Isometric land mass

[Savage Orc]

I've been practicing some mountains and other elements from an isometric POV but sometimes they look odd compared to the land mass itself, which looks more top down.

Is there a way to make the land mass look more isometric itself instead of top down?

[Warlin]

Xpian had made some good videos on his drawing technique and there is one of these that explained how to do this :
https://youtu.be/CcCDIECoFdw
I personnaly use a similar technique.

[Savage Orc]

Thanks so much for the reply and link. I had thought about something like this using the perspective tool in PS Elements, but I have yet to try it.

When you do this do you put your rivers or other features in first, then transform it?

As I practice I tend to put the mountains in first so I kind of know where the rivers are coming from, but it probably wouldn't be a good idea doing them until after I transform the top down land mass. I guess I would have to just practice putting in the rivers so they fit the isometric perspective. More width, not as much height, as the video shows. Or, do the rivers first and then transform.

[Warlin]

For my last map (Erandas) I drew a first draft with the landmass, mountains and the main rivers, and then I built my map on the top. For two reasons: the first in order to facilitate the course of rivers in isometric, the second to keep the height proportion of the mountains and show the perspective. I think for the start, it's more easy to draw the main course au the river, then transform it.

[Savage Orc]

I played around a little this morning before work and using the perspective tool in Photoshop Elements seems to work. But for each layer I had to select all, put a stroke around the layer, and then transform because if I didn't the bounding box only applied to areas with pixels, not the whole layer and it wouldn't line up.

Not the best solution, but workable while I'm still learning. Hopefully with practice I can draw elements in Iso without having to transform. We shall see

[Josiah VE]

I usually just do more horizontal strokes that vertical when trying to do isometric, but I've thought of doing something such as squashing it, but never actually done it before.

[Savage Orc]

Try making the land mass top down then squashing it 57% first.

I tried that this morning after watching the vid Warlin posted above and it seemed to work out. Thanks for the reply.

Just curious, why is it 57%(I've also seen 57.77%) and not 55 or 60?

[waldronate]

If I recall, when you churn through the rotations and projections, you end up with a Y scaling value that works out to be 180/pi or roughly 57.295779513082320876798154814105 (some rounding). The actual 3D rotations (according to Wackypedia under "isometric projection" [ https://en.wikipedia.org/wiki/Isometric_projection ]) work out to be rotation around the vertical axis by 45 degrees and then rotation by atan(1/sqrt(2)). There are some nice illustrations on the right-hand side of the article at Wikipedia that should help to understand what's happening. in this case, you're assuming that the rotations aren't needed and that the scaling is all that's left.

Disclaimer: Math is not my thing. I can churn through things slowly, but I never really mastered getting the right answer much beyond addition of two binary digits (no carry).

[xpian]

Why 57%? (Or 57.7777 percent?)

This is all in the service of being able to plan out a map from a top-down, 2D view and convert it over to a more interesting 3D isometric view. Going off the top of my head, from when I was investigating this a few years back...

Basically, the true "isometric" view is one where all three of the dimensions (X, Y, and Z axis) appear to take up equal distance on the map. The easiest way to visualize this is to think of a cube. Or pick up a standard 6-sided die and look at it. Put the cube (or the die) on the flat surface of a table in front of you. Aim one point of the cube directly at yourself. Now change your "angle of view" by raising or lowering your neck until all three of the lines where the three visible planes of the cube meet are equal in size, and are meeting at the vertex pointing toward you at the same angle. Each side of the cube--though in actuality a square side--should now appear to your eye as an equal diamond. You should be able to see the outline of the cube as a perfect hexagon at this point, if you were to flatten it to two dimensions.

The cube in front of you should look like this:


Now, the question is, how do you arrange for your whole map to have this "viewing angle?" What angle are you looking down at? How do you translate that into something useful in design software? I think it's pretty obvious that you're looking down from something like a 45 degree angle, but how does that help you?

Well, as Waldronate has said above, there's some math involved. I'm not a whiz at that stuff...but when I was investigating how to do something like translate an overhead view to an isometric view, I knew instinctively that there was some "squishing" amount that would be needed. Some percentage where, if you kept the horizontal dimension constant, you could squish the vertical dimension to just the right amount to end up with an isometric floor plan. After reading enough sources, it turned out that the right amount is 57.777...7 percent. This will take a square (as seen from overhead) and turn it into a diamond (the same square as seen from a 45 degree angle). And this diamond shape would be the perfect base for a cube that one might draw in an isometric way. As indicated before, it's just that the trigonometry of the angles works out this way.

With this percentage in hand, you can swiftly translate something that's an overhead, top-down, satellite style map into an isometric style map. Further, you'll then know that you can go back the other way--translate an isometric view to an overhead view--by using the reciprocal percentage. Stretching it out. I think it's something like 173%. Keep the horizontal constant and stretch the vertical by 173%.

All of that said, there are other percentages you could use. Anything other than 57.777% wouldn't give you TRUE isometric view, but could be just as valid for whatever effect you're trying to achieve. For instance, if you want a map that's more top-down, but not fully overhead, you could squish the vertical by only 70%, or 75%. This would give you a higher-up view, where the rooftops are bigger and the walls of your buildings are narrower. You'd get to see more of your city streets, for instance, without them being obscured by the tops of your tall buildings.

[Savage Orc]

Thanks for the replies. Xpian, the diagram you included helped.