Extending the Cube Example for Boxes

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

Section

A general rectangular box is just a cube with independent scaling per axis. Scale the unit-cube sample points by (a, b, c) to get a box of size a × b × c. Here we define a helper function and render two boxes with different proportions.

alias Plotly.{Figure, Mesh3d}

box_points = fn a, b, c ->
  steps = [0, 0.25, 0.5, 0.75, 1.0]
  pts =
    (for x <- steps, y <- steps, z <- [0, 1], do: {x * a, y * b, z * c}) ++
    (for x <- steps, z <- steps, y <- [0, 1], do: {x * a, y * b, z * c}) ++
    (for y <- steps, z <- steps, x <- [0, 1], do: {x * a, y * b, z * c})
  pts = Enum.uniq(pts)
  {Enum.map(pts, &elem(&1, 0)),
   Enum.map(pts, &elem(&1, 1)),
   Enum.map(pts, &elem(&1, 2))}
end

{x1, y1, z1} = box_points.(1, 2, 3)
{x2, y2, z2} = box_points.(3, 1, 1)

# Offset second box so they don't overlap
x2 = Enum.map(x2, &(&1 + 4))

Figure.new()
|> Figure.add_trace(
  Mesh3d.new(x: x1, y: y1, z: z1, alphahull: 0, color: "cyan", opacity: 0.6, name: "1×2×3")
)
|> Figure.add_trace(
  Mesh3d.new(x: x2, y: y2, z: z2, alphahull: 0, color: "magenta", opacity: 0.6, name: "3×1×1")
)
|> Figure.update_layout(
  title: "Rectangular Boxes via Trisurf",
  scene: %{
    xaxis: %{title: "X"},
    yaxis: %{title: "Y"},
    zaxis: %{title: "Z"}
  }
)
|> Plotly.show()