Type of system:
X Y Z lefthanded
X Y Z righthanded
Y X Z lefthanded
Y X Z righthanded
Northing Easting Height
Easting Northing Height
If required, rotate, scale and shear with respect to
origin of the system
barycentre of list
first point of list
last point of list
Rotation direct. for ε>0
01
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
02
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
03
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
04
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
05
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
06
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
07
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
08
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
09
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
10
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
11
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
12
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
13
no action
shift along x axis
shift along y axis
shift along z axis
scale factor of x axis
scale factor of y axis
scale factor of z axis
scale factor of x and y axis
scale factor of all axes
2D rotation angle
Eulerian angle for rotation about x axis
Eulerian angle for rotation about y axis
Eulerian angle for rotation about z axis
Eulerian axis, x vector component
Eulerian axis, y vector component
Eulerian axis, z vector component
rotation angle about Eulerian axis
quaternion, 0th component
quaternion, 1st component
quaternion, 2nd component
quaternion, 3rd component
shear factor for y vs. x axis
shear factor for z vs. x axis
shear factor for z vs. y axis
shear factor for x vs. y axis
shear factor for x vs. z axis
shear factor for y vs. z axis
shear angle for y vs. x axis
shear angle for z vs. x axis
shear angle for z vs. y axis
shear angle for x vs. y axis
shear angle for x vs. z axis
shear angle for y vs. z axis
14 if lefthanded ⇄ righthanded: reflexion at the yz plane