Geo-Information

E3: Georeferencing and Modifying Features

Warm Up

You will find detailed guidance and general information about CRS (Coordinate Reference Systems) and map projections in another document associated with this exercise.
Here, we will take a step further to deepen your understanding.

---

Mathematical aspects of projections

Why can’t the Earth (or an orange peel) be flattened without distortion?

This question is fundamentally about curvature. From a mathematical perspective, Gauss’s Theorema Egregium(thanks Gaussian again!) tells us that the intrinsic curvature of a surface is preserved under transformations that do not stretch or tear.
Since the Earth is (approximately) a sphere, and a sphere has positive curvature while a flat plane has zero curvature, you cannot map one onto the other without distortion.

For a fun and visual explanation, see: The clever way curvature is described in math, or There is a wonderful way of eating pizza, but you don’t know why

• Reversibility:
  Most common map projections are not perfectly reversible. Once a spherical surface is projected onto a plane, certain geometric properties are altered (e.g., distances, areas, or shapes).
  • Example: A Mercator projection preserves angles but heavily distorts area; reversing it requires knowing the original CRS and applying a non-linear transformation.
• Security considerations:
  In some sensitive applications, datasets may use intentionally unusual or undocumented projections to hinder reverse engineering or prevent accurate coordinate transformation — a kind of cartographic encryption. This is common in many applications you use every day, such as Google Maps or Apple Maps, especially when you use the API.

---

Great-circle navigation and shortest paths

On a sphere, the shortest path between two points is along a great circle (the intersection of the sphere with a plane passing through its center). In many map projections, this shortest route appears curved — especially in maps like Mercator — even though it is the geodesic path on the globe.

• This has practical importance in:
  • Aviation and maritime navigation: Great-circle routes minimize fuel and time.
  • Geodesy and surveying: Accurate shortest-path computation requires the Earth’s ellipsoidal shape, not just a sphere.

• Example: The flight path from Frankfurt to Los Angeles looks like an arc over Greenland on a Mercator map, but it is nearly a straight great-circle route on a globe. {figure} ../images/ex3/FRA-LAX.png --- name: FRA-LAX-fig --- The flight path from Frankfurt to Los Angeles

• From the perspective of geodesy, a geodetic line is the shortest path between two points on a curved surface, such as the Earth’s surface.
  • On a sphere, it corresponds to a great circle; on an ellipsoid, it is slightly curved and does not maintain a constant bearing.
  • An interesting fact is that the initial bearing from A to B is not the same as the initial bearing from B to A on an ellipsoid. This is because the Earth’s curvature is not uniform in all directions — the ellipsoid is flattened at the poles — so the geodetic azimuth changes along the path. Although the path itself is the same geometric curve in both directions, the bearings at the start and end points differ(Earth is not perfect sphere, even not a perfect ellipsoid).

Projections

• Classification by preserved property:
  1. Conformal projections — preserve local angles/shapes (e.g., Mercator, Lambert Conformal Conic).
  2. Equal-area projections — preserve area measurements (e.g., Albers Equal Area, Mollweide).
  3. Equidistant projections — preserve distances from one or two points/lines (e.g., Azimuthal Equidistant).
  4. Compromise projections — minimize overall distortion without fully preserving one property (e.g., Robinson, Winkel Tripel).

```{figure} ../images/ex3/mercator_size.gif

name: Mercator-fig — World Mercator projection with country going to true size

- **Units and computation in a CRS**:  
  - In **projected coordinate systems**, distances and areas are measured in linear units (meters, feet).  
  - In **geographic coordinate systems**, coordinates are in degrees; calculating distances requires spherical or ellipsoidal formulas.  
  - Area computation on a sphere/ellipsoid involves integrating over curved surfaces and must account for the CRS.

---

> **Takeaway**: No single projection can preserve all spatial properties. Your choice of projection should be guided by the task:  
> - Preserve shape for navigation and angular measurements.  
> - Preserve area for thematic mapping and statistics.  
> - Use compromise projections for balanced world maps.



## Task
### Descriptions
In this exercise, you’ll deepen your understanding of **coordinate reference systems (CRS)** and **map projections**, learn how to **minimize distortion** by reprojecting data into a local system, and practice **spatial editing workflows** in ArcGIS Pro. Detailed instructions in {download}`Lesson 3 <../doc/Lesson 3.docx>`

& You can [Click here to look](/Geo-Information/content/lessons/lesson3.html)

#### Data
  - `Data Students.gdb`
  - `orthophoto.tif`
  - `construction_plan.png`
  - `Address_points.txt`
  - `Housenumbers.txt`


### Overview
```{note}
:class: dropdown
- [ ] Change the map projection to a local **UTM** projection and set units to meters.
- [ ] Calculate and assign the correct **UTM zone** to your dataset.
- [ ] **Georeference** a raster (orthophoto and construction plan) to align with existing vector data.
- [ ] Add and visualize tabular data by:
  - Creating point features from XY coordinate tables.
  - Geocoding addresses without coordinates.
- [ ] Modify existing features by:
  - Editing and reshaping vertices.
  - Adding new polygons from construction plans.
  - Splitting polygons into separate features.
  - Clipping polygons to remove overlaps.

1. Specifying Map Projections and Coordinates

• Calculate the UTM Zone:
  • Add a new text field UTM_zone to the buildings layer (length = 600).
  • Use the Calculate UTM Zone tool to determine the correct zone (likely ETRS 1989 UTM Zone 32N).
• Change Map Projection:
  • Open Map Properties → Coordinate Systems.
  • Set to ETRS 1989 UTM Zone 32N under Projected Coordinate System > UTM > Europe.
  • Change display units to Meters.

2. Georeferencing a Raster

• Toggle on the orthophoto layer.
• Zoom to the target vector layer (buildings).
• Use Imagery → Georeference tools:
  • Set SRS, turn off unrelated layers.
  • Add 6–10 control points matching raster features (e.g., building corners) to vector data.
  • Use a 1st Order Polynomial transformation.
  • Remove points with high residuals, then Save.

3. Adding Tables

• Coordinate Table to Points:
  • Add Address_points.txt to the project.
  • Use XY Table To Point tool: X = Longitude, Y = Latitude, CRS = WGS84.
• Geocoding:
  • Add Housenumbers.txt.
  • Use Geocode Table guided workflow:
    • Locator: ArcGIS World Geocoding Service.
    • Map multiple address fields.
    • Preferred Location Type: Address Location.
    • Limit to Germany.
    • Output as point layer.

4. Modifying Features

• Snapping
  • Enable Vertex Snapping in Edit → Snapping.
• Modify Vertices
  • Select building with OBJECTID=954.
  • Enable Map Topology.
  • Use Modify → Edit Vertices to align it with adjacent building rows.
• Reshape & Add Vertices
  • Georeference construction_plan.png to buildings layer.
  • Delete demolished buildings (OBJECTID=1901 & 1902).
  • Reshape OBJECTID=1653 to reflect partial demolition.
  • Digitize new building footprints from the plan.
  • Save edits; create a new template if needed.
• Split a Feature
  • Select polygon with OBJECTID=1859 (State Museum of Egyptian Art + University of Television and Film).
  • Use Modify → Split to separate into two polygons.
  • Update name field accordingly.
• Clip a Feature
  • Select lawn polygon from Lesson 1.
  • Use Clip tool with Alte Pinakothek building as clip feature.
  • Discard clipped interior and preserve remainder.

Advance Task

• Vector data (e.g., Shapefile)
  • Load and print basic info: CRS, feature count, extent.
  • Reproject to another CRS and compare length/area differences.
  • Join attribute tables based on a key field.
• Raster data (e.g., GeoTIFF)
  • Load and check CRS, resolution, and extent.
  • Reproject to match a vector layer’s CRS.
  • Clip by a polygon boundary.
• Georeferencing check
  • Calculate RMS error from control points.
  • Test different transformation orders (1st-order vs. 2nd-order) and compare accuracy.

---

Materials

• Overview of georeferencing
• Work with Coordinate Systems
• Supported map projections
• Geographic datum transformations
• geopandas.GeoDataFrame.crs
• Georeferencing — rasterio 1.5.0.dev documentation