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Single backtick now used for all code quotes.

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Chris Palmer
2020-12-24 16:04:59 +00:00
parent 04b98a3786
commit 4cac382581
49 changed files with 2459 additions and 2459 deletions
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14
utils/catenary.scad
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@@ -20,25 +20,25 @@
//
//! Catenary curve to model hanging wires, etc.
//!
//! Although the equation of the curve is simply ```y = a cosh(x / a)``` there is no explicit formula to calculate the constant ```a``` or the range of ```x``` given the
//! Although the equation of the curve is simply `y = a cosh(x / a)` there is no explicit formula to calculate the constant `a` or the range of `x` given the
//! length of the cable and the end point coordinates. See <https://en.wikipedia.org/wiki/Catenary#Determining_parameters>. The Newton-Raphson method is used to find
//! ```a``` numerically, see <https://en.wikipedia.org/wiki/Newton%27s_method>.
//! `a` numerically, see <https://en.wikipedia.org/wiki/Newton%27s_method>.
//!
//! The coordinates of the lowest point on the curve can be retrieved by calling ```catenary_points()``` with ```steps``` equal to zero.
//! The coordinates of the lowest point on the curve can be retrieved by calling `catenary_points()` with `steps` equal to zero.
//
include <core/core.scad>
use <maths.scad>
function catenary(t, a) = let(u = argsinh(t)) a * [u, cosh(u)]; //! Parametric catenary function linear along the length of the curve.
function catenary_s(d, a) = 2 * a * sinh(d / a); //! Length of a symmetric catenary with width ```2d```.
function catenary_ds_by_da(d, a) = 2 * sinh(d / a) - 2 * d / a * cosh(d / a); //! First derivative of the length with respect to ```a```.
function catenary_s(d, a) = 2 * a * sinh(d / a); //! Length of a symmetric catenary with width `2d`.
function catenary_ds_by_da(d, a) = 2 * sinh(d / a) - 2 * d / a * cosh(d / a); //! First derivative of the length with respect to `a`.
function catenary_find_a(d, l, a = 1, best_e = inf, best_a = 1) = //! Find the catenary constant ```a```, given half the horizontal span and the length.
function catenary_find_a(d, l, a = 1, best_e = inf, best_a = 1) = //! Find the catenary constant `a`, given half the horizontal span and the length.
assert(l > 2 * d, "Not long enough to span the gap") assert(d) let(error = abs(catenary_s(d, a) - l))
error >= best_e && error < 0.0001 ? best_a
: catenary_find_a(d, l, max(a - (catenary_s(d, a) - l) / catenary_ds_by_da(d, a), d / argsinh(1e99)), error, a);
function catenary_points(l, x, y, steps = 100) = //! Returns a list of 2D points on the curve that goes from the origin to ```(x,y)``` and has length ```l```.
function catenary_points(l, x, y, steps = 100) = //! Returns a list of 2D points on the curve that goes from the origin to `(x,y)` and has length `l`.
let(
d = x / 2,
a = catenary_find_a(d, sqrt(sqr(l) - sqr(y))), // Find a to get the correct length