Mapping Concepts: Coordinate Systems, Map Projections, and Cartography

Coordinate Systems

• Expressing the position of a point requires more than a single quantity.

• Coordinates are two or more quantities or parameters that define a point's position within a coordinate system.

Coordinates

• Cartesian Coordinates:

  • 2-dimensional: $(x, y)$ (e.g., $(3, 3)$).

  • 3-dimensional: $(x, y, z)$.

• Polar Coordinates:

  • Defined by radius $(r)$ and angle $\theta$ (e.g., $(20, 30^\circ)$).

• Spherical Coordinates:

  • Defined by radius $(r)$, polar angle $\theta$, and azimuthal angle $\phi$ (e.g., $(10, 25^\circ, 55^\circ)$).

• Commonly-used Coordinates in Surveying:

  • Local Coordinates

  • Geographic Coordinates

  • Projected/Grid Coordinates

Local Coordinates

• Non-unique; typically use $(20000 N, 20000 E)$ as the coordinates of a tie point (reference point).

• Example tie points: BLLM No. 1 in Manila, QC, Malabon, Pasig, all using $(20000 N, 20000 E)$.

Geographic Coordinates

• Latitude and longitude.

• Assume the Earth is a sphere; radius is not included in the parameters.

• Unique.

• Examples:

  • BLLM No. 1, Manila: $14^\circ 35' 05.83” N, 120^\circ 58' 40.94” E$

  • BLLM No. 1, QC: $14^\circ 38' 36.70” N, 121^\circ 3' 29.12” E$

  • BLLM No. 1, Malabon: $14^\circ 40' 22.80” N, 120^\circ 57' 52.09” E$

  • BLLM No. 1, Pasig: $14^\circ 34' 3.26” N, 121^\circ 5' 21.48” E$

Projected/Grid Coordinates

• Northing and Easting values.

• Use a mathematical model (datum) to project coordinates onto a plane surface.

• 2-dimensional, same as local coordinates.

• Account for the fact that the Earth is not a perfect sphere.

• Unique.

• Examples:

  • BLLM No. 1, Manila: $1 258 177 N, 522 022 E$

  • BLLM No. 1, QC: $1 258 216 N, 522 043 E$

  • BLLM No. 1, Malabon: $1 258 251 N, 522 019 E$

  • BLLM No. 1, Pasig: $1 258 158 N, 522 057 E$

Geographic vs Projected/Grid

• Geographic: Latitude $\Phi$ and Longitude $\lambda$.

• Projected/Grid: Northings $(N)$ and Eastings $(E)$.

• The Philippine Reference System of 1992 (PRS 92) uses a datum coordinate system.

• Earlier system: Luzon Datum of 1911.

Map Projections

• A systematic projection of all or part of the surface of a round body (especially Earth) onto a plane (Snyder, 1987).

• Transforms the Earth’s surface for use in a map.

From Spheroidal to Plane Surface

• Mathematical transformations are used to convert from spheroidal to plane coordinates.

• Globes are