Creating Tangent Lines with Shapes

Mix.install([
  {:plotly_ex, "~> 0.3"},
  {:kino, "~> 0.18"}
])

Section

Compute tangent lines analytically and draw them as type: "line" shapes. This example uses sin(x) and its derivative cos(x) to place tangent lines at specific points.

alias Plotly.{Figure, Scatter}

x_curve = for i <- 0..100, do: i * :math.pi() / 50
y_curve = Enum.map(x_curve, &:math.sin/1)

# Tangent at x0: y = sin(x0) + cos(x0) * (x - x0)
tangent_at = fn x0 ->
  y0 = :math.sin(x0)
  slope = :math.cos(x0)
  x1 = x0 - 0.6
  x2 = x0 + 0.6
  {x1, y0 + slope * (x1 - x0), x2, y0 + slope * (x2 - x0)}
end

{tx1_a, ty1_a, tx2_a, ty2_a} = tangent_at.(:math.pi() / 4)
{tx1_b, ty1_b, tx2_b, ty2_b} = tangent_at.(:math.pi())

Figure.new()
|> Figure.add_trace(Scatter.new(x: x_curve, y: y_curve, mode: "lines", name: "sin(x)"))
|> Figure.update_layout(
  title: "Tangent Lines on sin(x)",
  shapes: [
    %{
      type: "line",
      xref: "x", yref: "y",
      x0: tx1_a, y0: ty1_a, x1: tx2_a, y1: ty2_a,
      line: %{color: "red", width: 2}
    },
    %{
      type: "line",
      xref: "x", yref: "y",
      x0: tx1_b, y0: ty1_b, x1: tx2_b, y1: ty2_b,
      line: %{color: "green", width: 2}
    }
  ]
)
|> Plotly.show()