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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.

spiral

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. – Billy Kerr Nov 29 '17 at 13:45
  • I was wondering if there was any technique for this. Will look into scripts too. – Bernardo Araujo Nov 29 '17 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. – Billy Kerr Nov 29 '17 at 13:51
  • It seems that the script "Round Any Corner" created by Hiroyuki Sato does the trick! – Bernardo Araujo Nov 29 '17 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. – Billy Kerr Nov 29 '17 at 14:11
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Illustrator's spiral is logarithmic. We can input

  • initial radius
  • 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

  • radius 10 millimeters
  • decay 110%
  • segments 8 (=2 full rounds)

We must draw 2 horizontal lines; one 10 mm long and a longer extension for it

enter image description here

The green line AB is 10mm long and the blue line is the extension.

We select the spiral and drag with the white arrow tool the beginning point to A. That's just done in the image. Smart quides and snap to point must be ON.

We keep the spiral selected. With the rotation tool we set the rotation center to A and drag the anchor point C to the extension line. Now the center of the spiral is point B.

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