Morph exp() to cosh()
The graph of cosh is the Catenary.

Modify the curve

morph, 0 ... 1:


Move/Stop Osculating Circles

Add/Remove Normals

B/W Background

Invert Curve in Circle

The curves are defined by these equations:
c(t) = [ x,  morph*exp(x) + (1-morph)*cosh(x) ]
Note:
(exp(x)*A + exp(-x)/A)/2 = cosh(x+log(A))
The name Catenary indicates that a hanging
chain (supported at both ends) has this shape.
The caustic of the normals is the Tractrix.

Inversion(vector) = (radius/vector)^2 * vector

catenary.pdf