Refactor the SBS chain generation a bit.

[nageru] / theme.lua

-- The theme is what decides what's actually shown on screen, what kind of
-- transitions are available (if any), and what kind of inputs there are,
-- if any. In general, it drives the entire display logic by creating Movit
-- chains, setting their parameters and then deciding which to show when.
--
-- Themes are written in Lua, which reflects a simplified form of the Movit API
-- where all the low-level details (such as texture formats) are handled by the
-- C++ side and you generally just build chains.

-- TODO: Deal with inputs that are different from our native 1280x720 resolution.

local transition_start = -2.0
local transition_end = -1.0
local zoom_src = 0.0
local zoom_dst = 1.0
local zoom_poi = 0   -- which input to zoom in on
local fade_src_signal = 0
local fade_dst_signal = 0

local input0_neutral_color = {0.5, 0.5, 0.5}
local input1_neutral_color = {0.5, 0.5, 0.5}

local live_signal_num = 0
local preview_signal_num = 1

-- Valid values for live_signal_num and preview_signal_num.
local INPUT0_SIGNAL_NUM = 0
local INPUT1_SIGNAL_NUM = 1
local SBS_SIGNAL_NUM = 2
local STATIC_SIGNAL_NUM = 3

-- “fake” signal number that signifies that we are fading from one input
-- to the next.
local FADE_SIGNAL_NUM = 4

function make_sbs_input(chain, signal, deint, hq)
        local input = chain:add_live_input(not deint, deint)  -- Override bounce only if not deinterlacing.
        input:connect_signal(signal)
        local wb_effect = chain:add_effect(WhiteBalanceEffect.new())

        local resample_effect = nil
        local resize_effect = nil
        if (hq) then
                resample_effect = chain:add_effect(ResampleEffect.new())
        else
                resize_effect = chain:add_effect(ResizeEffect.new())
        end

        local padding_effect = chain:add_effect(IntegralPaddingEffect.new())

        return {
                input = input,
                wb_effect = wb_effect,
                resample_effect = resample_effect,
                resize_effect = resize_effect,
                padding_effect = padding_effect
        }
end

-- The main live chain.
function make_sbs_chain(input0_deint, input1_deint, hq)
        local chain = EffectChain.new(16, 9)

        local input0 = make_sbs_input(chain, INPUT0_SIGNAL_NUM, input0_deint, hq)
        local input1 = make_sbs_input(chain, INPUT1_SIGNAL_NUM, input1_deint, hq)

        input0.padding_effect:set_vec4("border_color", 0.0, 0.0, 0.0, 1.0)
        input1.padding_effect:set_vec4("border_color", 0.0, 0.0, 0.0, 0.0)

        chain:add_effect(OverlayEffect.new(), input0.padding_effect, input1.padding_effect)
        chain:finalize(hq)

        return {
                chain = chain,
                input0 = input0,
                input1 = input1
        }
end

-- Make all possible combinations of side-by-side chains.
local sbs_chains = {}
for input0_type, input0_deint in pairs({live = false, livedeint = true}) do
        sbs_chains[input0_type] = {}
        for input1_type, input1_deint in pairs({live = false, livedeint = true}) do
                sbs_chains[input0_type][input1_type] = {}
                for _, hq in pairs({true, false}) do
                        sbs_chains[input0_type][input1_type][hq] =
                                make_sbs_chain(input0_deint, input1_deint, hq)
                end
        end
end

-- A chain to fade between two inputs, of which either can be a picture
-- or a live input. In practice only used live, but we still support the
-- hq parameter.
function make_fade_chain(input0_live, input0_deint, input1_live, input1_deint, hq)
        local chain = EffectChain.new(16, 9)

        local input0, wb0_effect, input0_last, input1, wb1_effect, input1_last

        if input0_live then
                input0 = chain:add_live_input(false, input0_deint)
                wb0_effect = chain:add_effect(WhiteBalanceEffect.new())
                input0:connect_signal(0)
                input0_last = wb0_effect
        else
                input0 = chain:add_effect(ImageInput.new("bg.jpeg"))
                input0_last = input0
        end

        if input1_live then
                input1 = chain:add_live_input(false, input1_deint)
                wb1_effect = chain:add_effect(WhiteBalanceEffect.new())
                input1:connect_signal(1)
                input1_last = wb1_effect
        else
                input1 = chain:add_effect(ImageInput.new("bg.jpeg"))
                input1_last = input1
        end

        local mix_effect = chain:add_effect(MixEffect.new(), input0_last, input1_last)
        chain:finalize(hq)

        return {
                chain = chain,
                input0 = {
                        input = input0,
                        wb_effect = wb0_effect
                },
                input1 = {
                        input = input1,
                        wb_effect = wb1_effect
                },
                mix_effect = mix_effect
        }
end

-- Chains to fade between two inputs, in various configurations.
local fade_chains = {}
for input0_type, input0_live in pairs({static = false, live = true, livedeint = true}) do
        local input0_deint = (input0_live == "livedeint")
        fade_chains[input0_type] = {}
        for input1_type, input1_live in pairs({static = false, live = true, livedeint = true}) do
                local input1_deint = (input1_live == "livedeint")
                fade_chains[input0_type][input1_type] = {}
                for _, hq in pairs({true, false}) do
                        fade_chains[input0_type][input1_type][hq] =
                                make_fade_chain(input0_live, input0_deint, input1_live, input1_deint, hq)
                end
        end
end

-- A chain to show a single input on screen.
function make_simple_chain(input_deint, hq)
        local chain = EffectChain.new(16, 9)

        local input = chain:add_live_input(false, input_deint)
        input:connect_signal(0)  -- First input card. Can be changed whenever you want.
        local wb_effect = chain:add_effect(WhiteBalanceEffect.new())
        chain:finalize(hq)

        return {
                chain = chain,
                input = input,
                wb_effect = wb_effect
        }
end

-- Make all possible combinations of single-input chains.
local simple_chains = {}
for input_type, input_deint in pairs({live = false, livedeint = true}) do
        simple_chains[input_type] = {}
        for _, hq in pairs({true, false}) do
                simple_chains[input_type][hq] = make_simple_chain(input_deint, hq)
        end
end

-- A chain to show a single static picture on screen (HQ version).
local static_chain_hq = EffectChain.new(16, 9)
local static_chain_hq_input = static_chain_hq:add_effect(ImageInput.new("bg.jpeg"))
static_chain_hq:finalize(true)

-- A chain to show a single static picture on screen (LQ version).
local static_chain_lq = EffectChain.new(16, 9)
local static_chain_lq_input = static_chain_lq:add_effect(ImageInput.new("bg.jpeg"))
static_chain_lq:finalize(false)

-- Used for indexing into the tables of chains.
function get_input_type(signals, signal_num)
        if signal_num == STATIC_SIGNAL_NUM then
                return "static"
        elseif signals:get_interlaced(signal_num) then
                return "livedeint"
        else
                return "live"
        end
end

-- Returns the number of outputs in addition to the live (0) and preview (1).
-- Called only once, at the start of the program.
function num_channels()
        return 4
end

-- Returns the name for each additional channel (starting from 2).
-- Called only once for each channel, at the start of the program.
function channel_name(channel)
        if channel == 2 then
                return "Input 1"
        elseif channel == 3 then
                return "Input 2"
        elseif channel == 4 then
                return "Side-by-side"
        elseif channel == 5 then
                return "Static picture"
        end
end

-- Returns if a given channel supports setting white balance (starting from 2).
-- Called only once for each channel, at the start of the program.
function supports_set_wb(channel)
        return channel == 2 or channel == 3
end

-- Gets called with a new gray point when the white balance is changing.
-- The color is in linear light (not sRGB gamma).
function set_wb(channel, red, green, blue)
        if channel == 2 then
                input0_neutral_color = { red, green, blue }
        elseif channel == 3 then
                input1_neutral_color = { red, green, blue }
        end
end

function finish_transitions(t)
        -- If live is SBS but de-facto single, make it so.
        if live_signal_num == SBS_SIGNAL_NUM and t >= transition_end and zoom_dst == 1.0 then
                live_signal_num = zoom_poi
        end

        -- If live is fade but de-facto single, make it so.
        if live_signal_num == FADE_SIGNAL_NUM and t >= transition_end then
                live_signal_num = fade_dst_signal
        end
end

-- Called every frame.
function get_transitions(t)
        finish_transitions(t)

        if live_signal_num == preview_signal_num then
                return {}
        end

        if live_signal_num == SBS_SIGNAL_NUM and t >= transition_start and t <= transition_end then
                -- Zoom in progress.
                return {"Cut"}
        end

        if (live_signal_num == INPUT0_SIGNAL_NUM or
            live_signal_num == INPUT1_SIGNAL_NUM or
            live_signal_num == STATIC_SIGNAL_NUM) and
           (preview_signal_num == INPUT0_SIGNAL_NUM or
            preview_signal_num == INPUT1_SIGNAL_NUM or
            preview_signal_num == STATIC_SIGNAL_NUM) then
                return {"Cut", "", "Fade"}
        end

        -- Various zooms.
        if live_signal_num == SBS_SIGNAL_NUM and
           (preview_signal_num == INPUT0_SIGNAL_NUM or preview_signal_num == INPUT1_SIGNAL_NUM) then
                return {"Cut", "Zoom in"}
        elseif (live_signal_num == INPUT0_SIGNAL_NUM or live_signal_num == INPUT1_SIGNAL_NUM) and
               preview_signal_num == SBS_SIGNAL_NUM then
                return {"Cut", "Zoom out"}
        end

        return {"Cut"}
end

function transition_clicked(num, t)
        if num == 0 then
                -- Cut.
                if live_signal_num == FADE_SIGNAL_NUM then
                        -- Ongoing fade; finish it immediately.
                        finish_transitions(transition_end)
                end

                local temp = live_signal_num
                live_signal_num = preview_signal_num
                preview_signal_num = temp

                if live_signal_num == SBS_SIGNAL_NUM then
                        -- Just cut to SBS, we need to reset any zooms.
                        zoom_src = 1.0
                        zoom_dst = 0.0
                        transition_start = -2.0
                        transition_end = -1.0
                end
        elseif num == 1 then
                -- Zoom.

                finish_transitions(t)

                if live_signal_num == preview_signal_num then
                        -- Nothing to do.
                        return
                end

                if (live_signal_num == INPUT0_SIGNAL_NUM and preview_signal_num == INPUT1_SIGNAL_NUM) or
                   (live_signal_num == INPUT1_SIGNAL_NUM and preview_signal_num == INPUT0_SIGNAL_NUM) then
                        -- We can't zoom between these. Just make a cut.
                        io.write("Cutting from " .. live_signal_num .. " to " .. live_signal_num .. "\n")
                        local temp = live_signal_num
                        live_signal_num = preview_signal_num
                        preview_signal_num = temp
                        return
                end

                if live_signal_num == SBS_SIGNAL_NUM and
                   (preview_signal_num == INPUT0_SIGNAL_NUM or preview_signal_num == INPUT1_SIGNAL_NUM) then
                        -- Zoom in from SBS to single.
                        transition_start = t
                        transition_end = t + 1.0
                        zoom_src = 0.0
                        zoom_dst = 1.0
                        zoom_poi = preview_signal_num
                        preview_signal_num = SBS_SIGNAL_NUM
                elseif (live_signal_num == INPUT0_SIGNAL_NUM or live_signal_num == INPUT1_SIGNAL_NUM) and
                       preview_signal_num == SBS_SIGNAL_NUM then
                        -- Zoom out from single to SBS.
                        transition_start = t
                        transition_end = t + 1.0
                        zoom_src = 1.0
                        zoom_dst = 0.0
                        preview_signal_num = live_signal_num
                        zoom_poi = live_signal_num
                        live_signal_num = SBS_SIGNAL_NUM
                end
        elseif num == 2 then
                finish_transitions(t)

                -- Fade.
                if (live_signal_num ~= preview_signal_num) and
                   (live_signal_num == INPUT0_SIGNAL_NUM or
                    live_signal_num == INPUT1_SIGNAL_NUM or
                    live_signal_num == STATIC_SIGNAL_NUM) and
                   (preview_signal_num == INPUT0_SIGNAL_NUM or
                    preview_signal_num == INPUT1_SIGNAL_NUM or
                    preview_signal_num == STATIC_SIGNAL_NUM) then
                        transition_start = t
                        transition_end = t + 1.0
                        fade_src_signal = live_signal_num
                        fade_dst_signal = preview_signal_num
                        preview_signal_num = live_signal_num
                        live_signal_num = FADE_SIGNAL_NUM
                else
                        -- Fades involving SBS are ignored (we have no chain for it).
                end
        end
end

function channel_clicked(num)
        preview_signal_num = num
end

-- Called every frame. Get the chain for displaying at input <num>,
-- where 0 is live, 1 is preview, 2 is the first channel to display
-- in the bottom bar, and so on up to num_channels()+1. t is the
-- current time in seconds. width and height are the dimensions of
-- the output, although you can ignore them if you don't need them
-- (they're useful if you want to e.g. know what to resample by).
--
-- <signals> is basically an exposed InputState, which you can use to
-- query for information about the signals at the point of the current
-- frame. In particular, you can call get_width() and get_height()
-- for any signal number, and use that to e.g. assist in chain selection.
--
-- You should return two objects; the chain itself, and then a
-- function (taking no parameters) that is run just before rendering.
-- The function needs to call connect_signal on any inputs, so that
-- it gets updated video data for the given frame. (You are allowed
-- to switch which input your input is getting from between frames,
-- but not calling connect_signal results in undefined behavior.)
-- If you want to change any parameters in the chain, this is also
-- the right place.
--
-- NOTE: The chain returned must be finalized with the Y'CbCr flag
-- if and only if num==0.
function get_chain(num, t, width, height, signals)
        if num == 0 then  -- Live.
                if live_signal_num == INPUT0_SIGNAL_NUM or live_signal_num == INPUT1_SIGNAL_NUM then  -- Plain input.
                        local input_type = get_input_type(signals, live_signal_num)
                        local chain = simple_chains[input_type][true]
                        prepare = function()
                                chain.input:connect_signal(live_signal_num)
                                set_neutral_color_from_signal(chain.wb_effect, live_signal_num)
                        end
                        return chain.chain, prepare
                elseif live_signal_num == STATIC_SIGNAL_NUM then  -- Static picture.
                        prepare = function()
                        end
                        return static_chain_hq, prepare
                elseif live_signal_num == FADE_SIGNAL_NUM then  -- Fade.
                        local input0_type = get_input_type(signals, fade_src_signal)
                        local input1_type = get_input_type(signals, fade_dst_signal)
                        local chain = fade_chains[input0_type][input1_type][true]
                        prepare = function()
                                if input0_type == "live" then
                                        chain.input0.input:connect_signal(fade_src_signal)
                                        set_neutral_color_from_signal(chain.input0.wb_effect, fade_src_signal)
                                end
                                if input1_type == "live" then
                                        chain.input1.input:connect_signal(fade_dst_signal)
                                        set_neutral_color_from_signal(chain.input1.wb_effect, fade_dst_signal)
                                end
                                local tt = calc_fade_progress(t, transition_start, transition_end)

                                chain.mix_effect:set_float("strength_first", 1.0 - tt)
                                chain.mix_effect:set_float("strength_second", tt)
                        end
                        return chain.chain, prepare
                end

                -- SBS code (live_signal_num == SBS_SIGNAL_NUM).
                local input0_type = get_input_type(signals, INPUT0_SIGNAL_NUM)
                local input1_type = get_input_type(signals, INPUT1_SIGNAL_NUM)
                if t > transition_end and zoom_dst == 1.0 then
                        -- Special case: Show only the single image on screen.
                        local chain = simple_chains[input0_type][true]
                        prepare = function()
                                chain.input:connect_signal(INPUT0_SIGNAL_NUM)
                                set_neutral_color(chain.wb_effect, input0_neutral_color)
                        end
                        return chain.chain, prepare
                end
                local chain = sbs_chains[input0_type][input1_type][true]
                prepare = function()
                        if t < transition_start then
                                prepare_sbs_chain(chain, zoom_src, width, height)
                        elseif t > transition_end then
                                prepare_sbs_chain(chain, zoom_dst, width, height)
                        else
                                local tt = (t - transition_start) / (transition_end - transition_start)
                                -- Smooth it a bit.
                                tt = math.sin(tt * 3.14159265358 * 0.5)
                                prepare_sbs_chain(chain, zoom_src + (zoom_dst - zoom_src) * tt, width, height)
                        end
                end
                return chain.chain, prepare
        end
        if num == 1 then  -- Preview.
                num = preview_signal_num + 2
        end

        -- Individual preview inputs.
        if num == INPUT0_SIGNAL_NUM + 2 then
                local input_type = get_input_type(signals, INPUT0_SIGNAL_NUM)
                local chain = simple_chains[input_type][false]
                prepare = function()
                        chain.input:connect_signal(INPUT0_SIGNAL_NUM)
                        set_neutral_color(chain.wb_effect, input0_neutral_color)
                end
                return chain.chain, prepare
        end
        if num == INPUT1_SIGNAL_NUM + 2 then
                local input_type = get_input_type(signals, INPUT1_SIGNAL_NUM)
                local chain = simple_chains[input_type][false]
                prepare = function()
                        chain.input:connect_signal(INPUT1_SIGNAL_NUM)
                        set_neutral_color(chain.wb_effect, input1_neutral_color)
                end
                return chain.chain, prepare
        end
        if num == SBS_SIGNAL_NUM + 2 then
                local input0_type = get_input_type(signals, INPUT0_SIGNAL_NUM)
                local input1_type = get_input_type(signals, INPUT1_SIGNAL_NUM)
                local chain = sbs_chains[input0_type][input1_type][false]
                prepare = function()
                        prepare_sbs_chain(chain, 0.0, width, height)
                end
                return chain.chain, prepare
        end
        if num == STATIC_SIGNAL_NUM + 2 then
                prepare = function()
                end
                return static_chain_lq, prepare
        end
end

function place_rectangle(resample_effect, resize_effect, padding_effect, x0, y0, x1, y1, screen_width, screen_height, input_width, input_height)
        local srcx0 = 0.0
        local srcx1 = 1.0
        local srcy0 = 0.0
        local srcy1 = 1.0

        -- Cull.
        if x0 > screen_width or x1 < 0.0 or y0 > screen_height or y1 < 0.0 then
                resample_effect:set_int("width", 1)
                resample_effect:set_int("height", 1)
                resample_effect:set_float("zoom_x", screen_width)
                resample_effect:set_float("zoom_y", screen_height)
                padding_effect:set_int("left", screen_width + 100)
                padding_effect:set_int("top", screen_height + 100)
                return
        end

        -- Clip.
        if x0 < 0 then
                srcx0 = -x0 / (x1 - x0)
                x0 = 0
        end
        if y0 < 0 then
                srcy0 = -y0 / (y1 - y0)
                y0 = 0
        end
        if x1 > screen_width then
                srcx1 = (screen_width - x0) / (x1 - x0)
                x1 = screen_width
        end
        if y1 > screen_height then
                srcy1 = (screen_height - y0) / (y1 - y0)
                y1 = screen_height
        end

        if resample_effect ~= nil then
                -- High-quality resampling.
                local x_subpixel_offset = x0 - math.floor(x0)
                local y_subpixel_offset = y0 - math.floor(y0)

                -- Resampling must be to an integral number of pixels. Round up,
                -- and then add an extra pixel so we have some leeway for the border.
                local width = math.ceil(x1 - x0) + 1
                local height = math.ceil(y1 - y0) + 1
                resample_effect:set_int("width", width)
                resample_effect:set_int("height", height)

                -- Correct the discrepancy with zoom. (This will leave a small
                -- excess edge of pixels and subpixels, which we'll correct for soon.)
                local zoom_x = (x1 - x0) / (width * (srcx1 - srcx0))
                local zoom_y = (y1 - y0) / (height * (srcy1 - srcy0))
                resample_effect:set_float("zoom_x", zoom_x)
                resample_effect:set_float("zoom_y", zoom_y)
                resample_effect:set_float("zoom_center_x", 0.0)
                resample_effect:set_float("zoom_center_y", 0.0)

                -- Padding must also be to a whole-pixel offset.
                padding_effect:set_int("left", math.floor(x0))
                padding_effect:set_int("top", math.floor(y0))

                -- Correct _that_ discrepancy by subpixel offset in the resampling.
                resample_effect:set_float("left", srcx0 * input_width - x_subpixel_offset / zoom_x)
                resample_effect:set_float("top", srcy0 * input_height - y_subpixel_offset / zoom_y)

                -- Finally, adjust the border so it is exactly where we want it.
                padding_effect:set_float("border_offset_left", x_subpixel_offset)
                padding_effect:set_float("border_offset_right", x1 - (math.floor(x0) + width))
                padding_effect:set_float("border_offset_top", y_subpixel_offset)
                padding_effect:set_float("border_offset_bottom", y1 - (math.floor(y0) + height))
        else
                -- Lower-quality simple resizing.
                local width = round(x1 - x0)
                local height = round(y1 - y0)
                resize_effect:set_int("width", width)
                resize_effect:set_int("height", height)

                -- Padding must also be to a whole-pixel offset.
                padding_effect:set_int("left", math.floor(x0))
                padding_effect:set_int("top", math.floor(y0))
        end
end

-- This is broken, of course (even for positive numbers), but Lua doesn't give us access to real rounding.
function round(x)
        return math.floor(x + 0.5)
end

function lerp(a, b, t)
        return a + (b - a) * t
end

function prepare_sbs_chain(chain, t, screen_width, screen_height)
        chain.input0.input:connect_signal(0)
        chain.input1.input:connect_signal(1)
        set_neutral_color(chain.input0.wb_effect, input0_neutral_color)
        set_neutral_color(chain.input1.wb_effect, input1_neutral_color)

        -- First input is positioned (16,48) from top-left.
        local width0 = round(848 * screen_width/1280.0)
        local height0 = round(width0 * 9.0 / 16.0)

        local top0 = 48 * screen_height/720.0
        local left0 = 16 * screen_width/1280.0
        local bottom0 = top0 + height0
        local right0 = left0 + width0

        -- Second input is positioned (16,48) from the bottom-right.
        local width1 = round(384 * screen_width/1280.0)
        local height1 = round(216 * screen_height/720.0)

        local bottom1 = screen_height - 48 * screen_height/720.0
        local right1 = screen_width - 16 * screen_width/1280.0
        local top1 = bottom1 - height1
        local left1 = right1 - width1

        -- Interpolate between the fullscreen and side-by-side views.
        local scale0, tx0, tx0
        if zoom_poi == INPUT0_SIGNAL_NUM then
                local new_left0 = lerp(left0, 0, t)
                local new_right0 = lerp(right0, screen_width, t)
                local new_top0 = lerp(top0, 0, t)
                local new_bottom0 = lerp(bottom0, screen_height, t)

                scale0 = (new_right0 - new_left0) / width0  -- Same vertically and horizonally.
                tx0 = new_left0 - left0 * scale0
                ty0 = new_top0 - top0 * scale0
        else
                local new_left1 = lerp(left1, 0, t)
                local new_right1 = lerp(right1, screen_width, t)
                local new_top1 = lerp(top1, 0, t)
                local new_bottom1 = lerp(bottom1, screen_height, t)

                scale0 = (new_right1 - new_left1) / width1  -- Same vertically and horizonally.
                tx0 = new_left1 - left1 * scale0
                ty0 = new_top1 - top1 * scale0
        end

        top0 = top0 * scale0 + ty0
        bottom0 = bottom0 * scale0 + ty0
        left0 = left0 * scale0 + tx0
        right0 = right0 * scale0 + tx0

        top1 = top1 * scale0 + ty0
        bottom1 = bottom1 * scale0 + ty0
        left1 = left1 * scale0 + tx0
        right1 = right1 * scale0 + tx0
        place_rectangle(chain.input0.resample_effect, chain.input0.resize_effect, chain.input0.padding_effect, left0, top0, right0, bottom0, screen_width, screen_height, 1280, 720)
        place_rectangle(chain.input1.resample_effect, chain.input1.resize_effect, chain.input1.padding_effect, left1, top1, right1, bottom1, screen_width, screen_height, 1280, 720)
end

function set_neutral_color(effect, color)
        effect:set_vec3("neutral_color", color[1], color[2], color[3])
end

function set_neutral_color_from_signal(effect, signal)
        if signal == INPUT0_SIGNAL_NUM then
                set_neutral_color(effect, input0_neutral_color)
        else
                set_neutral_color(effect, input1_neutral_color)
        end
end

function calc_fade_progress(t, transition_start, transition_end)
        local tt = (t - transition_start) / (transition_end - transition_start)
        if tt < 0.0 then
                tt = 0.0
        elseif tt > 1.0 then
                tt = 1.0
        end

        -- Make the fade look maybe a tad more natural, by pumping it
        -- through a sigmoid function.
        tt = 10.0 * tt - 5.0
        tt = 1.0 / (1.0 + math.exp(-tt))

        return tt
end