# How to make smooth logarithmic spiral with a specific size and decay?

I need to make a logarithmic spiral with a specific position for each cusp, is there a way to make it mathematically perfect? Or at least some way that does not rely on eyeballing curves.

The red lines on the drawing are the closest thing to what I want, the black circles are like boundaries.

• I should imagine there's a possibility that a script could be written to do it, but there is nothing that will do it automatically in Illustrator. Nov 29, 2017 at 13:45
• I was wondering if there was any technique for this. Will look into scripts too. Nov 29, 2017 at 13:47
• Techniques? Yes probably. You could turn all these other lines into guides, and use snap to guides to draw the lines, possibly use the Curvature tool - but this is not an automatic way, and I doubt it will achieve mathematical exactness either. Nov 29, 2017 at 13:51
• It seems that the script "Round Any Corner" created by Hiroyuki Sato does the trick! Nov 29, 2017 at 14:00
• Also just read somewhere online that Illustrator's Spiral tool is already logarithmic, although I can't verify that. Perhaps someone else can. If you single click with the Sprial tool on the page, some options come up. Nov 29, 2017 at 14:11

Illustrator's spiral is logarithmic. We can input

• decay as percents per 180 degrees. Decay < 1 means the spiral is convergent. Values >1 mean expanding spirals.
• number of segments; one segment is 90 degrees
• drawing direction CCW or CW

Unfortunately there's no explicit center point and the spiral clearly is rotated, the starting radius isn't horizontal. Illustrator can show the center of the bounding box, but it's useless.

Fortunately it's easy to normalize spiral's position. We can place and rotate it for horizontal starting radius and known centerpoint.

An example:

Let's click the artboard with the spiral tool and input