Chapter C. Mathematical Surface

1. Background

Point positions can be expressed in relative or absolute terms.

• A relative position is generally a distance and direction from another point. These are typical in smaller scale surveys.
• Absolute positions are angles or distances from a reference system origin. These require a mathematical framework covering larger, even global, areas.

Although we measure on the physical Earth while referenced to the geoid, both of those surfaces are irregular. For small areas measurements can be referenced to a flat plane. With larger projects, however, the Earth's configuration must be accounted for. For this, we need a mathematical model. Since the Earth (and geoid) are flattened at the poles and bulging at the equator, an oblate spheroid fits the bill.