How can I divide a hyperbola or one of its branches into many segmentations with equal length = l along the curve. hyperbola can be express as: $x^2/a^2 - y^2/b^2 = 1$
How to compute the x, y for the seperation points?
2026-03-25 07:47:44.1774424864
Segmentations with equal length on a hyperbola
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Arclength along a hyperbola doesn't have an expression in terms of familiar functions; e.g. it is given by an "elliptic integral of the second kind" (wikipedia link).
So, unless you happen to have access to (or can write) a function that computes elliptic integrals, you're going to have to use a numeric method to approximate arclength.
Here is a WolframAlpha expression for the indefinite integral of arclength of the hyperbola parametrized by $(a \cosh(u), b \sinh(u))$
Here is a mathworld reference for hyperbola mensuration formulas, which also includes the formula for arclength.rent notation conventions for the elliptic integral)