real number. One of the unit cell's angles, in degrees.

bb

A real number. One of the unit cell's angles, in degrees.

cc

A real number. One of the unit cell's angles, in degrees.

ochoice

A natural integer indicating the choice of orthogonal transformation. 1 corresponds to the first choice and 2 to the second choice in Giacovazzo's book (see xtal_mat01 and xtal_mat02).

Value

A n\times 3 matrix or data frame of fractional coordinates corresponding to the orthogonal coordinates provided in the input.

Examples

# Matrix containing 3 orthogonal coordinates
xyz <- matrix(c(5, 15, 10, 2, 10, 8, 1, 1, 1),ncol=3,byrow=TRUE)

# Fractional coordinates
xyzf <- orth_to_frac(xyz,10,30,20,90,90,90,1)