Week 2 · Ground Station Operator~7 min · 689 words

Vector vs raster, and map projections

Vector vs raster is the fundamental data-model split in GIS. Then comes projections: how do you flatten a sphere onto a screen? This week covers Web Mercator, UTM, equirectangular, and polar stereographic, and when each is right.

Why does Greenland look bigger than all of Africa on Google Maps — when in real life Africa is 14 times bigger?

It is not a mistake — it is a choice the map-makers made. The same choice happens every time you flatten a sphere onto a screen. This week, you will see exactly what's getting distorted, and you'll learn how to pick a projection that's honest for your work.

Learning objectives

Hawaiian Islands. This map uses Web Mercator (the same projection as Google Maps). At Hawaiian latitudes the distortion is small (~6%); at high latitudes it gets dramatic. Try zooming out — see how the curvature of Earth gets flattened away?

Try it: see Mercator distortion

Web Mercator preserves angles but distorts size at high latitudes. Move the slider; the bar shows how much one square kilometer of ground gets stretched on the map at that latitude.

truth Web Mercator at 21°

Primer

Geospatial data comes in two fundamental forms: vector and raster. Choosing the right model for a task is one of the highest-leverage decisions in a GIS workflow because almost every operation downstream (storage, querying, analysis, rendering) is asymmetric between the two.

Vector data: points, lines, polygons

Vector data represents the world as discrete geometric objects with attributes. A spaceport is a point. A rocket's ground track is a line (or a multiline if it crosses the dateline). A range-safety exclusion zone is a polygon. Each feature has a geometry and an attribute table — like a spreadsheet where one column happens to be geometry.

Vector data is best for things that are precisely located and countable. The GeoJSON format is the lingua franca:

{
  "type": "FeatureCollection",
  "features": [
    {
      "type": "Feature",
      "geometry": {"type": "Point", "coordinates": [-80.6, 28.6]},
      "properties": {"name": "Kennedy Space Center", "operator": "NASA"}
    }
  ]
}

Raster data: gridded pixels

Raster data is a grid of cells, each holding a value. A satellite image is a raster. A digital elevation model is a raster. A thermal brightness-temperature map is a raster. The grid is defined by an extent, a resolution (cell size in real-world units), and a coordinate system; every cell has an implicit position derived from its (row, col) index.

Raster data is best for continuous fields — temperature, elevation, reflectance — and for anything sampled at regular intervals. The GeoTIFF format is the lingua franca. rasterio is the standard Python library:

import rasterio
with rasterio.open('goes18_band7.tif') as src:
    band7 = src.read(1)  # numpy array, shape (height, width)
    transform = src.transform  # maps (row, col) → (x, y)
    print(f"Shape: {band7.shape}, dtype: {band7.dtype}, CRS: {src.crs}")

Map projections: flattening the sphere

Earth is approximately an ellipsoid. Screens are flat. Every projection is a mathematical compromise: you can preserve shape (conformal), area (equal-area), or distance (equidistant), but never all three. The right projection depends on what you're trying to do.

Web Mercator (EPSG:3857) is conformal — it preserves angles, which makes it ideal for slippy web maps where the user pans and zooms freely. It catastrophically distorts area near the poles (Greenland looks the size of Africa). Never compute areas in Web Mercator.

Universal Transverse Mercator (UTM) divides Earth into 60 zones, each 6° wide. Within a single zone, UTM is conformal AND nearly equidistant. It's the right projection for any local analysis where you need accurate distance and area at city or regional scale. Cape Canaveral is in UTM zone 17N (EPSG:32617).

Equirectangular (plate carrée, EPSG:32662) just plots latitude vs longitude as x vs y. It's the cheapest projection — a one-to-one map of degrees to pixels — and it's how most full-globe satellite imagery is published (including GOES "geographic" products). It badly stretches near the poles but is fine near the equator.

Polar stereographic (EPSG:3413 north, 3031 south) is the right choice when you actually care about the poles: Antarctic sea-ice extent, Arctic shipping lanes, polar-orbiting satellite ground tracks at high latitudes.

Picking a projection for a launch trajectory

A SpaceX Falcon 9 from Cape Canaveral arcs east over the Atlantic, ascending through ~120 km. To display the trajectory on a globe, equirectangular or Web Mercator is fine. To measure the downrange distance, project to UTM 17N for the early ascent, then use a great-circle calculation for the longer arc. To compute the maritime exclusion polygon (overlapping shipping lanes), keep everything in WGS84 lat/lon and use geodesic operations.

The lab walks through reprojecting a real Falcon 9 trajectory through three projections and shows visually (and numerically) what each one does to your distances. The takeaway you'll keep for the rest of the course: choose a projection per task, not per workflow. A single pipeline often touches three or four CRSes.

Connecting to Hawaiʻi: Projections and Hawaiʻi's place on the map

On most world maps you've seen in school, Hawaiʻi looks like a tiny speck near the edge. That is not because Hawaiʻi is small — it's because the projection used (Web Mercator) puts the focus on Europe and North America and stretches everything near the equator. Switch to a Pacific-centered projection (`+proj=merc +lon_0=180`) and suddenly Hawaiʻi is at the CENTER of the world map — because the Pacific Ocean really is the center of the world for the people who live in it. A map is never neutral. It always answers a question. The question European cartographers asked was 'how do I draw the Atlantic without breaking it?' The question we should ask is 'how do I draw the Pacific without breaking it?'

Try this: open Wikipedia, search 'Pacific-centered map.' That is the world from a Hawaiian perspective. Notice how it changes which countries feel like neighbors and which feel far away.

Hands-on lab: Reproject a launch trajectory

Take a Falcon 9 launch trajectory in lat/lon and reproject it into UTM, Web Mercator, and equirectangular. Compare the visual results and the computed track lengths.

Quiz — click an answer to check it

No grade, no shame. Tap any option; you'll see if it's right plus the answer if not. The point is to notice what you already know and what's still settling.

Q1. A satellite image is what kind of GIS data?
  1. Vector
  2. Raster
  3. Both
  4. Neither
Q2. Web Mercator is bad for showing what?
  1. Streets in Manhattan
  2. Antarctic ice extent
  3. Houston city limits
  4. Local highway networks
Q3. UTM zones are how wide?
  1. 3 degrees
  2. 6 degrees
  3. 10 degrees
  4. 15 degrees
Q4. Equirectangular is also called:
  1. Mercator
  2. Plate carrée
  3. Polar azimuthal
  4. Albers
Q5. For a polar orbiting satellite ground track, which projection is most appropriate?
  1. Web Mercator
  2. UTM
  3. Polar stereographic
  4. Albers conic

Reflection

Take five minutes with this. Write your answer somewhere. Carry it into next week.

Which projection do you think a map of Hawaiʻi should use? Why? What would change about your reasoning if the map were going to be used for navigation, vs. for teaching kids in school, vs. for measuring a coral reef's size?
Mark this week complete Visiting alone doesn't count it as 'done'. Click when you've actually worked through the primer + lab + quiz.
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