COMPUTATIONAL GEODESY · 4 WORKBENCHES

The Cartographic Laboratory

Interactive computational instruments for testing mathematical hypotheses, measuring geometric distortions, and simulating spatial travel manifolds.

1. Tissot Distortion Crucible

Distortion Math

THE PROJECTION DISTORTION CRUCIBLE

Mercator Projection (1569)

Inventor: Gerardus Mercator · Family: Cylindrical

Select Projection:

TEST LATITUDE:60° North

0° (Equator)30° (Subtropics)60° (Greenland)85° (Arctic)

Conformal (Angles)

Equal-Area (Sizes)

Compromise Map

Uninterrupted

CONTINENTAL SCALE DISTORTION RATIO:

True geographic area of Greenland (2.16M km²) is 1/14th (0.07×) of Africa (30.37M km²).

Projected Visual Ratio:1:1 (Equal Size!)

TISSOT INDICATRIX (Lat: 60°N)Area: 4.00×

MERIDIAN (h)

2.00

PARALLEL (k)

2.00

ANGULAR (2θ')

0.0°

Cartographic & Political Critique:

"When co-opted into classrooms and wall atlases, Mercator visually inflates imperial powers in North America and Europe while drastically shrinking the African continent, South America, and the equatorial belt."

Formula: h = k = \sec \phiFull Mathematical Dossier

2. Isochrone Travel Manifold Simulator

Mobility Manifolds

ISOCHRONE TRAVEL-TIME MANIFOLD

FRANCIS GALTON (1881) MODEL

TRAVEL DURATION:15 Minutes

5m (Immediate block)15m (15-Minute City)30m (Metropolitan zone)60m (Regional horizon)

REACH RADIUS

1.3 km

CATCHMENT AREA

5.3 km²

THEORETICAL REACH

Local District

3. Gerrymander Compactness Dissector

Political Geometry

POLSBY-POPPER COMPACTNESS DISSECTOR

FORMULA: 4πA / P²

POLSBY-POPPER COMPACTNESS SCORE:

1.000

Area: 314.15 km² · Perimeter: 62.83 km

Standard Compactness

Score demonstrates natural convex geometry.

Distortion Math

Tissot Distortion Crucible

Compute local scale distortion $h, k$, area factor $hk$, and angular shear $2\theta'$ across 14 map projections

Workbench Manual

Mobility Manifolds

Isochrone Travel Manifold

Transform Euclidean metric distance into temporal travel manifolds across multiple transit modes

Workbench Manual

Political Geometry

Gerrymander Compactness Dissector

Calculate Polsby-Popper and Reock geometric compactness metrics for custom electoral polygons

Workbench Manual

Terrain Synthesis

Topographic Contour Synthesizer

Generate procedural island topography with customizable contour intervals and hypsometric OKLCH ramps

Workbench Manual