# How to draw a precise celtic knot

How would one go about creating this Celtic knot in Illustrator without tracing over the edges?

It seems to be like a Möbius strip making it rather complicated to draw with mathematic precision, I have tried using triangles and circles in various ways but nothing seems to work.

• If that is the exact artwork required, I would buy it for \$5 and save yourself the time and trouble. I may be a designer but I am also a business man and sometimes purchasing makes economical sense. If this is not close enough, just keep searching. There are tons of vector based celtic knots to choose from. Other sites like RF123 or iStock also have boatloads of vectors. Oct 16, 2017 at 15:06
• The problem is that particular shape is not precise so mathematic precision isn't going to help beyond placement of the outer triangle points. The curves are bastardized to fit the desired outcome. Oct 17, 2017 at 3:30
• @jhurley With all due respect my question was not asking how to purchase artwork, It was about how I would go about creating such a pattern which would in turn enhance my skills on Illustrator. If I resorted to money every time a challenge appears, not only would I be out of pocket, but I wouldn't learn anthing! Dec 30, 2018 at 20:00

1. Draw a triangle and flip it vertically.
2. Draw a circle, with the origin on one of the triangle vertices
3. Copy and paste the circle, and move to intersect the circle centre with the remaining triangle vertices.
4. Remove the triangle.
5. Select all, and apply a wide stroke to the circles
6. Click Object > Expand
7. With the Shape Builder tool, delete the parts of the circle you don't need.
8. With the Shape Builder tool, join the shapes to make the illusion of the overlapping parts.
9. Apply a fill and stroke as required.

Alternatively rather than circles you can also use ellipses, with each ellipse rotated 120 degrees, which is slightly closer to the shape of your original.

You could also use this same Shape Builder tool technique for drawing more irregular shapes, and rotating each part 120 degrees around a triangle. This is even closer to your example, but less regular.

Your photo is probably taken from a freeform drawing. Its not at all symmetric. I layered in Photoshop with the original two plus and minus 120 degrees rotated copies and tried to find the best fitting by moving the copies. Here's the best placing that I found:

Lines are quite thick. That actually gives some freedom on how the replicate should be drawed, if one wants rotational symmetry and the lines must be inside the layered black lines (the photo was made lighter to have some light left after layering with multiply blending.

Here is my attempt to make a symmetric replicate:

1.Two main arcs were drawn with the pen tool. I cheated and dragged the endpoints of the red arc to the same y-coordinate

2.Both arcs were copied twice rotating 120 degrees (=Object > Transform > Rotate > Copy)

3.The arcs were dragged to the right places. A thinner stroke was taken to see better coarse errors. A selected arc can be moved to snap by dy dragging its endpoint with the direct selection tool. Be sure you have smart guides and snap to points on, no other snaps=ON!

4.The centerpoints of the propellers must coincide. Normal alignment does not work because it aligns the bounding boxes. A couple of chords were added to both and the propellers with their chords were grouped to keep them together.The chords needed an anchor point at the beoth ends when drawing the chords. Otherwise the line ends didnt snap. Plenty of anchor points will be needed, so it's a good idea to add them to every arc crossings and to the chord mid crossings, too.

5.The green arc group was dragged to its place.Actually the cord crossing anchor was dragged. I found the result looks better when the green group was rotated with the rotation tool. The rotation was made by setting the rotation center to the common symmetry point and one chord end was dragged onto the red group chord.

6.The groups were ungrouped, the chords were removed, a black stroke was given to all arcs. With the direct selection tool the unwanted arc segments were selected. Pressing DEL made them to vanish.

Te result seems somehow unbalanced altough the down corners are in the same Y-level. Consider to use some simple left-right symmetric arcs - even circular or elliptical rather than trying to copy a non-perfect drawing. Then you'll get also the left-right symmetry ok.

The following design is composed of half circles:

If needed, the areas can be filled with the live paint bucket. It make new shapes that have a fill. Here's a heavily colored version:

ADDENDUM: This is not like a Moebius ring because that's in 3D and has only one edge and one surface half. This has 2 edges.

You might want the shape as a single colorable area. I do not believe it's possible in 2D programs like Illustrator or Inkscape.

The most "mathematical" method would be to mark it out and connect the lines. My result is a little dirty but if you dedicated some time to perfecting it the results are good.

1. Draw out an equilateral triangle and mark the center of each side (1/2 way point)

2. Trace a line from each side to their opposing corner

3. Mark out the 1/4 way point on each side and draw a curve to each

4. Next draw an arc through the middle of the triangle to each 1/4 way points

5. Draw a second arc that terminates on the cross-guide lines

6. Mirror the arcs and position them to create 3 quadrants

7. Join the segments

8. Expand the paths into shapes

9. Use the `Shape Builder` tool (Ctrl + M) to cut away the unwanted segments to make your overlaps