What projections does this skill support?

It includes implementation patterns for standard projections like Mercator, Albers Equal-Area, and Stereographic, while providing a generic framework for any functor-based projection.

What is the benefit of using category theory for maps?

Treating projections as functors between manifolds ensures mathematical coherence when performing natural transformations between different coordinate systems.

Can this be used with spatial databases?

Yes, it provides specific integration patterns for DuckDB-spatial, including schema designs for projection lookups and suitability analysis.

How does it measure map distortion?

It utilizes Tissot's indicatrix to calculate meridian scale (h), parallel scale (k), and angular or area distortion factors via finite difference Jacobians.

Map Projection Geometry & Analysis

Name: Map Projection Geometry & Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Provides advanced mathematical frameworks for map projection selection, coordinate transformations, and distortion analysis using category theory.

This skill enables Claude to handle complex cartographic tasks by treating map projections as functors between manifolds. It provides implementation patterns for conformal, equal-area, and equidistant projections, along with rigorous distortion analysis using Tissot’s indicatrix. Built for geospatial developers and data scientists, it integrates category theory concepts with practical Python and SQL implementations to ensure mathematical coherence in geographic data transformations and spatial analysis workflows.

Key Features

01Automated distortion analysis using Tissot's indicatrix

02DuckDB-spatial integration for cartographic metadata management

03Functor-based map projection modeling (S² → ℝ²)

04Natural transformation logic for switching between projections

05Transformation patterns for Mercator, Albers, and Stereographic systems

068 GitHub stars

Use Cases

01Implementing custom coordinate transformation functors in Python

02Analyzing and minimizing map distortion for specific geographic regions

03Designing cartographic systems that require rigorous mathematical proofs of property preservation

What are Skills?·How to Install

Install with 🐟 Skill.Fish

npx skillfish add plurigrid/asi map-projection

For use in Claude.ai and ChatGPT

Download Skill