11454

Projecting a Circle on a Sphere to an Enclosing Cylinder

A cylindrical projection maps points on a sphere to a cylinder wrapped around the sphere at its equator.
Several cylindrical mappings are possible, depending on the function that maps on the sphere to on the enclosing cylinder. The most common ones are the equidistant and the equal area cylindrical projections.
This Demonstration shows those two projections of a spherical circle. You can move the circle on the sphere by rotating it about either the or axis.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The transformation formulas used in this Demonstration are based on the Mathematica built-in function ToSphericalCoordinates and the conversion formulas in [1, 2].
For the equidistant projection, the following mapping is used to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the cylinder wrapped around it: 
.
The equidistant projection to a plane uses the following mapping to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the 2D plane: .
For the equal area projection, the following mapping is used to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the cylinder wrapped around it: .
The equal-area projection to a plane uses the following mapping to convert the Cartesian coordinates of a point on the unit sphere to the corresponding point on the 2D plane: .
References
[1] E. W. Weisstein. "Cylindrical Equidistant Projection" from MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/CylindricalEquidistantProjection.html.
[2] E. W. Weisstein. "Cylindrical Equal-Area Projection" from MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/CylindricalEqual-AreaProjection.html.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+