What is the correct sequence in transforming from a geoid to a projected coordinate system?

The correct sequence of transformation from a geoid to a projected coordinate system starts with the geoid, which represents the mean sea level and is an irregular surface that serves as a reference for understanding elevations and depths on Earth.

From the geoid, the transition to the spheroid occurs next. A spheroid is a mathematically simplified version of the Earth's shape, which approximates it as an oblate ellipsoid. This transformation is crucial because the spheroid provides a consistent and manageable mathematical model to represent the Earth's surface.

After defining the spheroid, the geographic coordinate system is established. This system uses angular measurements (latitude and longitude) based on the spheroid model to describe locations on the Earth's surface. Geographic coordinates allow for a standard way to reference positions globally.

Finally, the transformation concludes with the projection of these geographic coordinates onto a flat surface, resulting in a projected coordinate system. This step is essential for mapping and spatial analysis because it creates a two-dimensional representation that can be measured and analyzed on paper or digital screens.

This sequence illustrates the logical and necessary steps involved in transitioning from the geoid through to a projected coordinate system, effectively capturing the hierarchy of representation from a physical, three-dimensional earth model to a two-dimensional mapping framework.