Datum conversions are accomplished by various methods. Complete datum conversion is based on seven parameter transformations that include:

• A. Four translation parameters, two rotation parameters and a scale parameter
• B. Two translation parameters, three rotation parameters and a scale parameter
• C. Three translation parameters, three rotation parameters and a scale parameter
• D. One translation parameter, four rotation parameters and a scale parameter

Answer: (C)

In 3D datum conversions, you need enough freedom to align both position and orientation between datums, plus adjust for overall size differences. The seven-parameter model achieves this by using three translations, three rotations, and a single scale factor. The three translations shift the origin along X, Y, and Z so coordinates can be placed in the new datum’s origin. The three rotations account for small angular differences between the axes, aligning the orientation of the two systems. The scale parameter adjusts for any overall size difference between the datums, ensuring distances scale correctly. Together these seven independent adjustments describe the full rigid-body shift plus a uniform scale change, which is why this combination is the standard complete datum-conversion method.

Fewer translations or rotations would leave misalignment uncorrected along one or more axes or orientation components, and more rotations would add unnecessary degrees of freedom without improving the fit.