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