change_coordinate_system

[zuofy]

Is there an issue here? When I used the change_coordinate_system function to invert the directions of the y-axis and z-axis (OpenCV → OpenGL), the c2w and w2c matrices did not update correctly. Is there a problem with my configuration? Or should the statement in the change_coordinate_system function (self.R = self.R @ basis_change) be modified?

[orperel]

Hi @zuofy -

you're attempting to follow this conversion:

so you did right by negating the axes in the basis change matrix.

What were the target W2C and C2W matrices you expected after the basis change? I see the new W2C has the 2nd and 3rd columns negated, and the C2W matrix has the 2nd and 3rd rows negated, that should be the intended behavior

[orperel]

To clarify, see this internal comment which explains the derivation of this function:

        # One prevalent form of performing coordinate change is swapping / negating the inverse view matrix rows.
        # That is - we want to alter the camera axes & position in WORLD coordinates.
        # Note it's enough however, to multiply the R component of the view matrix by the basis change matrix transpose
        # (recall we rotate about the world origin, which remains in place).
        #
        # Compare the inverse matrix before after basis change:
        #               Pre basis change:
        #     view_matrix =             inverse_view_matrix =           Rt is R transposed
        #       [ R | t ]                 [ Rt | -Rt @ t ]              @ denotes matrix column multiplication
        #       [ 0 | 1 ]                 [ 0  |   1     ]
        #
        #               Post basis change:
        #     view_matrix =             inverse_view_matrix =                    P is the basis change matrix
        #       [ R @ Pt | t ]                 [ P @ Rt | -(P @ Rt) @ t ]        Pt is the transposition of P
        #       [ 0      | 1 ]                 [ 0      |       1       ]
        #
        #                                =     [ P @ Rt | P @ (-Rt @ t) ]
        #                                      [ 0      |       1       ]

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