Cartography and Geographic Information Systems
Reference systems and projections
Every layer sits on a coordinate reference system: a datum plus a projection. Geographic coordinates in degrees cannot be used directly for area, distance or buffer operations. Choose projections by purpose: UTM is conformal, preserving angles and small shapes but distorting area by the square of the scale factor; Albers and Lambert azimuthal equal-area preserve area; equidistant projections preserve distance along specified lines only. Trap: "reprojecting" a raster actually resamples it, and categorical data must use nearest-neighbour to avoid inventing classes.
Data models and analysis
Vector models (points, lines, polygons) represent discrete features; raster models represent continuous fields as cells. Topology encodes adjacency, connectivity and containment, prevents slivers and gaps, and enforces shared boundaries. Distinguish overlay operations (union, intersect, clip) from buffering and from spatial joins; each answers a different question.
Design and generalization
Generalization operators include simplification, smoothing, aggregation, amalgamation, collapse, displacement, exaggeration and classification; what is retained depends on scale. Symbolization: choropleth for rates and densities (never raw counts), isopleth for continuous surfaces, graduated symbols for magnitudes, dot density for distributions.
Data quality and accuracy
Quality elements are positional accuracy, attribute accuracy, logical consistency, completeness, temporal quality and lineage (metadata). National map accuracy standards require well-defined points to plot within about 0.5 mm at map scale for 90% of points; ASPRS reports at 95% confidence. Rule of thumb: minimum mapping unit is roughly 0.5 mm at map scale.
Worked example
At 1:50 000, 0.5 mm on the map equals 0.0005 x 50 000 = 25 m on the ground. A dataset with horizontal RMSE of 18 m corresponds to about 1.96 x 18 = 35 m at 95% confidence - so state which standard and confidence level you are quoting before declaring a dataset compliant.