en

# Etienne Werly

## My personal website

Independent mathematics teacher, I teach at the moment at the University of Toulouse and as a private teacher.

# Inkscape tutorial: crabby

Crabby monday... I am trying out another only circles drawing, a bit more rigorously than last monday's drawing. I am again inspired by one of Logos By Nick's video.

## Inspiration

One of the difference with the bat drawing is that I will choose some circle sizes first, and then only use those to draw a logo. I decided not to go with the well-known Fibonacci sequence to have the size ratio of my circles:

• Choose a starting circle, with some arbitrary unit size,
• The other circles have some prescribed sizes with respect to the first,
• The sizes go as follows: 1, 2, 3, 5, 8, 13, 21, etc (always add the two last numbers to get a new one).

Instead, I spend more time than I would admit in looking for a sequence whose ratios would approximate the square root of 2, and trying to have a nice geometric pattern to construct the circles.

I ended up not finding such a sequence... and just went with an integer rounding of the first powers of root 2: 1, 2, 3, 4, 6, 8, 11 (16, 23, 32, ...). And I constructed these circles trying to arrange them in a nice spiralling pattern. But those numbers don't come close to following a pattern as neat as the Fibonacci ones...

## Techniques

### Drawing the circles

To draw circles of appropriate sizes, I first drew bounding boxes with appropriate sizes: squares the would follow the same pattern in size. Once the boxes are constructed, juste take the Ellipse tool (`E`) click one of the corners and drag your mouse to the diagonally opposed corner. The resulting circle fits snuggly in its box.

With all circles drawn, I duplicated them and arranged them in a concentric pattern.

### Arranging the circles

This is the meat of the procedure, but it was really trial and error. I can devise a procedure to reconstruct the crab:

Call the circles a to g from smallest to largest (a is 1, b is 2, c is 3, d is 4, e is 6, f is 8 and g is 11).

• Body: Take f and g, and snap f's lower handle to g's lower handle.

• Body: Take another g and snap its centre to f's upper handle.

• Rear leg and brows: Take another f and snap its centre to the lower g's left handle, then take a e and snap its left handle to the previous f's left handle. Proceed symmetrically to the right.

• Pincers: Take a b and snap its centre to where the upper g and the lower f intersect (right, and left), then take a c and snap its lower handle to b's lower handle.

• Rear leg: Take a d and snap its lower handle to the previous c's upper handle. For the left eye, take an a and snap the lower left border of the bounding box to the upper left corner of the bounding box of the lower f.

### From the circles to the logo

To get solid shapes from those circles, follow these steps:

• Turn all circles in path (`Shift+Ctrl+C`) and join them (`Ctrl+K`)
• Draw a rectangle that can cover the drawing
• Put the rectangle beneath the circles (`End`), select the rectangle and the grouped circles
• Divide the rectangle (`Ctrl+/`)

What you are left with is a lot of shapes that you can delete if you don't need it, or unite with others (`Ctrl++`) to have the design you want!

### Critiques

When I add the smaller shapes to have the crab body parts, I am sometimes left with artefact nodes in the middle of a shape. Maybe I did something wrong, or maybe Inkscape is a bit limited with precision cutting like this.

Additionally, the path have a lot of nodes. I tried simplifying them (`Ctrl+L`), which divided the number of nodes by nearly 6 while pretty much keeping the shape unchanged.

## Link to the `svg`

The `svg` file is here