local function getPixelPosition(point, minPoint, maxPoint, drawBounds)
    if
        point[1] < minPoint[1]
        or point[1] > maxPoint[1]
        or point[2] < minPoint[2]
        or point[2] > maxPoint[2]
    then
        error("Point ("..point[1]..", "..point[2]..") outside the bounds ("
            ..minPoint[1]..", "..minPoint[2]..") to ("..maxPoint[1]..", "..maxPoint[2]..")")
    end
    local pointBound = {maxPoint[1] - minPoint[1], maxPoint[2] - minPoint[2]}
    local pointOffset = {point[1] - minPoint[1], -point[2] - minPoint[2]}
    local position = {
        (pointOffset[1] / pointBound[1]) * drawBounds.width + drawBounds.x,
        (pointOffset[2] / pointBound[2]) * drawBounds.height + drawBounds.y
    }
    return position[1], position[2]
end

function GraphFunction(x, y, width, height, func)
    local points = {}
    local origin = {x = (width + x) / 2, y = (height + y) / 2}
    local neg_x, neg_y = -math.floor(origin.x), -math.floor(origin.y)
    local pos_x, pos_y = math.floor(origin.x), math.floor(origin.y)
    for i = neg_x, pos_x, 1 do
        local j = math.floor(func(i))
        if j > neg_y and j < pos_y then
            local k, l = getPixelPosition({i,j}, {neg_x,neg_y}, {pos_x,pos_y},
                {x=x,y=x,width=width,height=height})
            table.insert(points, k)
            table.insert(points, l)
        end
    end
    return points
end

function GetLineFromSlope(midpoint, slope, length, color)
    color = color or {1, 1, 1}
    local delta_x, delta_y
    if slope == nil then
        delta_x, delta_y = 0, length
    else
        delta_x = math.sqrt((length ^ 2) / (1 + slope ^ 2))
        delta_y = -(slope * delta_x)
    end
    local x1 = midpoint.x - delta_x / 2
    local y1 = midpoint.y - delta_y / 2
    local x2 = x1 + delta_x
    local y2 = y1 + delta_y
    return {
        p1 = {x = x1, y = y1},
        p2 = {x = x2, y = y2},
        midpoint = midpoint,
        color = color
    }
end