#import "@preview/fletcher:0.5.8" as fletcher: diagram, node, edge
#import "@preview/cetz:0.4.2" //Grafiken
#import "@preview/cetz-plot:0.1.3": plot

#let bent-edge(from, to, ..args) = {
  let midpoint = (from, 50%, to)
  let vertices = (
    from,
    (from, "|-", midpoint),
    (midpoint, "-|", to),
    to,
  )
  edge(..vertices, "-|", ..args)
}


#let b3_0 = diagram(
  node-stroke: luma(80%),
  edge-corner-radius: none,
  spacing: (10pt, 20pt),

  // Nodes
  node((1.5,0), [1.#h(3mm)2.#h(3mm)3.1.], name: <a>),
  node((0.5,1), [4.1.-4.3.], name: <b>),
  node((2.5,1), [3.2.-3.3.], name: <c>),

  node((0,2), [4.4.-4.5.], name: <d>),
  node((1,2), [4.6.], name: <e>),

  node((2.501,2), [5.1.-5.5.], name: <f>),
  node((2,3), [5.6.], name: <g>),
  node((3,3), [5.7.], name: <h>),
  node((4,3), [5.8.], name: <i>),
  node((5,3), [5.9.], name: <j>),
  node((6,3), [5.10.], name: <k>),
  node((2.001,4), [#h(1mm)6.#h(1mm) ], name: <m>),

  // Edges
  bent-edge(<a>, <b>),
  bent-edge(<a>, <c>),
  bent-edge(<b>, <d>),
  bent-edge(<b>, <e>),
  bent-edge(<c>, <f>),
  bent-edge(<c>, <f>),
  bent-edge(<f>, <g>),
  bent-edge(<f>, <h>),
  bent-edge(<f>, <i>),
  bent-edge(<f>, <j>),
  bent-edge(<f>, <k>),
  bent-edge(<g>, <m>),
)


#let b2_4 = cetz.canvas({
  import cetz.draw: *
  //import cetz-plot: *
  
  let f = x => (0.01 * calc.pow(x, 3) - 0.2 * calc.pow(x, 2) + 0.8 * x + 3) + 5
  let g = x => -(0.01 * calc.pow(x, 3) - 0.2 * calc.pow(x, 2) + 0.8 * x + 3) + 5

  plot.plot(
    size: (6, 7),
    name: "plot",
    axis-style: "school-book",
    x-tick-step: none,
    y-tick-step: none,
    x-label: $x$,
    y-label: $y$,
    x-ticks: ((3, $x_1$), (12, $x_2$), (8, $x$)),

    {
      plot.add(domain: (2, 13), f, style: (stroke: red), samples: 300)
      plot.add(domain: (2, 13), g, style: (stroke: blue), samples: 300)

      plot.add-fill-between(  
        domain: (3, 12),
        g,
        f,
        style: (
          stroke: none,
          fill: tiling(size: (3pt, 3pt), square(stroke: gray)),
        ),)



      // Hilfslinie damit Koordinatensystem nicht verrutscht
      plot.add(((0, 0), (0, 0.1)), style: (stroke: none))

      plot.add-anchor("G1", (3, g(3)))
      plot.add-anchor("F1", (3, f(3)))
      plot.add-anchor("G1", (12, g(12)))
      plot.add-anchor("G1", (12, g(12)))

      plot.add(((3, 0), (3, f(3))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
      plot.add(((12, 0), (12, f(12))), style: (stroke: (dash: "dashed", paint: gray, thickness: 1pt)))
    },
  )
})


#let EC_func(x) = {
  let y = x*x*x - 4*x + 6
  if y < 0 {
    return 0
  }
  return calc.sqrt(y)
}


#let EC_drawing = cetz.canvas({
  plot.plot(
  size: (10, 10), 
  x-tick-step: 5, 
  y-tick-step: 20, 
  x-min: -5, 
  max: 10, 
  x-grid: true,
  y-grid: true,
  
  {
    plot.add(domain: (-5, 10), EC_func, samples: 300)
    plot.add(domain: (-5, 10), t => (t, -EC_func(t)),samples: 300)
  })
})

#let EC_func2(x) = {
  let y = (x - 3)*(x - 3)*(x - 3) - 4*(x - 3) + 12
  if y < 0 {
    return 0
  }
  return calc.sqrt(y)
}


#let EC_func3(x) = {
  let y = -((x - 3)*(x - 3)*(x - 3) - 4*(x - 3)) + 4
  if y < 0 {
    return 0
  }
  return calc.sqrt(y)
}


#let EC_drawing2 = cetz.canvas({
  plot.plot(
  name: "plot",
   
  axis-style: "school-book", 
  size: (10, 10), 
  x-tick-step: none, 
  y-tick-step: 20, 
  x-min: 0, 
  x-max: 7, 
  x-grid: true,
  y-grid: true,
  
  {
    plot.add(((0, 0), (0, 0.1)), style: (stroke: none)) 

    plot.add(domain: (1, 6), EC_func2, samples: 300)
    
    plot.add(domain: (1, 6), EC_func3,samples: 300)
  })
})