playing around with finding the length of garland needed for different sags

catenary-garland.go

package main

import (
	"fmt"
	"image/color"
	"math"

	"gonum.org/v1/plot"
	"gonum.org/v1/plot/plotter"
	"gonum.org/v1/plot/vg"
)

const (
	h   = float64(1)
	a   = float64(0.54)
	png = "garland.png"
)

func s(a, t float64) float64 {
	return a * math.Sinh(t/a)
}

func y(a, t float64) float64 {
	return a * math.Cosh(t/a)
}

// catenaryPoints generates coordinates for a catenary curve.
func catenaryPoints(n int, a float64) plotter.XYs {
	pts := make(plotter.XYs, n)
	dx := h / float64(n)
	x := -h / 2
	c := y(a, h/2)

	for i := range pts {
		pts[i].X = x + 0.5
		pts[i].Y = y(a, x) - c
		x += dx
	}

	return pts
}

func main() {
	n := 1000
	lineData := catenaryPoints(n, a)

	// Create a new plot, set its title and axis labels.
	p, err := plot.New()
	if err != nil {
		panic(err)
	}
	p.Title.Text = fmt.Sprintf("Catenary Garland w/ "+
		"sag: %0.0f%% extra length: %0.0f%%\n"+
		"y = a cosh((x-h)/a) - c\n"+
		"a=%0.3f h=%0.3f, c=%0.3f\n",
		(y(a, h/2)-y(a, 0))*100,
		(s(a, h/2)*2-1)*100,
		a, h/2, y(a, h/2),
	)
	// Draw a grid behind the data
	p.Add(plotter.NewGrid())

	// Make a line plotter and set its style.
	l, err := plotter.NewLine(lineData)
	if err != nil {
		panic(err)
	}
	l.LineStyle.Color = color.RGBA{B: 255, A: 255}

	// Add series to the plot
	p.Add(l)

	p.X.Min = -0.1
	p.X.Max = 1.1
	p.Y.Min = -0.9
	p.Y.Max = 0.1

	// Save the plot to a PNG file.
	if err := p.Save(4*vg.Inch, 4*vg.Inch, png); err != nil {
		panic(err)
	}
}