Mollweide Interrupted

images\sc_projections_mollweide_int.gif

 

A pseudocylindrical, equal area projection. Also known as Homolographic projection, Homalographic projection, Babinet projection, and Elliptical projection. The Molleweide Interrupted projection is a variation of the Mollweide projection.

 

The Clip Coordinates checkbox must be checked when projecting maps into Mollweide Interrupted.

 

Scale

 

True along latitudes 40°44’ North and South.

 

Scale is constant along any given latitude and the same for the latitude of opposite sign.

 

Distortion

 

Free of distortion only at latitudes 40°44’ North and South on the central meridian. Distortion is severe near outer meridians at high latitudes.

 

Usage

 

The Mollweide Interrupted is used to display the oceans of the world. For example, for voyagers it's a nearly perfect projection to show the path of a circumnavigation via the Panama Canal and the Red Sea.

 

Origin

 

Presented by Carl B. Mollweide (1774 - 1825) of Germany in 1805.

 

Options

 

Clip Coordinates must be checked.

 

Tech Tip

 

Interrupted projections are not continuous coordinate systems. They employ multiple conversion domains with blank space between the different lobes of the conversion domains. It is absolutely essential to check the Clip Coordinates box in the Projection dialog whenever using such projections. This box causes Manifold to clip each object so that it exists only within the allowed conversion domain lobes and does not extend or cross through disallowed blank space. This is a highly computationally intensive process so the Clip Coordinates box is not checked by default, so that significant overhead is not imposed if it is unnecessary.

 

Dealing with the separate conversion domain lobes of an interrupted projection requires a manual approach to creating graticules, since the graticule lines normally extend through the blank space between lobes.

 

Use the following procedure:

 

1. Create a latitude / longitude drawing.

2. Use the View - Graticule tool to create the desired graticule, using the option to Create the graticule as line objects.

3. Project the drawing into the desired interrupted projection, making sure to check Clip Coordinates.

4. Edit the graticule lines by selecting undesired lines and deleting them, or by adding lines.

 

For many uses the fastest method is to add lines. Suppose we begin with a latitude / longitude drawing in which a graticule was created with lines every 10 degrees from -180 to 180 longitude and from -70 to 70 latitude.

 

images\sc_graticule_int_01.gif

 

After projection into Mollweide Interrupted with Clip Coordinates checked, the lines that appear on the edges of the conversion domain lobes will have been deleted.

 

images\sc_graticule_int_02.gif

 

images\btn_snapto_lines.gif images\btn_shp_line.gif We can add lines by clicking Snap To Lines and then using the Insert Line tool to add lines between the "dangling" parallels. This goes very rapidly with less than a minute required to complete the graticule.

 

images\sc_graticule_int_03.gif

 

The result will be a graticule grid with lines restored that were deleted by Clip Coordinates. This procedure was used to create the graticule seen in the interrupted projection illustration above.