The involute of a curve is the locus traced out by the end of a piece of string as it wraps around the given curve.
Here's how to create an involute in Geometry Expressions. (In the picture, our given curve is a logarithmic spiral)
- First create an arc on the given curve.
constrain the parametric location of the arc's endpoints. One should be
a constant, the other variable (we've used pi and t).
- Measure the arc length.
- Create a tangent to the curve at the variable end of the arc.
- Place a point on the tangent and constrain its distance to be a constant minus the arc length.
The constant represents the length of the string.
The locus of the point on the tangent is the involute curve.
For the logarithmic spiral, the involute is simply a 90 degree rotation of the original curve.