Introduction

In this project we analyzed and implemented an algorithm for embedding points on a sphere unto a plane. Low distortion embeddings are used in a variety of applications. A practical example of low distortion embeddings is gel electrophoresis images which involves surveying the protein contents of cells and then using this for DNA matchings and genetics. Embeddings also make it possible to compare certain structures, like images of fingerprints, DNA, bacteria and so on.

The input metric space is the surface of a sphere with the geodesic distances between pairs of points and the output metric space is the plane with the euclidean distances between pairs of points.

Introduction
Theoretical Background
Overview
Code
Input Points
Projection Point
Transforming the Points
Results
Screenshots of Results
Analysis of Results
Characteristics of Map Projections 
Comparison with other Map Projections
Modified Stereographic Projection
Modified Stereographic Projection Results
Screenshots of Results (Modified Stereographic Projection)
Conclusion

PDF files
Report on Sphere Embedding Project