The tangent is the line which is perpendicular to the local radius. Intuitively, it’s the line “resting” or “balanced” on that point in the curve.
The perpendicular (or the normal) is the line crossing the tangent at a right angle.
How can I draw these, besides eyeballing it?
There are quite many plugins that make this easy to do. Its even relatively easy to script.
- Hotdoor CAD tools
- Astute Graphics, have tools for this
- Some scripts by Hiroyuki Sato might help also, here and here
In any case you may want to know how to do this manually. I often do as not all the computers i use have all the tools i have at my workstation. This is how you do it.
- Insert a point to the curve where you want to be tangent.
- With the tangents visible use line tool to snap the tangent point, and drag to the to the point on curve that you made.
- (Optional) Scale this line up say to 400% or so.
- (Optional, for normal) Rotate the tangent by 90 degrees centered on point:
- With rotate tool, Alt + click on the point on curve
- Type 90 degrees
- Hit copy.
Timelapse 1: How to make a tangent line in AI (Scale step missing, sorry).