Photoshop Compass & Straightedge

line tangent to two circles

If you've done any basic geometry, you might have come across compass and straightedge constructions, ways of constructing (i.e. drawing precisely) a shape using only two tools:

  • a compass to draw arcs and circles
  • a straightedge to draw straight lines

Ever since the ancient Greeks, compass and straightedge constructions have been used to draw a vast number of shapes and patterns, which means there are a great deal of these constructions available all over the place. If you've been trying to figure out how to use them in Photoshop, read on.A

There are only five basic operations in compass and straightedge constructions:

  • drawing an infinite line that goes through two points
  • drawing a circle centered on one point and intersecting another
  • finding the point where two lines intersect
  • finding the point where a circle intersects a line
  • finding the point where a circle intersects a circle

Since the whole point of compass and straightedge work is to draw precisely, in Photoshop we'll do all our drawing using the vector tools. We can use guides to define points, looking at the intersection of a horizontal guide and a vertical guide.

Line from Two Points

Start with two points, defined by the intersection of two guides. Draw a vector that connects them. Use the transform tool (Ctrl-T) to expand it until the ends are off the edge of the image.

If, however, the line is exactly orthogonal (that is, either horizontal or vertical) Photoshop won't let you transform it.B In that case, draw a random circle centered on one of the ends, then copy it to the other end, and then you can transform the line. Delete the circles when you're done.

Circle from Two Points

Drawing a circle centered at one pair of guides and reaching another is a trivial task in Photoshop (assuming you know how to draw anything with the vector tools), so we'll just skip to the next task.

Intersections

Start with two lines. Take the first line and draw vectors connecting one end around to the other, making a shape of some kind. Do the same thing with the other line. Subtract one shape from the other so that you get a point where the two lines intersected – all the other points in the resulting shape are unimportant.

The next problem is placing guides precisely at a point. Photoshop doesn't let you snap guides to points, but it does let you snap guides to the edges of layer shapes – and you can define a layer's shape by using a vector path.

At this point, you have a path that includes the point where the two original lines intersected. Drag the other points of the path around (or delete them and draw new ones) so that the point you want is both the leftmost (or rightmost) and the topmost (or bottommost) point in the path. Make a fill layer using this path.

Other Intersections

There are two other kinds of intersections in compass and straightedge constructions: line and circle, and two circles. These are both done using the same principle as finding the intersection of two lines.