map-projection

Map projections transform spherical geographic data onto a 2D plane, each introducing different distortions. Selection depends on your region's scale and purpose: conformal projections preserve angles, equal-area preserve total area, equidistant preserve distance from center, and compromise projections balance multiple properties. This Skill helps you identify optimal projections for global, regional, or local data and analyze their distortion trade-offs.

Tissot's indicatrix visualizes how a projection distorts infinitesimal circles on the sphere into ellipses on the plane. It quantifies local scale, angle, and area distortion at any map location. This Skill computes indicatrix metrics to reveal where your chosen projection performs well or poorly, enabling data-driven decisions about projection fit and visualization design.

Yes. This Skill supports both forward transformations (sphere to plane) and inverse transformations (plane back to sphere), paired with distortion metric calculations. You can project geospatial coordinates, compute Tissot indicatrix values at those locations, and categorize projections by type—all within a unified workflow for comparative analysis and cartographic design.

Category theory provides a formal framework for understanding natural transformations between different projections. GF(3)-aware coloring uses mathematical structures to encode and visualize distortion patterns systematically. This Skill leverages both to enable data-driven color-coding of projection properties, making distortion analysis and projection comparison more rigorous and interpretable.

This Skill implements conformal (Mercator, Stereographic), equal-area (Lambert Azimuthal), equidistant, and compromise projection classes. You can instantiate any projection type, apply forward/inverse transformations, compute distortion metrics, and categorize results. Support spans global, regional, and local scales for flexible geospatial analysis.

Yes. By computing Tissot's indicatrix at sample points across your study area and applying GF(3)-based coloring, you can visualize distortion intensity and type spatially. This Skill generates distortion maps that reveal which regions suffer angle loss, area compression, or distance scaling—critical for cartographic design and projection selection across scales.