: 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?

@BetL875

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



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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