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I want to create an SVG image that looks like a spherical triangle with three circles positioned at each vertex. Here's what I'm trying to achieve:
Is it possible to do this in Photoshop? (If not, is there any other graphic design tool out there suited for this that I might want to hear about?)
The shape you are trying to draw is a reuleaux triangle with circles on each corner. Seeing as you are asking if it can be done in Photoshop I am going to assume you have Illustrator as well.
The main thing to remember is that a reuleaux triangle is fundamentally an equilateral triangle but with curved edges. So that is what we will create first.
Select the polygon tool
Put 3 in the text box and illustrator will create an equilateral triangle
Using the eclipse tool, hold shift and draw a perfect circle around one of the 3 anchor points.
Repeat the process for the other 2 anchor points
Now we use the "Shape Builder Tool"
Press and hold the Option/ALT key to delete the shapes you don't want.
Now with what is left, drag across the shapes you do want to merge them together
Outcome = 1 reuleaux triangle
Now just draw on the circles at each corner
Add colours, adjust it to make it pretty!
I would use a vector image editor instead. Photoshop could do it, but it's like using a hammer to screw in a nail. Photoshop only has very basic vector capabilities in comparison to proper vector image editing software.
Although Illustrator could be used to do this, it is probably easier in Inkscape, since it has a Polygon tool, with a rounding option, which not only rounds the corners but also curves the edges.
Update: The above example was made using Inkscape 0.48. In the most recent version of Inkscape 0.92 the polygon tool works somewhat differently, in that rounded triangles have no nodes at the vertices, so there are a couple of extra steps required.
When you draw the triangle, adjust it to the desired roundness, then click Path > Object to Path, then Extensions > Modify Paths > Add Nodes, using the setting shown below. This will create additional nodes at the vertices for placing the circles accurately with snapping.
As commented already, nearly any graphic software can be used. In photoshop the easiest tool is the normal brush. Have your model in the background and paint onto a half-transparent layer. The result is easily quite near your original:
But if you are after an exact 2D projection of a spherical triangle - even without a perspective - you must carefully calculate which elliptic arcs you shoud draw.
Symmetric straight ahead -view is easy, but still mathematically perfect (no perspective, unfortunately) if the triangle has equal sides. The following method is general altough it's done in Inkscape:
Draw an ellipse and a rectangle, align them vertically to have the same horizontal symmetry line. They must be paths. For ex. in Inkscape they are at first preset shapes which must be converted to paths
Insert nodes to the ellipse at the crossings, separate an arc between them
Make two copies. Rotate the arcs -30, +90 and -150 degrees
Move the arcs to their places. They fit exactly if you have snap to endpoints ON. Insert the circles. Fill them, if you want to hide the corners. As well you can cut off the extras.
You must join the arcs, if you want insert vector color fills or subtract the circles. This image only demonstrates them. Some programs allow flood fills with a paint bucket => no joining is needed. Warning: in Inkscape that tool is inaccurate, it's only for screen resolution.
