Lecture 2 Cartographic Principles

Study Notes

Geodesy is the science of determining Earth's size and shape.
Early maps often depicted Earth as flat, but Aristotle (384-322 BC) understood Earth to be spherical.
Aristotle roughly calculated Earth's circumference to be 45,500 miles (approximately 24,902 miles).
Eratosthenes (around 250 BC) refined this calculation, using observations of sun rays to get a nearer estimate (approximately 25,000 miles).
Modern GPS satellites now accurately determine Earth's shape.
Earth's surface is irregular, not perfectly oblate.
A geoid is a smoothed representation of Earth's topography.
An ellipsoid (oblate spheroid) is typically used for mapping because it's simpler and more accurate for most purposes.

A map projection is a mathematical process to represent a spherical or ellipsoidal Earth on a flat surface.
This process leads to unavoidable distortions in shape, area, distance, or direction.
Various projections exist, each designed for specific purposes, some in widespread use.

The simplest form uses parallel rays to project a globe onto a flat surface (orthographic).
Other variations (like stereographic) adjust ray positions.

The Earth is wrapped around an imaginary cone, which is then "unfolded" to produce a map.
Rays are traced onto the cone and then the surface is unfolded into a flat map.

The Earth is wrapped around an imaginary cylinder.
Rays are traced onto the cylinder, then the cylinder is "unfolded" to produce a flat map.

Distortion in maps is inevitable due to the transition from a spherical/ellipsoid shape to a flat surface.
Every projection has a characteristic distortion pattern.
Cones and cylinders are used to create surfaces with zero curvature when representing the earth.

All map projections introduce errors.
Distortion can affect conformity (consistent scale), shape, direction, area, and scale relative to Earth's surface.

Geodesy has a long history, and Earth is not flat; it's an oblate spheroid.
Maps are projected, converting 3D to 2D.
Map projections are planar, cylindrical, or conic, and all have associated distortions.