## Creation of orientation

### Description

The orientation.create function creates the orientation vectors of a plane:

• from 3 points A, B and C (see details),

• or from 2 vectors B and C, resp. defining x and y-axis (see details),

• or from 2 points A, B defining x-axis, and the normal vector to the plane (see details),

• or from a vector B defining x-axis, and the normal vector to the plane (see details).

### Usage

orientation.create(A = c(0, 0, 0), B = NULL, C = NULL, normal = NULL)


### Arguments

 A Vector of the x, y and z coordinates of point A, by default equal to c(0,0,0) in the case where B and C are vectors. B Vector of x, y and z coordinates of point or vector B. C Vector of x, y and z coordinates of point or vector C. normal Vector of x, y and z coordinates of normal vector.

### Details

When using B and C, B-A define the x-axis unit vector. The unit vector of the y-axis is orthonormal to the x-axis, coplanar with A, B and C, and in the direction of A to C.

When using B and normal, the unit vector of the x-axis is orthonormal to the normal vector, in the direction of A to B. The unit vector of the y-axis is defined so as to constitute a direct orthonormal basis with the unit vector of the x-axis and the normal vector of the plane.

### Value

Returns the orientation of the plane. That means the concatenation of 2 vectors, defining an orthonormal basis of the plane.

### Examples

A <- c (-29.93, 18.85, 4.34)
B <- c (28.73, 15.36, 4.46)
C <- c (1.53, 75.21, 13.51)
orientation.create (A, B, C)