I have two points in 3D space, A and B. I need to have a parametric equation of the catenary curve such that:

Cat(0) = A,

Cat(1) = B,

Cat(t)= f(t, A, B)

How can I derive the function f


1 Answer 1


The catenary is known to follow the equation

$$y=a\left(\cosh\left(\frac{x-x_0}a\right)-1\right)+y_0$$ in 2D, where $a, x_0$ and $y_0$ are adjustable parameters.

You need to change the coordinates to work in the vertical plane that contains $A$ and $B$, and you also need a third piece of information to determine the parameters, such as the length of the curve.

Unfortunately, due to the transcendental nature of the equations, only a numerical resolution is possible.


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