path: root/src/animation.zig

//! Animation curves and the panel transition records every shell reads:
//! easing presets, transition kinds and their tracks, the fractional boxes
//! they move through, the character effects' per-cell sources, and the
//! generic displayed-value Transition the chrome colours use.
const std = @import("std");

pub const ascii_max_movement_frames: u16 = 12;

pub const Easing = enum(u8) {
    linear,
    smooth,
    /// Quintic ease-in-out. It creeps at both ends and crosses the middle of
    /// the distance fast, inside the same frame count a linear walk would use.
    smoother,
    in_cubic,
    out_cubic,
    out_back,
};

pub const Transition = enum(u8) {
    // Numeric values are shared with the GUI shader ABI.
    off = 0,
    slide = 1,
    zoom = 2,
    dissolve = 3,
    ascii = 4,
    vertical = 5,
    edges = 6,
    fall = 7,
    wave = 8,
    curtain = 9,
    scramble = 10,
    typewriter = 11,

    pub fn easing(effect: Transition) Easing {
        return switch (effect) {
            .off, .dissolve, .wave => .smooth,
            .slide, .vertical, .edges => .out_cubic,
            .zoom => .out_back,
            // Character walks and per-cell locks read best with a slow start,
            // a fast middle, and a slow settle over their fixed frame count.
            .ascii, .fall, .scramble => .smoother,
            // A sweep and a typewriter are constant-rate by definition: easing
            // their head would make the pass visibly hesitate mid-pane.
            .curtain, .typewriter => .linear,
        };
    }

    pub fn frames(effect: Transition) u16 {
        return switch (effect) {
            .off => 0,
            .slide => 12,
            .zoom => 14,
            .dissolve => 10,
            .ascii => ascii_max_movement_frames + 1,
            .vertical => 12,
            .edges, .curtain, .scramble => 12,
            // Travelling motion needs a couple more samples than a lock or a
            // rigid slide before it stops reading as a jump.
            .fall, .wave, .typewriter => 14,
        };
    }

    pub fn composedByCore(effect: Transition) bool {
        return switch (effect) {
            .ascii, .edges, .fall, .wave, .curtain, .scramble, .typewriter => true,
            .off, .slide, .zoom, .dissolve, .vertical => false,
        };
    }

    pub fn needsPreviousGrid(effect: Transition) bool {
        return effect == .dissolve or effect == .vertical or effect.composedByCore();
    }

    pub fn lifecycleOnly(effect: Transition) bool {
        return effect == .vertical;
    }
};

pub const Phase = enum(u8) {
    opening = 0,
    moving = 1,
    /// Presentation-only content whose pane lifetime has already ended.
    /// It is never a valid input target.
    closing = 2,
};

pub const Box = extern struct {
    x: f32 = 0,
    y: f32 = 0,
    w: f32 = 0,
    h: f32 = 0,

    pub fn eql(a: Box, b: Box) bool {
        return a.x == b.x and a.y == b.y and a.w == b.w and a.h == b.h;
    }

    // A cell belongs to a fractional box when its center lies inside.
    pub fn contains(box: Box, col: u16, row: u16) bool {
        const x: f32 = @floatFromInt(col);
        const y: f32 = @floatFromInt(row);
        return x >= box.x and x < box.x + box.w and y >= box.y and y < box.y + box.h;
    }
};

// Drawing and hit testing share this moving/opening/closing order.
pub fn paintOrder(live: []const ?Track, closing: []const Track, out: []Track) usize {
    var len: usize = 0;
    for ([_]Phase{ .moving, .opening }) |phase| for (live) |maybe| {
        const track = maybe orelse continue;
        if (!track.active() or track.phase != phase) continue;
        if (len == out.len) return len;
        out[len] = track;
        len += 1;
    };
    for (closing) |track| {
        if (!track.active()) continue;
        if (len == out.len) return len;
        out[len] = track;
        len += 1;
    }
    return len;
}

/// One POD record is enough for every backend. `from` and `to` are logical
/// cell boxes; frontends convert them to pixels only at their render edge.
pub const Track = extern struct {
    serial: u32 = 0,
    pane: u8 = 0,
    phase: Phase = .moving,
    effect: Transition = .off,
    /// The Motion flavour a pane's move follows, plus one; 0 is the
    /// effect's own easing (Presentation.stamp).
    motion: u8 = 0,
    frame: u16 = 0,
    frame_count: u16 = 0,
    from: Box = .{},
    to: Box = .{},

    pub fn active(track: Track) bool {
        return track.effect != .off and track.frame < track.frames();
    }

    pub fn frames(track: Track) u16 {
        return if (track.frame_count != 0) track.frame_count else track.effect.frames();
    }

    pub fn amount(track: Track) f32 {
        // Opening rises quickly and settles; closing reverses that motion and
        // accelerates down out of the fixed clip.
        if (track.phase == .closing and track.effect == .vertical)
            return progressEased(.in_cubic, track.frames(), track.frame);
        if (track.flavour()) |motion|
            return motion.ease(track.progress());
        return progressEased(track.effect.easing(), track.frames(), track.frame);
    }

    /// The flavour an opening or moving pane follows; a closing one keeps
    /// its effect's own exit.
    fn flavour(track: Track) ?Motion {
        if (track.motion == 0 or track.phase == .closing) return null;
        const which = std.enums.fromInt(Motion.Flavour, track.motion - 1) orelse return null;
        return Motion.of(which);
    }

    fn progress(track: Track) f32 {
        if (track.frames() <= 1 or track.frame >= track.frames() - 1) return 1;
        return @as(f32, @floatFromInt(track.frame)) / @as(f32, @floatFromInt(track.frames() - 1));
    }

    pub fn presented(track: Track) Box {
        // A flavour's wind-up goes back past where the move began.
        const t = track.amount();
        // Landed, it is exactly where it goes: no stretch or float residue.
        if (track.flavour() != null and track.progress() >= 1) return track.to;
        var box = if (t < 0) lerpBox(track.to, track.from, 1 - t) else lerpBox(track.from, track.to, t);
        // Squash and stretch: along its path a moving pane lengthens with
        // its speed and, landing past its mark and coming back, squashes
        // (the user's choice: its text with it; a pointer inverts the same
        // box, so a click lands on the glyph it is drawn as).
        const motion = track.flavour() orelse return box;
        if (motion.stretch == 0) return box;
        const factor = 1 + motion.stretch * std.math.clamp(motion.speed(track.progress()) / 4, -1, 1);
        if (@abs(track.to.x - track.from.x) >= @abs(track.to.y - track.from.y)) {
            const w = box.w * factor;
            box.x -= (w - box.w) / 2;
            box.w = w;
        } else {
            const h = box.h * factor;
            box.y -= (h - box.h) / 2;
            box.h = h;
        }
        return box;
    }

    pub fn visualBox(track: Track) Box {
        return switch (track.effect) {
            .slide, .zoom, .vertical => track.presented(),
            .off, .dissolve => track.to,
            // Every character effect stays inside the pane's final rectangle.
            .ascii, .edges, .fall, .wave, .curtain, .scramble, .typewriter => track.to,
        };
    }

    pub fn contentBox(track: Track) Box {
        return if (track.phase == .closing) track.from else track.to;
    }
};

pub fn openingBox(effect: Transition, target: Box, screen_width: u16) Box {
    return switch (effect) {
        .slide => blk: {
            var from = target;
            const middle = target.x + target.w * 0.5;
            from.x = if (middle < @as(f32, @floatFromInt(screen_width)) * 0.5)
                -target.w
            else
                @floatFromInt(screen_width);
            break :blk from;
        },
        .zoom => .{
            .x = target.x + target.w * 0.5,
            .y = target.y + target.h * 0.5,
            .w = 0,
            .h = 0,
        },
        .vertical => blk: {
            var from = target;
            from.y += target.h;
            break :blk from;
        },
        .off, .dissolve => target,
        // Character effects own the glyphs inside a fixed rectangle, so their
        // panel opens at exactly its final geometry.
        .ascii, .edges, .fall, .wave, .curtain, .scramble, .typewriter => target,
    };
}

pub fn closingBox(effect: Transition, source: Box) Box {
    return switch (effect) {
        .vertical => blk: {
            var to = source;
            to.y += source.h;
            break :blk to;
        },
        else => source,
    };
}

pub fn sample(easing: Easing, raw: f32) f32 {
    const t = std.math.clamp(raw, 0.0, 1.0);
    return switch (easing) {
        .linear => t,
        .smooth => t * t * (3.0 - 2.0 * t),
        .smoother => t * t * t * (t * (6.0 * t - 15.0) + 10.0),
        .in_cubic => t * t * t,
        .out_cubic => 1.0 - (1.0 - t) * (1.0 - t) * (1.0 - t),
        // Robert Penner's ease-out-back polynomial. It intentionally travels
        // a little past one before settling exactly on the endpoint.
        .out_back => blk: {
            const c1: f32 = 1.70158;
            const c3 = c1 + 1.0;
            const u = t - 1.0;
            break :blk 1.0 + c3 * u * u * u + c1 * u * u;
        },
    };
}

pub fn progress(effect: Transition, frame: u16) f32 {
    return progressEased(effect.easing(), effect.frames(), frame);
}

fn progressEased(easing: Easing, frames: u16, frame: u16) f32 {
    if (frames <= 1 or frame >= frames - 1) return 1.0;
    return sample(easing, @as(f32, @floatFromInt(frame)) / @as(f32, @floatFromInt(frames - 1)));
}

pub fn lerpBox(from: Box, to: Box, t: f32) Box {
    const u = @max(0.0, t);
    return .{
        .x = from.x + (to.x - from.x) * u,
        .y = from.y + (to.y - from.y) * u,
        .w = @max(0.0, from.w + (to.w - from.w) * u),
        .h = @max(0.0, from.h + (to.h - from.h) * u),
    };
}

/// Stable cell noise shared by the TTY reveal and shader ports. Integer-only
/// hashing means resizing or repainting a frame does not make cells flicker.
pub fn cellNoise(serial: u32, col: u16, row: u16) f32 {
    var x = serial ^ (@as(u32, col) *% 0x9e37_79b9) ^ (@as(u32, row) *% 0x85eb_ca6b);
    x ^= x >> 16;
    x *%= 0x7feb_352d;
    x ^= x >> 15;
    x *%= 0x846c_a68b;
    x ^= x >> 16;
    return @as(f32, @floatFromInt(x & 0xffff)) / 65535.0;
}

/// Whether a changed dissolve cell has crossed from the frozen old grid to
/// the new one. Exact endpoints are part of the presentation contract.
pub fn dissolveRevealed(serial: u32, col: u16, row: u16, raw_progress: f32) bool {
    const t = std.math.clamp(raw_progress, 0.0, 1.0);
    if (t <= 0) return false;
    if (t >= 1) return true;
    return cellNoise(serial, col, row) < t;
}

pub const CellArea = struct {
    x0: u16 = 0,
    y0: u16 = 0,
    cols: u16 = 1,
    rows: u16 = 1,

    pub fn of(box: Box) CellArea {
        return .{
            .x0 = floorCell(box.x),
            .y0 = floorCell(box.y),
            .cols = ceilCell(box.w),
            .rows = ceilCell(box.h),
        };
    }
};

fn floorCell(value: f32) u16 {
    return @intFromFloat(std.math.clamp(@floor(value), 0.0, @as(f32, std.math.maxInt(u16))));
}

fn ceilCell(value: f32) u16 {
    return @intFromFloat(std.math.clamp(@ceil(value), 1.0, @as(f32, std.math.maxInt(u16))));
}

pub const CharSource = union(enum) {
    /// Nothing has arrived here yet: keep the frozen old cell.
    old,
    at: Offset,
    /// Paint this printable byte in the destination cell's own style, whatever
    /// that cell holds — a caret marching over empty space is still a caret.
    byte: u8,
    churn: u8,

    pub const Offset = struct { cols: i32 = 0, rows: i32 = 0 };

    pub const settled: CharSource = .{ .at = .{} };
};

pub fn charSource(track: Track, col: u16, row: u16, area: CellArea) CharSource {
    const t = track.amount();
    if (t >= 1.0) return .settled;
    const w: f32 = @floatFromInt(area.cols);
    const h: f32 = @floatFromInt(area.rows);
    const c: f32 = @floatFromInt(col);
    const r: f32 = @floatFromInt(row);
    const remaining = 1.0 - t;
    return switch (track.effect) {
        .edges => blk: {
            const travel = cellsOf(remaining * (w + 1.0));
            break :blk .{ .at = .{ .cols = if (row % 2 == 0) travel else -travel } };
        },
        // Columns rain down, each with its own stable head start, so the pane
        // fills from the top and the last glyphs land at the bottom.
        .fall => blk: {
            const local = staggered(t, cellNoise(track.serial, col, 0) * 0.4);
            if (local <= 0.0) break :blk .old;
            break :blk .{ .at = .{ .rows = cellsOf((1.0 - local) * (h + 1.0)) } };
        },
        // A vertical ripple travels left to right and its amplitude decays, so
        // the pane settles out of a wave instead of a fade.
        .wave => .{ .at = .{
            .rows = cellsOf(remaining * @min(4.0, h) * @sin(c * 0.55 - t * 9.0)),
        } },
        // A curtain of glyphs marches in from the right, column by column, left
        // to right; each column still has a short slide of its own.
        .curtain => blk: {
            const lead = t * (w + 1.0) - c;
            if (lead <= 0.0) break :blk .old;
            break :blk .{ .at = .{ .cols = -cellsOf(@max(0.0, 3.0 - lead)) } };
        },
        // Every cell churns through printable ASCII and locks onto its final
        // glyph at its own stable threshold: the pane resolves out of noise.
        .scramble => blk: {
            if (t >= cellNoise(track.serial, col, row) * 0.8) break :blk .settled;
            const churn = cellNoise(
                track.serial ^ (@as(u32, track.frame) *% 0x27d4_eb2f),
                col,
                row,
            );
            break :blk .{ .churn = @intCast(33 + @min(93, @as(u32, @intFromFloat(churn * 94.0)))) };
        },
        // Reading-order reveal with a caret sitting on the write head.
        .typewriter => blk: {
            const head = t * w * h;
            const index = r * w + c;
            if (index + 1.0 <= head) break :blk .settled;
            if (index <= head) break :blk .{ .byte = '_' };
            break :blk .old;
        },
        // PanelAscii walks its own byte distance per cell, and the geometry
        // effects never reach this path at all.
        .off, .slide, .zoom, .dissolve, .vertical, .ascii => .settled,
    };
}

fn cellsOf(distance: f32) i32 {
    return @intFromFloat(@round(std.math.clamp(distance, -65535.0, 65535.0)));
}

/// Remap track progress into one cell's own window. A stagger delays a glyph
/// without making the effect as a whole end after its last frame.
fn staggered(t: f32, delay: f32) f32 {
    if (delay >= 1.0) return t;
    return (t - delay) / (1.0 - delay);
}

test "easing presets have exact endpoints and intended shapes" {
    inline for (std.enums.values(Easing)) |easing| {
        try std.testing.expectEqual(@as(f32, 0), sample(easing, 0));
        try std.testing.expectEqual(@as(f32, 1), sample(easing, 1));
    }
    try std.testing.expectEqual(@as(f32, 0.5), sample(.linear, 0.5));
    try std.testing.expect(sample(.in_cubic, 0.5) < sample(.linear, 0.5));
    try std.testing.expect(sample(.out_cubic, 0.5) > sample(.linear, 0.5));
    try std.testing.expect(sample(.out_back, 0.8) > 1.0);
    // Slow at both ends, fast through the middle, and symmetric about the
    // halfway point: the same curve the integer byte walk reproduces.
    try std.testing.expectEqual(@as(f32, 0.5), sample(.smoother, 0.5));
    try std.testing.expect(sample(.smoother, 0.15) < sample(.smooth, 0.15));
    try std.testing.expect(sample(.smoother, 0.85) > sample(.smooth, 0.85));
    try std.testing.expect(sample(.smoother, 0.6) - sample(.smoother, 0.4) >
        sample(.linear, 0.6) - sample(.linear, 0.4));
}

test "transition progress completes exactly" {
    inline for (std.enums.values(Transition)) |effect| {
        try std.testing.expectEqual(@as(f32, 1), progress(effect, effect.frames()));
        if (effect.frames() > 0)
            try std.testing.expectEqual(@as(f32, 1), progress(effect, effect.frames() - 1));
        try std.testing.expectEqual(@as(f32, 1), progress(effect, std.math.maxInt(u16)));
    }
    try std.testing.expectEqual(@as(f32, 1), progress(.off, 0));

    const shrinking = lerpBox(.{ .w = 100, .h = 40 }, .{}, sample(.out_back, 0.8));
    try std.testing.expectEqual(@as(f32, 0), shrinking.w);
    try std.testing.expectEqual(@as(f32, 0), shrinking.h);
    const opening = lerpBox(.{}, .{ .w = 100, .h = 40 }, sample(.out_back, 0.8));
    try std.testing.expect(opening.w > 100);
    try std.testing.expect(opening.h > 40);
}

test "character effects are core-composed and settle on the canonical glyph" {
    const box: Box = .{ .x = 4, .y = 2, .w = 20, .h = 6 };
    const area: CellArea = .of(box);
    try std.testing.expectEqual(@as(u16, 4), area.x0);
    try std.testing.expectEqual(@as(u16, 2), area.y0);
    try std.testing.expectEqual(@as(u16, 20), area.cols);
    try std.testing.expectEqual(@as(u16, 6), area.rows);

    inline for (std.enums.values(Transition)) |effect| {
        if (comptime !effect.composedByCore()) continue;
        // Core composition needs the frozen old grid for every glyph which has
        // not arrived, so no character effect may animate without it.
        try std.testing.expect(effect.needsPreviousGrid());
        if (comptime effect == .ascii) continue; // owns its own per-cell byte walk

        const last: Track = .{ .effect = effect, .frame = effect.frames() - 1, .to = box };
        const first: Track = .{ .effect = effect, .frame = 0, .to = box };
        var moving = false;
        var row: u16 = 0;
        while (row < area.rows) : (row += 1) {
            var col: u16 = 0;
            while (col < area.cols) : (col += 1) {
                // The last active sample is the exact canonical grid: no cell
                // is displaced, churning, or still frozen.
                try std.testing.expectEqual(CharSource.settled, charSource(last, col, row, area));
                if (!std.meta.eql(CharSource.settled, charSource(first, col, row, area)))
                    moving = true;
            }
        }
        try std.testing.expect(moving);
    }
}

test "each character effect moves glyphs along its own axis" {
    const box: Box = .{ .w = 30, .h = 8 };
    const area: CellArea = .of(box);

    // Rows alternate which screen edge they come from, and every glyph in a row
    // travels as one rigid slide: one offset, no vertical component.
    var edges: Track = .{ .effect = .edges, .frame = 2, .to = box };
    const even = charSource(edges, 5, 0, area).at;
    const odd = charSource(edges, 5, 1, area).at;
    try std.testing.expect(even.cols > 0);
    try std.testing.expectEqual(-even.cols, odd.cols);
    try std.testing.expectEqual(@as(i32, 0), even.rows);
    try std.testing.expectEqual(even, charSource(edges, 17, 0, area).at);
    edges.frame = 5;
    try std.testing.expect(charSource(edges, 5, 0, area).at.cols < even.cols);

    // Falling columns are vertical only, staggered, and sample from below the
    // destination because the new text is still above the pane.
    const fall: Track = .{ .effect = .fall, .frame = 4, .to = box };
    var falling = false;
    var col: u16 = 0;
    while (col < area.cols) : (col += 1) switch (charSource(fall, col, 0, area)) {
        .old => {},
        .byte, .churn => return error.FallShouldNotChurn,
        .at => |offset| {
            try std.testing.expectEqual(@as(i32, 0), offset.cols);
            try std.testing.expect(offset.rows >= 0);
            if (offset.rows > 0) falling = true;
        },
    };
    try std.testing.expect(falling);

    // The wave displaces rows both ways as it travels, and only rows.
    const wave: Track = .{ .effect = .wave, .frame = 1, .to = box };
    var above = false;
    var below = false;
    col = 0;
    while (col < area.cols) : (col += 1) {
        const offset = charSource(wave, col, 3, area).at;
        try std.testing.expectEqual(@as(i32, 0), offset.cols);
        if (offset.rows < 0) above = true;
        if (offset.rows > 0) below = true;
    }
    try std.testing.expect(above and below);

    // The curtain has a head: columns behind it hold the old grid, columns the
    // head has passed are settled, and the head itself is still sliding.
    const curtain: Track = .{ .effect = .curtain, .frame = 5, .to = box };
    try std.testing.expectEqual(CharSource.settled, charSource(curtain, 0, 0, area));
    try std.testing.expectEqual(CharSource{ .old = {} }, charSource(curtain, 29, 0, area));
    var sliding = false;
    col = 0;
    while (col < area.cols) : (col += 1) switch (charSource(curtain, col, 0, area)) {
        .at => |offset| if (offset.cols < 0) {
            sliding = true;
        },
        .old, .byte, .churn => {},
    };
    try std.testing.expect(sliding);

    var scramble: Track = .{ .effect = .scramble, .frame = 3, .to = box };
    var churning: usize = 0;
    var locked: usize = 0;
    var changed = false;
    col = 0;
    while (col < area.cols) : (col += 1) switch (charSource(scramble, col, 0, area)) {
        .churn => |byte| {
            try std.testing.expect(byte >= ' ' and byte <= '~');
            churning += 1;
            scramble.frame = 4;
            switch (charSource(scramble, col, 0, area)) {
                .churn => |next| changed = changed or next != byte,
                .old, .at, .byte => {},
            }
            scramble.frame = 3;
        },
        .at => locked += 1,
        .old, .byte => return error.ScrambleShouldNotFreeze,
    };
    try std.testing.expect(churning > 0 and locked > 0 and changed);

    // The typewriter writes in reading order with a caret on its head.
    const typewriter: Track = .{ .effect = .typewriter, .frame = 7, .to = box };
    try std.testing.expectEqual(CharSource.settled, charSource(typewriter, 0, 0, area));
    try std.testing.expectEqual(
        CharSource{ .old = {} },
        charSource(typewriter, area.cols - 1, area.rows - 1, area),
    );
    var carets: usize = 0;
    var row: u16 = 0;
    while (row < area.rows) : (row += 1) {
        col = 0;
        while (col < area.cols) : (col += 1) switch (charSource(typewriter, col, row, area)) {
            .byte => |byte| {
                try std.testing.expectEqual(@as(u8, '_'), byte);
                carets += 1;
            },
            .old, .at, .churn => {},
        };
    }
    try std.testing.expectEqual(@as(usize, 1), carets);
}

test "opening presets separate geometry and content transitions" {
    const target: Box = .{ .x = 30, .y = 2, .w = 20, .h = 8 };
    try std.testing.expectEqual(target, openingBox(.ascii, target, 80));
    try std.testing.expectEqual(@as(f32, 0), openingBox(.zoom, target, 80).w);
    try std.testing.expectEqual(@as(f32, 80), openingBox(.slide, target, 80).x);
    try std.testing.expectEqual(@as(f32, target.y + target.h), openingBox(.vertical, target, 80).y);
    try std.testing.expectEqual(@as(f32, target.y + target.h), closingBox(.vertical, target).y);

    var track: Track = .{ .effect = .slide, .from = target, .to = target };
    try std.testing.expect(track.active());
    track.frame = track.effect.frames();
    try std.testing.expect(!track.active());

    track = .{ .effect = .dissolve, .frame = 3, .from = .{}, .to = target };
    try std.testing.expectEqual(target, track.visualBox());

    var closing: Track = .{
        .phase = .closing,
        .effect = .vertical,
        .from = target,
        .to = closingBox(.vertical, target),
    };
    try std.testing.expectEqual(target, closing.contentBox());
    closing.frame = 2;
    try std.testing.expect(closing.amount() < progress(.vertical, closing.frame));
}

test "dissolve has exact stable endpoints" {
    for (0..64) |col| {
        const x: u16 = @intCast(col);
        try std.testing.expect(!dissolveRevealed(42, x, 7, 0));
        try std.testing.expect(dissolveRevealed(42, x, 7, 1));
        if (dissolveRevealed(42, x, 7, 0.25))
            try std.testing.expect(dissolveRevealed(42, x, 7, 0.75));
    }
}

pub const frame_ms: u32 = 16;
pub const frame_ns: u64 = frame_ms * std.time.ns_per_ms;
pub const transition_steps: u16 = 10;

/// How the fx track moves (`Motion <flavour>`, docs/effects.md): one set of
/// parameters a flavour picks, read by every animation that follows the
/// classic principles, so a flavour is data and no effect branches on it.
pub const Motion = struct {
    pub const Flavour = enum(u8) { off, crisp, smooth, bouncy, playful };

    /// Nothing moves: every change lands at once (reduced motion).
    instant: bool = false,
    /// Timing: the spring's natural frequency, rad/s; slow in / slow out
    /// come from the spring itself.
    omega: f32 = 36,
    /// Follow-through: 1 is critically damped (no overshoot); below 1 it
    /// settles past its target and back.
    zeta: f32 = 1,
    /// Anticipation: a move from rest first winds up the other way, by
    /// this fraction of the distance.
    anticipate: f32 = 0,
    /// Squash and stretch: how much a moving thing lengthens along its
    /// velocity and squashes as it lands (G3's cursor, G7's panes).
    stretch: f32 = 0,
    /// Secondary action: how far behind a follower trails its leader (the
    /// shadow behind a pane, a notice's text behind its chip), as the
    /// follower's frequency over the leader's; 1 is in step.
    follow: f32 = 1,
    /// Arcs: how far a two-dimensional path bows, as a fraction of its
    /// length (the cursor's glide).
    arc: f32 = 0,
    /// Exaggeration: how far a small motion goes, as a multiple of its
    /// plain distance (a lift of 1 rises `gain`), so a flavour's character
    /// shows on a motion only a few pixels big.
    gain: f32 = 1,
    /// Timing: a move from rest leaves at this fraction of full speed (1:
    /// out of the gate at once and easing in, 0: slow in and slow out).
    launch: f32 = 0,
    /// For a motion of fixed length (a pane's move, a notice's drop): its
    /// length as a multiple of the effect's own, and the spring's frequency
    /// over that length (`ease`).
    span: f32 = 1,
    norm: f32 = 10,

    pub fn of(flavour: Flavour) Motion {
        return switch (flavour) {
            .off => .{ .instant = true },
            // Productivity: quick and exact, nothing past its mark.
            .crisp => .{ .omega = 60, .launch = 1, .span = 0.6, .norm = 10 },
            // Longer and softer, easing in and out, still without a bounce.
            // The default: within §8.1's 220 ms for an arrival.
            .smooth => .{ .omega = 34, .follow = 0.85, .arc = 0.04, .span = 1.1, .norm = 6 },
            // Clearly past its mark and back, once or twice, stretching
            // with its speed.
            .bouncy => .{ .omega = 24, .zeta = 0.35, .stretch = 0.15, .follow = 0.8, .arc = 0.08, .gain = 1.25, .span = 1.4, .norm = 13 },
            // A cartoon's: winds up, flies past, squashes as it lands,
            // its followers trailing.
            .playful => .{ .omega = 18, .zeta = 0.28, .anticipate = 0.15, .stretch = 0.35, .follow = 0.55, .arc = 0.15, .gain = 1.4, .span = 1.7, .norm = 18 },
        };
    }

    /// A move of fixed length from 0 to 1, `u` of the way through it: the
    /// flavour's spring (wind-up, overshoot and all), landing exactly on 1
    /// at its end. `instant` is there at once.
    pub fn ease(motion: Motion, u: f32) f32 {
        if (motion.instant or u >= 1) return 1;
        if (u <= 0) return 0;
        const spring: Spring = .{ .omega = motion.norm, .zeta = motion.zeta, .target = 1, .from = 0, .velocity = (motion.launch - 2 * motion.anticipate) * motion.norm, .settled = false };
        return spring.value(@intFromFloat(u * std.time.ns_per_s));
    }

    /// The same move's speed at `u`, in lengths per unit of `u`.
    pub fn speed(motion: Motion, u: f32) f32 {
        const h: f32 = 1.0 / 256.0;
        return (motion.ease(@min(1, u + h)) - motion.ease(@max(0, u - h))) / (@min(1, u + h) - @max(0, u - h));
    }
};

/// A value that follows its target on a damped spring, in closed form
/// (docs/render-pipeline.md §7.2), critically damped or under: a new target
/// taken partway keeps the value AND its velocity, so a quick run of changes
/// never snaps or starts over. A move from rest can wind up first
/// (Motion.anticipate). Settled, it is exactly its target and asks for no
/// frames.
pub const Spring = struct {
    omega: f32 = 36,
    zeta: f32 = 1,
    target: f32 = 0,
    /// The value and velocity (per second) at `from_ns`.
    from: f32 = 0,
    velocity: f32 = 0,
    from_ns: u64 = 0,
    settled: bool = true,

    const State = struct { value: f32, velocity: f32 };

    fn at(spring: *const Spring, now_ns: u64) State {
        if (spring.settled) return .{ .value = spring.target, .velocity = 0 };
        const t: f32 = @floatCast(@as(f64, @floatFromInt(now_ns -| spring.from_ns)) / std.time.ns_per_s);
        const w = spring.omega;
        const x0 = spring.from - spring.target;
        const v0 = spring.velocity;
        if (spring.zeta >= 1) {
            const c = v0 + w * x0;
            const decay = @exp(-w * t);
            return .{ .value = spring.target + (x0 + c * t) * decay, .velocity = (v0 - w * t * c) * decay };
        }
        // Underdamped: it rings about its target as it decays.
        const z = spring.zeta;
        const wd = w * @sqrt(1 - z * z);
        const b = (v0 + z * w * x0) / wd;
        const decay = @exp(-z * w * t);
        const cos = @cos(wd * t);
        const sin = @sin(wd * t);
        return .{
            .value = spring.target + decay * (x0 * cos + b * sin),
            .velocity = decay * ((b * wd - z * w * x0) * cos - (x0 * wd + z * w * b) * sin),
        };
    }

    pub fn value(spring: *const Spring, now_ns: u64) f32 {
        return spring.at(now_ns).value;
    }

    /// Moves what it shows by `by` at `now_ns`, its speed kept, toward the
    /// same target (a scroll's picture falling behind the text it follows),
    /// at `motion`'s pace, never past its mark.
    pub fn carry(spring: *Spring, by: f32, now_ns: u64, motion: Motion) void {
        const state = spring.at(now_ns);
        spring.* = .{ .omega = motion.omega, .zeta = 1, .target = spring.target, .from = state.value + by, .velocity = state.velocity, .from_ns = now_ns, .settled = false };
    }

    /// Heads for `target` from wherever it is at `now_ns`, moving as it was,
    /// at the pace and damping `motion` gives: at once when it is `off`.
    pub fn retarget(spring: *Spring, target: f32, now_ns: u64, motion: Motion) void {
        if (target == spring.target) return;
        if (motion.instant) {
            spring.* = .{ .omega = motion.omega, .zeta = motion.zeta, .target = target, .from = target };
            return;
        }
        const state = spring.at(now_ns);
        // From rest, a launch, or a wind-up: set off the other way, a little.
        const kick: f32 = if (spring.settled) (motion.launch - 2 * motion.anticipate) * (target - state.value) * motion.omega else 0;
        spring.* = .{ .omega = motion.omega, .zeta = motion.zeta, .target = target, .from = state.value, .velocity = state.velocity + kick, .from_ns = now_ns, .settled = false };
    }

    /// Settles once it is within half a percent of its target and barely
    /// moving (no pixel of a shadow tells the rest): it is its target from
    /// then on. True while it still moves.
    pub fn step(spring: *Spring, now_ns: u64) bool {
        if (spring.settled) return false;
        const state = spring.at(now_ns);
        if (@abs(state.value - spring.target) < 5e-3 and @abs(state.velocity) < 5e-2) spring.settled = true;
        return !spring.settled;
    }
};

test "a carried spring keeps its speed, heads back to its mark and never passes it" {
    const ms = std.time.ns_per_ms;
    var spring: Spring = .{};
    const smooth = Motion.of(.smooth);
    spring.carry(-3, 0, smooth);
    try std.testing.expectEqual(@as(f32, -3), spring.value(0));
    const mid = spring.at(40 * ms);
    try std.testing.expect(mid.value > -3 and mid.value < 0 and mid.velocity > 0);
    // Another notch mid-way: one more row behind, still moving back.
    spring.carry(-1, 40 * ms, smooth);
    const after = spring.at(40 * ms);
    try std.testing.expectApproxEqAbs(mid.value - 1, after.value, 1e-5);
    try std.testing.expectApproxEqAbs(mid.velocity, after.velocity, 1e-4);
    var t: u64 = 40 * ms;
    while (spring.step(t)) : (t += frame_ns) try std.testing.expect(spring.value(t) <= 1e-4);
    try std.testing.expect(t < 400 * ms);
}

test "a spring settles without overshoot and keeps its velocity when retargeted" {
    var spring: Spring = .{};
    const ms = std.time.ns_per_ms;
    const crisp = Motion.of(.crisp);
    spring.retarget(1, 0, crisp);
    var last: f32 = 0;
    var t: u64 = 0;
    while (spring.step(t)) : (t += frame_ns) {
        const v = spring.value(t);
        try std.testing.expect(v >= last and v <= 1);
        last = v;
    }
    try std.testing.expect(t >= 80 * ms and t <= 200 * ms);
    try std.testing.expectEqual(@as(f32, 1), spring.value(t + 5 * ms));
    // Back the other way partway up: it carries on up for a moment, then
    // turns, never jumping.
    spring = .{};
    spring.retarget(1, 0, crisp);
    const before = spring.at(60 * ms);
    spring.retarget(0, 60 * ms, crisp);
    const after = spring.at(60 * ms);
    try std.testing.expectApproxEqAbs(before.value, after.value, 1e-6);
    try std.testing.expectApproxEqAbs(before.velocity, after.velocity, 1e-4);
    try std.testing.expect(spring.value(60 * ms + 500_000) > before.value);
}

test "each flavour is its own motion: off lands at once, bouncy overshoots, playful winds up first" {
    const ms = std.time.ns_per_ms;
    var spring: Spring = .{};
    spring.retarget(1, 0, Motion.of(.off));
    try std.testing.expect(spring.settled);
    try std.testing.expectEqual(@as(f32, 1), spring.value(0));
    var settle: [5]u64 = @splat(0);
    for ([_]Motion.Flavour{ .crisp, .smooth, .bouncy, .playful }) |flavour| {
        spring = .{};
        spring.retarget(1, 0, Motion.of(flavour));
        var peak: f32 = 0;
        var low: f32 = 0;
        var t: u64 = 0;
        var last = spring.at(0);
        while (spring.step(t)) : (t += ms) {
            const now = spring.at(t);
            peak = @max(peak, now.value);
            low = @min(low, now.value);
            // Continuous, a millisecond at a time: no jump anywhere.
            try std.testing.expect(@abs(now.value - last.value) < 0.07);
            last = now;
        }
        try std.testing.expect(t < 1600 * ms);
        settle[@intFromEnum(flavour)] = t;
        switch (flavour) {
            .crisp, .smooth => try std.testing.expect(peak <= 1.0005 and low >= 0),
            // Clearly past the mark, not a hint of it.
            .bouncy => try std.testing.expect(peak > 1.25 and low >= 0),
            .playful => try std.testing.expect(peak > 1.35 and low < -0.03),
            .off => unreachable,
        }
    }
    // Smooth takes twice crisp's time and more: a character, not a tuning.
    // Yet as the default a pane's arrival (a slide's 12 frames, scaled) is
    // inside §8.1's 220 ms, and a lift is still before 300 ms.
    try std.testing.expect(settle[@intFromEnum(Motion.Flavour.smooth)] > 2 * settle[@intFromEnum(Motion.Flavour.crisp)]);
    try std.testing.expect(settle[@intFromEnum(Motion.Flavour.smooth)] <= 300 * ms);
    try std.testing.expect(@round(@as(f32, 12) * Motion.of(.smooth).span) * frame_ms <= 220);
    // A fixed-length move lands exactly on its mark, whatever the flavour.
    for (std.enums.values(Motion.Flavour)) |flavour| try std.testing.expectEqual(@as(f32, 1), Motion.of(flavour).ease(1));
}

test "a flavour's stretched pane lands exactly on its box, and a click finds the glyph drawn there" {
    const from: Box = .{ .x = 0, .y = 2, .w = 30, .h = 10 };
    const to: Box = .{ .x = 37.3, .y = 2, .w = 30, .h = 10 };
    for (std.enums.values(Motion.Flavour)) |flavour| {
        var track: Track = .{ .effect = .slide, .motion = @intFromEnum(flavour) + 1, .frame_count = 20, .from = from, .to = to };
        track.frame = track.frames() - 1;
        const landed = track.presented();
        // Bit for bit: no stretch or float residue once it lands.
        try std.testing.expectEqual(to, landed);
    }
    // Playful at its most stretched: the pane is drawn wider than its box,
    // and the drawn place of a cell maps back to that cell (the pointer
    // inverts the same box: target + (x - shown.x) / shown.w * target.w).
    var track: Track = .{ .effect = .slide, .motion = @intFromEnum(Motion.Flavour.playful) + 1, .frame_count = 20, .from = from, .to = to };
    var most: u16 = 0;
    var widest: f32 = 0;
    while (track.frame < track.frames()) : (track.frame += 1) {
        if (track.presented().w > widest) {
            widest = track.presented().w;
            most = track.frame;
        }
    }
    track.frame = most;
    const shown = track.presented();
    try std.testing.expect(shown.w > to.w * 1.05);
    for (0..30) |k| {
        const cell = to.x + @as(f32, @floatFromInt(k)) + 0.5;
        const drawn = shown.x + (cell - to.x) / to.w * shown.w;
        const back = to.x + (drawn - shown.x) / shown.w * to.w;
        try std.testing.expectApproxEqAbs(cell, back, 1e-3);
    }
}

/// The focused cursor's quad (docs/render-pipeline.md §5.4), in grid cells:
/// four corners, each on its own springs, so a jump smears along its path
/// (the leading corners stiffer than the trailing ones, Motion.follow) and
/// collapses at rest; a long jump bows (Motion.arc). A move of a cell or
/// less, or any the caller calls a snap, lands at once.
pub const CursorGlide = struct {
    /// Top left, top right, bottom right, bottom left; x then y.
    corners: [4][2]Spring = @splat(@splat(.{})),
    target: Box = .{},
    from_centre: [2]f32 = .{ 0, 0 },
    placed: bool = false,

    /// How much faster than the flavour's own pace a cursor moves: it
    /// follows input (§8.1: settles in 90-150 ms on the default).
    pub const pace: f32 = 2.4;
    /// A jump longer than this, in cells, bows.
    pub const arc_from: f32 = 8;

    fn cornersOf(box: Box) [4][2]f32 {
        return .{ .{ box.x, box.y }, .{ box.x + box.w, box.y }, .{ box.x + box.w, box.y + box.h }, .{ box.x, box.y + box.h } };
    }

    fn centre(box: Box) [2]f32 {
        return .{ box.x + box.w / 2, box.y + box.h / 2 };
    }

    /// Heads for `box` at `now_ns`.
    pub fn aim(glide: *CursorGlide, box: Box, now_ns: u64, motion: Motion, snap: bool) void {
        // The same mark: nothing to do, unless a snap lands a glide under way.
        if (glide.placed and std.meta.eql(box, glide.target) and !(snap and glide.moving())) return;
        const to = cornersOf(box);
        const from_c = if (glide.placed) glide.centreAt(now_ns) else centre(box);
        const to_c = centre(box);
        const dx = to_c[0] - from_c[0];
        const dy = to_c[1] - from_c[1];
        const jump = @abs(dx) > 1.01 or @abs(dy) > 1.01;
        const land = !glide.placed or snap or motion.instant or !jump;
        glide.from_centre = from_c;
        glide.target = box;
        glide.placed = true;
        for (&glide.corners, to) |*corner, point| {
            // Leading: the corner ahead of the move, on the side it goes.
            const ahead = (point[0] - to_c[0]) * dx + (point[1] - to_c[1]) * dy;
            var own = motion;
            own.omega *= pace * (if (ahead > 0) 1 else motion.follow);
            if (land) {
                for (corner, point) |*axis, value| axis.* = .{ .omega = own.omega, .zeta = own.zeta, .target = value, .from = value };
                continue;
            }
            for (corner, point) |*axis, value| axis.retarget(value, now_ns, own);
        }
    }

    fn centreAt(glide: *const CursorGlide, now_ns: u64) [2]f32 {
        var c: [2]f32 = .{ 0, 0 };
        for (glide.corners) |corner| for (&c, corner) |*sum, axis| {
            sum.* += axis.value(now_ns) / 4;
        };
        return c;
    }

    /// Text under the cursor moved by (dx, dy) cells (a scroll): the quad
    /// moves with it, rather than gliding against text that jumped.
    pub fn shift(glide: *CursorGlide, dx: f32, dy: f32) void {
        for (&glide.corners) |*corner| for (corner, [2]f32{ dx, dy }) |*axis, d| {
            axis.from += d;
            axis.target += d;
        };
        glide.from_centre = .{ glide.from_centre[0] + dx, glide.from_centre[1] + dy };
        glide.target.x += dx;
        glide.target.y += dy;
    }

    /// The quad at `now_ns`, bowed on a long jump by the flavour's arc.
    pub fn sample(glide: *const CursorGlide, now_ns: u64, motion: Motion) [4][2]f32 {
        var out: [4][2]f32 = undefined;
        for (&out, glide.corners) |*point, corner| for (point, corner) |*value, axis| {
            value.* = axis.value(now_ns);
        };
        const to_c = centre(glide.target);
        const dx = to_c[0] - glide.from_centre[0];
        const dy = to_c[1] - glide.from_centre[1];
        const length = @sqrt(dx * dx + dy * dy);
        if (motion.arc == 0 or length < arc_from) return out;
        const now_c = glide.centreAt(now_ns);
        const left = @sqrt((to_c[0] - now_c[0]) * (to_c[0] - now_c[0]) + (to_c[1] - now_c[1]) * (to_c[1] - now_c[1]));
        const travelled = std.math.clamp(1 - left / length, 0, 1);
        const bow = motion.arc * length * 4 * travelled * (1 - travelled);
        // Perpendicular to the path, to its left.
        for (&out) |*point| {
            point[0] += -dy / length * bow;
            point[1] += dx / length * bow;
        }
        return out;
    }

    /// Steps the springs to `now_ns`; true while the quad still moves.
    pub fn step(glide: *CursorGlide, now_ns: u64) bool {
        var any = false;
        for (&glide.corners) |*corner| for (corner) |*axis| {
            if (axis.step(now_ns)) any = true;
        };
        return any;
    }

    /// How far, in cells, the furthest corner still is from its mark.
    pub fn remaining(glide: *const CursorGlide, now_ns: u64) f32 {
        var most: f32 = 0;
        for (glide.corners) |corner| for (corner) |axis| {
            most = @max(most, @abs(axis.value(now_ns) - axis.target));
        };
        return most;
    }

    pub fn moving(glide: *const CursorGlide) bool {
        for (glide.corners) |corner| for (corner) |axis| {
            if (!axis.settled) return true;
        };
        return false;
    }
};

/// The cursor's opacity under blink (§5.4): solid while typing and for
/// `hold_ns` after, then on and off with an eased edge, solid again after
/// `idle_ns` of no input. `edge` says whether it is mid-edge (a frame is
/// owed), `next_ns` when the next edge starts (a wake).
pub const Blink = struct {
    pub const hold_ns: u64 = 500 * std.time.ns_per_ms;
    pub const idle_ns: u64 = 10 * std.time.ns_per_s;
    pub const half_ns: u64 = 530 * std.time.ns_per_ms;
    pub const edge_ns: u64 = 80 * std.time.ns_per_ms;

    alpha: f32,
    edge: bool,
    next_ns: ?u64,

    pub fn at(now_ns: u64, input_ns: u64) Blink {
        const since = now_ns -| input_ns;
        if (since < hold_ns) return .{ .alpha = 1, .edge = false, .next_ns = input_ns + hold_ns + half_ns - edge_ns };
        if (since >= hold_ns + idle_ns) return .{ .alpha = 1, .edge = false, .next_ns = null };
        const t = (since - hold_ns) % (2 * half_ns);
        const cycle_start = now_ns - t;
        // On for a half, easing out over its last `edge_ns`; off for a half,
        // easing back in over its last.
        if (t < half_ns - edge_ns) return .{ .alpha = 1, .edge = false, .next_ns = cycle_start + half_ns - edge_ns };
        if (t < half_ns) return .{ .alpha = 1 - smooth(@as(f32, @floatFromInt(t - (half_ns - edge_ns))) / @as(f32, @floatFromInt(edge_ns))), .edge = true, .next_ns = null };
        if (t < 2 * half_ns - edge_ns) return .{ .alpha = 0, .edge = false, .next_ns = cycle_start + 2 * half_ns - edge_ns };
        return .{ .alpha = smooth(@as(f32, @floatFromInt(t - (2 * half_ns - edge_ns))) / @as(f32, @floatFromInt(edge_ns))), .edge = true, .next_ns = null };
    }

    fn smooth(x: f32) f32 {
        const u = std.math.clamp(x, 0, 1);
        return u * u * (3 - 2 * u);
    }
};

test "a cursor snaps a cell at a time and glides a jump, smearing, bowing and landing exactly" {
    const ms = std.time.ns_per_ms;
    const smooth_motion = Motion.of(.smooth);
    var glide: CursorGlide = .{};
    const cell: Box = .{ .x = 3, .y = 4, .w = 1, .h = 1 };
    glide.aim(cell, 0, smooth_motion, false);
    try std.testing.expect(!glide.moving());
    // One cell over: lands at once.
    glide.aim(.{ .x = 4, .y = 4, .w = 1, .h = 1 }, ms, smooth_motion, false);
    try std.testing.expect(!glide.moving());
    // A jump of 30 cells: glides, the leading edge ahead of the trailing one.
    const far: Box = .{ .x = 34, .y = 4, .w = 1, .h = 1 };
    glide.aim(far, 2 * ms, smooth_motion, false);
    try std.testing.expect(glide.moving());
    const mid = glide.sample(40 * ms, smooth_motion);
    const width = mid[1][0] - mid[0][0];
    try std.testing.expect(width > 1.5);
    // Bowed off the straight line on a long jump.
    try std.testing.expect(@abs(mid[0][1] - 4) > 0.05);
    var t: u64 = 2 * ms;
    while (glide.step(t)) t += ms;
    // Arrives within §8.1's 90-150 ms on the default, within a twentieth of
    // a cell (under a pixel); settles to rest just after, landing exactly.
    const arrived = glide.sample(152 * ms, smooth_motion);
    try std.testing.expect(@abs(arrived[3][0] - 34) < 0.05 and @abs(arrived[1][0] - 35) < 0.05);
    try std.testing.expect(t <= 220 * ms);
    const rest = glide.sample(t, smooth_motion);
    try std.testing.expectEqual([2]f32{ 34, 4 }, rest[0]);
    try std.testing.expectEqual([2]f32{ 35, 5 }, rest[2]);
    // A scroll carries it with the text.
    glide.shift(0, -3);
    try std.testing.expectEqual([2]f32{ 34, 1 }, glide.sample(t, smooth_motion)[0]);
}

test "a blink holds while typing, eases at its edges and stops when idle" {
    const ms = std.time.ns_per_ms;
    try std.testing.expectEqual(@as(f32, 1), Blink.at(100 * ms, 0).alpha);
    const out = Blink.at(Blink.hold_ns + Blink.half_ns + 100 * ms, 0);
    try std.testing.expectEqual(@as(f32, 0), out.alpha);
    const edge = Blink.at(Blink.hold_ns + Blink.half_ns - Blink.edge_ns / 2, 0);
    try std.testing.expect(edge.edge and edge.alpha > 0.2 and edge.alpha < 0.8);
    try std.testing.expectEqual(@as(?u64, null), Blink.at(Blink.hold_ns + Blink.idle_ns + ms, 0).next_ns);
    try std.testing.expectEqual(@as(f32, 1), Blink.at(Blink.hold_ns + Blink.idle_ns + ms, 0).alpha);
}

/// A displayed value that fades from one target to the next over
/// `transition_steps` frames; the chrome colours are one.
pub fn Fade(comptime Value: type) type {
    return struct {
        const Self = @This();

        from: Value,
        to: Value,
        displayed: Value,
        step: u16 = transition_steps,

        pub fn init(value: Value) Self {
            return .{ .from = value, .to = value, .displayed = value };
        }

        pub fn isActive(a: *const Self) bool {
            return a.step < transition_steps;
        }

        pub fn retarget(a: *Self, target: Value) void {
            a.from = a.displayed;
            a.to = target;
            a.step = if (std.meta.eql(a.from, target)) transition_steps else 0;
            if (a.step == transition_steps) a.displayed = target;
        }

        pub fn advance(a: *Self) void {
            if (!a.isActive()) return;
            a.step += 1;
            a.displayed = if (a.step == transition_steps)
                a.to
            else
                Value.interpolate(a.from, a.to, a.step, transition_steps);
        }

        pub fn snap(a: *Self, value: Value) void {
            a.* = init(value);
        }
    };
}

pub fn Immediate(comptime Value: type) type {
    return struct {
        const Self = @This();

        displayed: Value,

        pub fn init(value: Value) Self {
            return .{ .displayed = value };
        }

        pub fn isActive(_: *const Self) bool {
            return false;
        }

        pub fn retarget(a: *Self, target: Value) void {
            a.displayed = target;
        }

        pub fn advance(_: *Self) void {}

        pub fn snap(a: *Self, value: Value) void {
            a.displayed = value;
        }
    };
}

pub fn interpolateRgb(from: [3]u8, to: [3]u8, step: u16, steps: u16) [3]u8 {
    if (step == 0) return from;
    if (step >= steps) return to;
    var out: [3]u8 = undefined;
    for (&out, from, to) |*dst, a, b| {
        const numerator = @as(u32, a) * (steps - step) + @as(u32, b) * step;
        dst.* = @intCast((numerator + steps / 2) / steps);
    }
    return out;
}

const TestColor = struct {
    rgb: [3]u8,

    pub fn interpolate(from: TestColor, to: TestColor, step: u16, steps: u16) TestColor {
        return .{ .rgb = interpolateRgb(from.rgb, to.rgb, step, steps) };
    }
};

test "Immediate lands where a completed Transition lands" {
    const from: TestColor = .{ .rgb = .{ 240, 3, 90 } };
    const to: TestColor = .{ .rgb = .{ 5, 222, 90 } };

    var faded = Fade(TestColor).init(from);
    faded.retarget(to);
    for (0..transition_steps) |_| faded.advance();

    var instant = Immediate(TestColor).init(from);
    try std.testing.expect(!instant.isActive());
    instant.retarget(to);
    try std.testing.expectEqual(faded.displayed, instant.displayed);

    // Never active, so a frontend that renders only while something is animating stops immediately
    // rather than spending ten frames discovering there is nothing to draw.
    try std.testing.expect(!instant.isActive());
    instant.advance();
    try std.testing.expectEqual(to, instant.displayed);

    instant.snap(from);
    try std.testing.expectEqual(from, instant.displayed);
}

test "fixed-step interpolation has exact monotonic endpoints" {
    const Tween = Fade(TestColor);
    const from: TestColor = .{ .rgb = .{ 240, 3, 90 } };
    const to: TestColor = .{ .rgb = .{ 5, 222, 90 } };
    var tween = Tween.init(from);
    tween.retarget(to);
    try std.testing.expectEqual(from, tween.displayed);

    var previous = tween.displayed;
    for (0..transition_steps) |_| {
        tween.advance();
        try std.testing.expect(tween.displayed.rgb[0] <= previous.rgb[0]);
        try std.testing.expect(tween.displayed.rgb[1] >= previous.rgb[1]);
        try std.testing.expectEqual(@as(u8, 90), tween.displayed.rgb[2]);
        previous = tween.displayed;
    }
    try std.testing.expect(!tween.isActive());
    try std.testing.expectEqual(to, tween.displayed);
    tween.advance();
    try std.testing.expectEqual(to, tween.displayed);
}

test "retarget starts at the currently displayed value" {
    const Tween = Fade(TestColor);
    const first: TestColor = .{ .rgb = .{ 0, 40, 200 } };
    const second: TestColor = .{ .rgb = .{ 200, 140, 0 } };
    const third: TestColor = .{ .rgb = .{ 20, 10, 250 } };
    var tween = Tween.init(first);
    tween.retarget(second);
    tween.advance();
    tween.advance();
    tween.advance();
    const on_screen = tween.displayed;

    tween.retarget(third);
    try std.testing.expectEqual(on_screen, tween.from);
    try std.testing.expectEqual(on_screen, tween.displayed);
    try std.testing.expect(tween.isActive());
    for (0..transition_steps) |_| tween.advance();
    try std.testing.expectEqual(third, tween.displayed);
}