bookshelf/Common/Geometry/StepFunction.lean

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import Common.Finset
import Common.Geometry.Rectangle.Orthogonal
import Common.List.Basic
import Common.Set.Partition
/-! # Common.Geometry.StepFunction
Characterization of step functions.
-/
namespace Geometry
open Set Partition
/--
A function `f`, whose domain is a closed interval `[a, b]`, is a `StepFunction`
if there exists a `Partition` `P = {x₀, x₁, …, xₙ}` of `[a, b]` such that `f` is
constant on each open subinterval of `P`.
Instead of maintaining a function from `[a, b]` to ``, we instead maintain a
function that maps each `Partition` index to some constant value.
-/
structure StepFunction where
p : Partition
toFun : Fin p.ivls.length →
namespace StepFunction
/--
The ordinate set of the `StepFunction`.
-/
def toSet (sf : StepFunction) : Set Point :=
i ∈ Finset.finRange sf.p.ivls.length,
let I := sf.p.ivls[i]
Rectangle.Orthogonal.toSet
{
tl := ⟨I.left, sf.toFun i⟩,
bl := ⟨I.left, 0⟩,
br := ⟨I.right, 0⟩,
has_right_angle := sorry
},
by simp
end StepFunction
end Geometry