Camera-to-Model Space Coordinates Mapping

Molecule Tutorials - Herong's Tutorial Examples

∟Camera-to-Model Space Coordinates Mapping

This section provides a tutorial on how to map camera space coordinates to model space coodinates manually using the reverse of the rotation matrix in PyMol.

In the last tutorial, we have used the following mapping relation to map a point in model space to camera space, which is very easy.

Assuming:
  [A_x, A_y, A_z]: a point in model space
  [B_x, B_y, B_z]: model rotation center
  [M₁₁, ..., M₃₃]: the rotation matrix
  [C_x, C_y, C_z]: same point in camera space
  [D_x, D_y, D_z]: camera rotation center

We have the following mapping relation:
  |C_x-D_x|   |M₁₁ M₁₂ M₁₃|   |A_x-B_x|
  |C_y-D_x| = |M₂₁ M₂₂ M₂₃| * |A_y-B_y|
  |C_z-D_x|   |M₃₁ M₃₂ M₃₃|   |A_z-B_z|

But what about mapping a point in the camera space to the model space? It is also easy to do, if you know how to reverse the rotation matrix, using the "numpy" Python module.

1. Load the methane molecule structure to PyMol again. And convert viewing parameters into 'numpy' matrix and vectors:

PyMOL>delete all
PyMOL>load Molecule-Methane.sdf
 CmdLoad: loaded as "Molecule-Methane".

PyMOL>view = cmd.get_view()
PyMOL>M1 = [view[i] for i in range(0,3)]
PyMOL>M2 = [view[i] for i in range(3,6)]
PyMOL>M3 = [view[i] for i in range(6,9)]

PyMOL>M = numpy.matrix([M1, M2, M3])
PyMOL>D = numpy.matrix([[view[9]],[view[10]],[view[11]]])
PyMOL>B = numpy.matrix([[view[12]],[view[13]],[view[14]]])