CoordinateSystemsC

Version 0.92
9/12/91
by John B. Schneider

Spherical Coordinates

Two dimensions

There is no such thing as a two-dimensional spherical coordinate system.  However, we could construct one.  It wouldn't be very interesting, though.  It would be the same as two-dimensional cylindrical coordinates.  So, there is nothing to see here.  On to three dimensions¼

Three dimensions

The spherical coordinate system is similar to the three-dimensional cylindrical coordinate system.  In spherical coordinates, a point is specified by an ordered triplet (r,theta,phi).  The value of r gives the distance from the origin and by itself describes the surface of a sphere which has the origin at its center.  The value theta specifies the angle that is formed between a ray that starts at the origin and passes through the point of interest and the positive z axis.  Theta, by itself, specifies a cone which has its apex at the origin and is concentric with the z axis.  Phi is the same as phi in cylindrical coordinates.  The phi value of a particular point is obtained by first projecting the line that joins the origin and the point of interest onto the xy plane.  Then, phi is the angle formed by this projected line and the positive x axis (measured in the counter-clockwise direction).  The intersection of the sphere, cone and half plane specifies a unique point.
       
       As before, we will move from the origin to the point (3,2,1) (Cartesian coordinates).  We will move by first increasing r, then theta, and then phi.  A dot will indicate the point specified by the current values of the coordinates.  If one of the coordinates has a value of zero, the surface that it specifies will not be shown.

Increasing r

Increasing theta

Increasing phi

Increasing r, theta, and phi

You can tie all of the three-dimensional spherical coordinate system animations together.  To do this you must have at least one of the cells above open that shows the three-dimensional graphics.  You then must click on the line that is the second furthest to the right, then hit Command-y.