Tutorial
New: There is a similar tutorial with illustrations in the article Flex Projector—Interactive Software for Designing World Map Projections (PDF, 2 MB, tutorial on page 17 and 18).
The example below is a sample workflow that transforms the Plate Carrée projection, a cylindrcal projection with a rectangular shape, to a customized projection with curves similar to the Winkel Tripel. Designing the new projection involves six steps, all of which are controlled from the Flex Projection panel to the right of the map:
1) Reset to projection – Click the Options popup menu in the upper right of the Flex Projection panel and open the Reset to Projection dialog. From the list of projections, replace the default Robinson projection with the Equidistant Cylindrical (Plate Carrée).
2) Proportions – Using the Proportions slider at the top of the Flex Projection panel, increase the height-to-width proportion from 0.50 to 0.61, a value that approximates the proportions of the Winkel Tripel projection.
3) Length of parallels – In the next step you will adjust Length of Parallels to give the new projection the classic bowed shape of a pseudocylindrical projection. With the Length tab selected, specify the following settings at the bottom of the Flex Projection panel:
......Linked Sliders – 17
......Move – Peak-shaped curve
Drag the 90 degree slider to the left until the numerical value for that slider is about 0.35. As you drag the 90 degree slider the other linked sliders will move with it by progressively smaller amounts closer to the equator.
4) Distance of parallels from equator – To lessen areal distortion at the poles, click the Distance tab and specify these settings at the bottom of the panel:
......Linked Sliders – 7
......Move – Peak-shaped curve
Drag the 90 degree slider to the left until the numerical value for that slider is about 0.85. As you do this the size of polar areas will decrease on the map.
5) Bending of parallels – To reduce the north-south elongation of Africa and South America, in the next step you will give the parallels concave bending, except at the poles and equator. Click the Bending tab and specify these settings:
......Curve – Cubic
......Linked Sliders – 17
......Move – Bell-shaped curve
Drag 45 degree slider left until the numerical value for that slider is about -0.20. Then drag the 90 degree slider to right back to 0.0. Doing this will remove concave bending from the pole lines, restricting bending to mid latitude areas only.
6) Projection size – To finish, click the Options popup menu found in the upper right of the Flex Projection panel and open the Projection Size dialog. Click the Minimize Areal Distortion button and then click Okay. Flex Projector will automatically calculate a scale factor that minimizes the overall areal distortion of the new map projection.
To compare how the new projection you just made compares to the real Winkel Tripel projection, click the Display tab at the top of the Flex Projector panel. Select the Winkel tripel projection from the Show Second Projection menu and click the Same Width size option.
The above tutorial consists of a few general steps to introduce users to how Flex projector works. In an actual workflow it is likely that more steps, micro adjustments, and back and forth experimentation would take place. Also, to create a projection similar to the Winkel Tripel was the goal, starting with the Winkel Tripel itself instead of the Plate Carrée projection would offer a more direct route to completion.