1 files changed, 115 insertions, 24 deletions

diff --git a/src/animation.zig b/src/animation.zig
index ca933b82..b02a242b 100644
--- a/src/animation.zig
+++ b/src/animation.zig
@@ -586,19 +586,58 @@ pub const frame_ms: u32 = 16;
 pub const frame_ns: u64 = frame_ms * std.time.ns_per_ms;
 pub const transition_steps: u16 = 10;
 
-/// A value that follows its target on a critically damped spring, in closed
-/// form (docs/render-pipeline.md §7.2): no overshoot, and a new target taken
-/// partway keeps the value AND its velocity, so a quick run of changes never
-/// snaps or starts over. `omega` sets the pace: it is within 1% of a jump
-/// after about 6.6 / omega seconds, and settles (half a percent, nearly
-/// still) at about 8.6 / omega. Settled, it is exactly its target and asks
-/// for no frames.
-pub const Spring = struct {
-    /// Within 1% of a jump in 6.6 / 36 ≈ 180 ms, settled by 240 ms: a
-    /// state change (§8.1).
-    pub const state_change: f32 = 36;
+/// 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,
 
-    omega: f32 = state_change,
+    pub fn of(flavour: Flavour) Motion {
+        return switch (flavour) {
+            .off => .{ .instant = true },
+            // Productivity: quick and exact, nothing past its mark.
+            .crisp => .{ .omega = 44 },
+            // A longer, softer ease in and out, still without a bounce.
+            .smooth => .{ .omega = 26, .follow = 0.85, .arc = 0.04 },
+            // Settles past and back, and stretches with its speed.
+            .bouncy => .{ .omega = 30, .zeta = 0.55, .stretch = 0.12, .follow = 0.8, .arc = 0.08 },
+            // A cartoon's: winds up, overshoots, stretches, follows through.
+            .playful => .{ .omega = 24, .zeta = 0.42, .anticipate = 0.08, .stretch = 0.25, .follow = 0.7, .arc = 0.15 },
+        };
+    }
+};
+
+/// 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,
@@ -613,20 +652,41 @@ pub const Spring = struct {
         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 c = spring.velocity + w * x0;
-        const decay = @exp(-w * t);
-        return .{ .value = spring.target + (x0 + c * t) * decay, .velocity = (spring.velocity - w * t * c) * decay };
+        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;
     }
 
-    /// Heads for `target` from wherever it is at `now_ns`, moving as it was.
-    pub fn retarget(spring: *Spring, target: f32, now_ns: u64) void {
+    /// 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);
-        spring.* = .{ .omega = spring.omega, .target = target, .from = state.value, .velocity = state.velocity, .from_ns = now_ns, .settled = false };
+        // From rest, a wind-up: set off the other way, just a little.
+        const kick: f32 = if (spring.settled) -motion.anticipate * (target - state.value) * motion.omega * 2 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
@@ -643,7 +703,8 @@ pub const Spring = struct {
 test "a spring settles without overshoot and keeps its velocity when retargeted" {
     var spring: Spring = .{};
     const ms = std.time.ns_per_ms;
-    spring.retarget(1, 0);
+    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) {
@@ -651,21 +712,51 @@ test "a spring settles without overshoot and keeps its velocity when retargeted"
         try std.testing.expect(v >= last and v <= 1);
         last = v;
     }
-    // Settled within a frame or two of 6.6 / omega.
-    try std.testing.expect(t >= 180 * ms and t <= 260 * ms);
+    try std.testing.expect(t >= 150 * ms and t <= 260 * ms);
     try std.testing.expectEqual(@as(f32, 1), spring.value(t + 5 * ms));
-    // Back the other way halfway up: it carries on up for a moment, then
+    // Back the other way partway up: it carries on up for a moment, then
     // turns, never jumping.
     spring = .{};
-    spring.retarget(1, 0);
+    spring.retarget(1, 0, crisp);
     const before = spring.at(60 * ms);
-    spring.retarget(0, 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(64 * ms) > 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));
+    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) < 0.05);
+            last = now;
+        }
+        try std.testing.expect(t < 1200 * ms);
+        switch (flavour) {
+            .crisp, .smooth => try std.testing.expect(peak <= 1.0005 and low >= 0),
+            .bouncy => try std.testing.expect(peak > 1.05 and low >= 0),
+            .playful => try std.testing.expect(peak > 1.05 and low < -0.01),
+            .off => unreachable,
+        }
+    }
+}
+
 /// 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 {