The graph of cosh is the Catenary.

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

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