Build a Mercator
Style 2 -- A Wireframe Sphere
You can also create an Action to do a lot of the grunt work for you. While an Action won't be able to create this effect completely, it can do most of the steps involved.
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!
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). Create a New Layer (Ctrl+Shift+N). Then create a circular selection that fills most of the canvas area. Hold down the ALT and SHIFT keys to create a perfect circle that draws from the center outward.
Apply a white-to-black Radial Gradient to the selection. Holding the Shift key down, start the gradient tool at the very top center of the circle, and drag it to the very bottom center. Leave the selection going.
Add an Adjustment Layer right above the sphere layer (click the split black and white circle image at the bottom of the Layers palette). Choose the "Posterize" filter for this adjustment layer. Set the filter to 6.
Now just see what happens. We get 6 individually shaded sections, which will end up becoming our wireframe rings. So set the filter to the number of rings you want. If your selection is no longer active, Ctrl-click on the gradient sphere layer again to reselect it.
Add another Adjustment Layer right above the previous one. Choose the "Brightness and Contrast" filter for this layer. Set the Brightness up to +25, and Contrast down to -50. This will allow you to see every level of gray clearly. This shall also be helpful in the steps to come. If your selection is no longer active, Ctrl-click on the gradient sphere layer again to reselect it. Now you have left this part until after the Adjustment layers were added, specifically so you could see what happens when you apply the "Spherize" filter. Click on the gradient sphere layer to make it the active layer. Apply the "Spherize" filter (FILTER>Distort>Spherize) using the 'Normal' mode, and set to 100% strength.
Did you notice how applying this filter made the gray sections of the sphere flatter, and gave them a better, proper shape for our effect? If you didn't apply this filter to your gradient, your globe's lines would be too steep -- they wouldn't look correct. Once you've done this, leave the selection going. Under the EDIT menu choose 'Copy Merged' (Ctrl+Shift+C). Open the Channels palette and create a new channel. Then paste what you just copied into the channel (press Ctrl+V). Now you can deselect. Now under the FILTER menu, choose 'Noise>Median'. Set it to 3px, and click OK. Then apply it twice more by pressing Ctrl+F twice. And now, also from the FILTER>Noise menu, choose 'Dust and Scratches'. Apply this with the settings Radius=6 and Threshold=0. Before going on, create a duplicate of your new channel as a backup.
These filters are used to help smooth out the lines dividing the different shades. Unfortunately, they can't smooth them completely, which is one of the limitations of trying to achieve this effect with filters only. Actually the problem filter here is the 'Posterize' filter, not the other two, but don't worry – you shall get the lines even cleaner by applying one more filter.
Now open the FILTER menu and choose Stylize>Glowing Edges. Use the settings 5/20/15. And now for the secret ingredient -- a filter that will smooth our lines out even more! Under the 'FILTER>Stylize' menu, choose 'Diffuse>Anisotropic'. Apply it once, and then press Ctrl+F 4 times to apply the filter a total of 5 times.
Lastly, press Ctrl+L to open the Levels filter. Drag the right slider left, to 128. Then start dragging the left slider to the right until your lines get cleaner, harder edges. Don't go too far, or the lines will look jagged. If that happens, move the left slider back a bit. Click OK to apply.
Ctrl-Click the channel to select the lines. Then go back to the Layers palette and create a New Layer, filling the selection with black. Then Deselect. Now you'll need to 'hide' the bottom 3 layers -- the original gradient sphere layer, and the two adjustment layers. Click on their 'eye' icons to hide those layers.
You should end up seeing a negative version of your channel. Name this layer 'base sphere'. If your lines are a little uneven, then run the 'Diffuse>Anisotropic' filter again, and apply the Unsharp Mask set to 250% / 0.5 / 0. If they're just a little fuzzy, then only apply the Unsharp Mask filter set to 100% / 0.5 / 0.
Extra Tips
This entire effect can be made into an Action. But as an Action it would be best if you followed the advice given in tip 4, below. I would also advise that if you make it into an Action, you get the Action to create a new document for the Mercator effect, and not combine it with any current image you may be working with. Once the effect is made, you can just merge the layers and drag it into the document you're working on. If your circle's border is uneven, just select the gradient sphere and invert the selection. Then while on the outline layer -- 'base sphere' -- press Delete. Now invert the selection back again and under the EDIT menu choose Stroke. Apply a 7 pixel stroke, in the center. That should give you a nice clean border. If you want the lines to be thicker, then apply the 'Minimum' filter to the layer (FILTER>Other>Minimum). I wouldn't go higher than 1 or 2 pixels using this filter though, as the lines will start to look distorted. There's a way to get slightly nicer results for this effect. Start out by making your globe twice the size you intend on using. Then, after you've completed all the steps, resize your document down by 50%. Because Photoshop re-interpolates the image, the lines become a little smoother. This is especially good if you plan on thickening the lines up, as mentioned in the previous tip. Actually the 'Anisotropic' setting of the 'Diffuse' filter is the filter that would allow us to really clean up and smooth out the edges of the lines. And the point here is that just because you don't find a solution to a problem right away, doesn't mean there isn't one to find. You ought to have patience and make continuous efforts with your actions until you discover the right filter using the perfect settings. It is like trial and error method where in you don’t have any alternative.
Next, you are going to add the vertical lines to the sphere to give it a look of a wireframe globe.
Initially this process might seem tedious but once you get into the groove of the steps, this effect can take only few minutes to achieve -- especially if you create an Action to do most of the work. This is the part that would be difficult to create using an Action, as it involves manual selections.
Create a New Layer above your 'base sphere' layer. You don't have to name this one. Ctrl-Click the original shaded sphere layer to make a selection of it. Now Stroke this selection by 5 pixels, in the center (EDIT>Stroke...)
Again under the EDIT menu, go to the 'Transform' option and choose the 'Scale' function. Hold down the ALT key, grab one of the side control handles, and drag it inward so the circle gets thinner. Make it look like an oval -- like the example image here.
Create another New Layer, and repeat the same steps as above, but this time, resize the circle until it's even thinner than the first one. You'll notice that this step makes the line really thin. We can easily fix this using the 'Maximum' filter found under the 'Other' option (FILTER>Other>Minimum...).
After both the vertical line layers have been created to your satisfaction, click on the top one and press Ctrl+E to merge them together. Then merge the vertical lines layer to the 'base shape' layer. Now you should have only one layer that has your entire Mercator on it, and you're free to colour it, fill it with a texture, etc.
And that's all about the end result. You are through!
Extra Tips
There is one more tiny detail that really finishes off the effect. Select the 'Transform>Scale' tool and reduce the height of both of the vertical line layers by 2 or 3 pixels. Basically, you want the tops of these lines to sit just below the top line of the 'base sphere' layer. But don't let any white area show in between them (see the example image). If you 'Link' these layers together you can resize them both at the same time.
At this point, you might do well to create a new custom Brush out of your Mercator shape. That way, next time it will only be one click away. So, how can you do it? In PS7: Just make sure the Mercator layer is active, then under the EDIT menu choose "Define Brush". In PS6 and 5.5: Ctrl-Click the Mercator layer to select it, then open the EDIT menu and choose "Define Brush". If you're wondering why I don't suggest creating a Vector Shape from this, it's because Photoshop's pretty terrible when it tries to convert this image to vector -- the lines are just not smooth enough for it. You'd be better off to create one in a vector (Illustration) program and import it. At least as brush, you have the option of scaling it before you create it (in PS7 only. In earlier versions you'll have to create it, then use the 'Transform>Scale' tool).
We shall throw more light on giving effects to the so called “Mercator” in our next article. Wait for that exciting and informative article.
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