Purpose of `3.f` offset in Pixel-Grid Point Conversions about camera_calibration HOT 1 CLOSED

Looking at the computation in PixelCornerConvToGridPoint() for the x coordinate as an example:

1.f + (m_grid_width - 3.f) * (x - m_calibration_min_x) / (m_calibration_max_x + 1 - m_calibration_min_x)

• If the function is called with x == m_calibration_min_x, then (x - m_calibration_min_x) will be zero, so this will result in a grid point x coordinate of 1.f.
• If the function is called with x == m_calibration_max_x + 1, then the quotient on the right will be one, so this will result in a grid point x coordinate of m_grid_width - 2.f.

This range of values is returned because there is one extra grid point placed beyond the calibrated image area on each of its sides. This has the purpose of providing a full 4x4 surrounding patch of grid values for interpolation for every pixel location within the calibrated image area.

So, a more descriptive formulation might for example be:

constexpr int kExternalPoints = 1;
[...]
kExternalPoints + (m_grid_width - 2 * kExternalPoints - 1) * (x - m_calibration_min_x) / (m_calibration_max_x + 1 - m_calibration_min_x)

The -3.f is thus computed from - 2 * kExternalPoints - 1, where 2 * kExternalPoints accounts for the external points on each side, and the -1 accounts for "computing the index of the last point from the point count" with a starting index of zero (rather than one).

from camera_calibration.