# EquidistantGrid is a grid with equidistant grid spacing per coordinat
# direction. The domain is defined through the two points P1 = x̄₁, P2 = x̄₂
# by the exterior product of the vectors obtained by projecting (x̄₂-x̄₁) onto
# the coordinate directions. E.g for a 2D grid with x̄₁=(-1,0) and x̄₂=(1,2)
# the domain is defined as (-1,1)x(0,2).

struct EquidistantGrid{Dim,T<:Real} <: AbstractGrid
    numberOfPointsPerDim::NTuple{Dim, Int} # First coordinate direction stored first, then

    limit_lower::NTuple{Dim, T}
    limit_upper::NTuple{Dim, T}

    # General constructor
    function EquidistantGrid(nPointsPerDim::NTuple{Dim, Int}, limit_lower::NTuple{Dim, T}, limit_upper::NTuple{Dim, T}) where Dim where T
        @assert all(nPointsPerDim.>0)
        @assert all(limit_upper.-limit_lower .!= 0)
        return new{Dim,T}(nPointsPerDim, limit_lower, limit_upper)
    end

    # # 1D constructor which can be called as EquidistantGrid(m, (xl,xr))
    # function EquidistantGrid(nPointsPerDim::Integer, lims::NTuple{2,Real})
    #     return EquidistantGrid((nPointsPerDim,), ((lims[1],),(lims[2],)))
    # end

end

# Returns the number of dimensions of an EquidistantGrid.
#
# @Input: grid - an EquidistantGrid
# @Return: numberOfPoints - The number of dimensions
function numberOfDimensions(grid::EquidistantGrid)
    return length(grid.numberOfPointsPerDim)
end

# Computes the total number of points of an EquidistantGrid.
#
# @Input: grid - an EquidistantGrid
# @Return: numberOfPoints - The total number of points
function numberOfPoints(grid::EquidistantGrid)
    return prod(grid.numberOfPointsPerDim)
end

# Computes the grid spacing of an EquidistantGrid, i.e the unsigned distance
# between two points for each coordinate direction.
#
# @Input: grid - an EquidistantGrid
# @Return: h̄ - Grid spacing for each coordinate direction stored in a tuple.
function spacings(grid::EquidistantGrid)
    return abs.(grid.limit_upper.-grid.limit_lower)./(grid.numberOfPointsPerDim.-1)
end

# Computes the points of an EquidistantGrid as a vector of tuples. The vector is ordered
# such that points in the first coordinate direction varies first, then the second
# and lastely the third (if applicable)
#
# @Input: grid - an EquidistantGrid
# @Return: points - the points of the grid.
function points(grid::EquidistantGrid)
    # Signed grid spacing
    dx̄ = (grid.limit_upper.-grid.limit_lower)./(grid.numberOfPointsPerDim.-1)
    # Compute the points based on their Cartesian indices and the signed
    # grid spacings
    points = Vector{typeof(dx̄)}(undef, numberOfPoints(grid))
    cartesianIndices = CartesianIndices(grid.numberOfPointsPerDim)
    for i ∈ 1:numberOfPoints(grid)
        ci = Tuple(cartesianIndices[i]) .-1
        points[i] = grid.limit_lower .+ dx̄.*ci
    end

    # TBD: Keep? this? How do we want to represent points in 1D?
    if numberOfDimensions(grid) == 1
        points = broadcast(x -> x[1], points)
    end
    return points
end

function pointsalongdim(grid::EquidistantGrid, dim::Integer)
    @assert dim<=numberOfDimensions(grid)
    @assert dim>0
    points = range(grid.limit_lower[dim],stop=grid.limit_lower[dim],length=grid.numberOfPointsPerDim[dim])
end

# # TODO: Move to own plotting module.
using PyPlot, PyCall

function plotgridfunction(grid::EquidistantGrid, gridfunction)
    if numberOfDimensions(grid) == 1
        plot(pointsalongdim(grid,1), gridfunction, linewidth=2.0)
    elseif numberOfDimensions(grid) == 2
        mx = grid.numberOfPointsPerDim[1]
        my = grid.numberOfPointsPerDim[2]
        X = repeat(pointsalongdim(grid,1),1,my)
        Y = permutedims(repeat(pointsalongdim(grid,2),1,mx))
        plot_surface(X,Y,reshape(gridfunction,mx,my));
    else
        error(string("Plot not implemented for dimension ", string(numberOfDimensions(grid))))
    end
end