Build a Mercator

Gerhardus Mer•ca•tor : Flemish cartographer, who developed the "Mercator projection" (1568).

3D artists know this as "Spherical Projection, or Mapping": A map in which the meridians and the parallels of latitude are shown as straight lines that cross at right angles, and in which areas appear more distorted the farther they are from the equator.

This image can have a number of different looks to it, the most popular being the one where the lines all appear like strings that have been wrapped around the shape of a sphere ('Style 2' in this tutorial). This kind of image is most often created with an Illustration program, but with a little resourcefulness, it can also be created using a non-illustrative program, such as Photoshop.

We'll be covering 2 styles here -- the one you see above (style 1), and 'Style 2' mentioned above. And as a bonus, I'll show a couple of quick ways you can alter and add to this image, to give it a number of different looks.

Note to Mac Users: The PC key Ctrl = the Mac key Cmd. And the PC key Alt = the Mac key Option. Don't forget to Save after every 2 or 3 steps!

Ok, let's get started!

Style 1 -- The Basic Mercator

1. Create a new document and give it equal length and width dimensions, i.e. 300px by 300px. Use a white background (for this example, at least).
2. Create a New Layer (Ctrl+Shift+N), and name it 'Mercator'. Then fill it with White (press the D key, then Ctrl+Delete).
3. Under the FILTER menu, choose "Sketch", then "Halftone Pattern..." Set the 'Pattern Type' to LINE. Then set the Contrast to full, and the line thickness to 6px. Press OK to apply these settings.
4. Under the SELECT menu, choose "Color Range...". Then within the 'Select' dropdown menu, change the option to 'Highlights'. Click OK to apply, then press the Delete key. And finally, Deselect (Ctrl+D).

   In case anyone is curious, the reason we didn't use the Magic Wand tool to select the white area was because the 'Select Color Range' function gives cleaner results.

5. Also, older versions of Photoshop don't have the new 'Background Eraser' and 'Magic Eraser' tools -- but they do have the 'Select Color Range' function. So the method explained here applies to all version of Photoshop.
6. This step is optional, and can be used if you want thinner lines. Under the FILTER menu, choose "Other", then "Maximum..." and set it to 3px. This, as you'll notice, will reduce the thickness of your lines by 3 pixels.

   In case you're wondering, this step cannot be done automatically using the "Halftone Pattern" filter; it doesn't work like that.

7. Press Ctrl+J to duplicate this layer. And under the EDIT menu, choose "Transform/Rotate 90 CCW". Press Ctrl+E to merge these 2 layers together.
8. Under the FILTER menu choose "Distort/Spherize...". Use the "Normal" setting at maximum levels, and click OK to apply. Then press Ctrl+F to apply the same filter again.
9. Now under the EDIT menu, choose "Transform/Scale...". Hold the ALT and Shift keys down together, then grab and drag inward one of the corner control points. Resize it to about 2/3 its original size. Once scaled, make sure it's in the true center of the canvas -- press Ctrl+A (select all), Ctrl+X (cut selected), Ctrl+V (paste). Now it's really centered.
10. Now use the Elliptical selection tool. Hold the ALT and Shift keys down; click as close to the exact middle of the sphere as you can, and scale a selection that is almost exactly the same size as the globe shape. You can get it close, then nudge it into perfect position afterwards using the arrow keys. You want the selection centered within the globe shape. Note that I've lightened my image here so you can see my selection more easily.
11. Press Ctrl+Shift+I to Invert the selection. Then press your Delete key, followed by Ctrl+D to Deselect. Then apply the 'Spherize' filter one more time. This will increase the spherical look of the lines, as well as increasing the size of the sphere, which is why we scaled the sphere down in Step 8. This is the secret to making this effect look good and clean.
12. The last step to making this effect complete is to spherize just the very center of the line grid, to improve the 'Mercator projection' of the lines. So, create a circular selection like the one shown in the example image.

    Use the Elliptical selection tool, and hold the ALT and Shift keys down; click as close to the exact middle of the sphere as you can, and drag your mouse outward. Note that you only want to select the radius of 3 squares, starting from the center and moving outward.

    Once that's done, Feather the selection by 10 pixels (SELECT>Feather). Then apply the Spherize filter with a setting of only 10, using the 'Normal' mode. Then you can Deselect.

Your image should now look a lot like the one at the top of this page. And if you'd like your sphere to tilt, just use the Rotate function under the 'EDIT/Transform' menu. Try plus or minus 30 degrees. Voila! A Mercator!

Extra Tips

• If the lines look a bit fuzzy from the rescaling step, use the 'Unsharp Mask' filter on the sphere to sharpen the lines. Don't overdo this though -- try using 100% / 0.5 / 0 for the settings.
• The trick to getting the best results from this effect are is in Step 8 -- scaling down the sphere before re-applying the 'Spherize' filter a second time. If you want to see the difference in quality and effect, then at Step 7, just apply the filter 2 times in a row. Most tutorials that show how to create this image use the Spherize filter this way, but it just doesn't look as good.
• If you wanted to make the effect look even more spherical, you'd simply repeat Step 8, then re-apply the 'Spherize' filter. Be careful about overdoing the filter though, because your lines near the center will begin to get too fuzzy (see sample image), which will require you to zoom in and clean them up manually -- because the Unsharp Mask filter will no longer be useful for that.