Build your own easing curve and use it on keys and Lerp (#247)

The built-in eases cover the usual shapes, but a game often wants its
own: a coin that bounces twice, a door that overshoots and settles.
A new asset type holds such a curve, and keys and the Lerp node can
pick it instead of a built-in ease.

- New asset type "curve": points like in Vector art, x is t and y is
  the value. A new curve is the straight line from (0, 0) to (1, 1).
- One pure evaluation in src/core/model/curve.ts serves the timeline
  preview, the running game and the Lerp node.
- The curve always has one value per t. The end points stay at t 0
  and 1, points cannot pass each other, and a handle that reaches past
  its neighbour is shortened along its direction. Loading a hand-edited
  file applies the same rules.
- Curve tab: click on the line to insert a point that keeps the shape,
  click on free space to put one there, drag points and handles,
  double-click or Delete removes, Alt-click toggles round and sharp.
  Every step is one undo step.
- Presets: all 30 built-in eases plus Linear, fitted with adaptive
  subdivision. Each stays within 0.4 % of the built-in ease.
- Preview: a dot runs along the curve once a second, a second dot
  shows only the value. The Preview button stops it.
- Animation keys get "Curve" under Easing with a curve picker. Lerp
  gets "Curve" under Ease, and its result may overshoot b.
- A missing or unpicked curve runs linear. The inspector says so, the
  node shows it as a problem, and deleting a used curve warns with the
  number of keys and Lerp nodes.

Tests:
- ./check.sh: 180 files, 2612 tests, CHECK EXIT 0
- GM_STEPS=1-6,25,53: ALL PASSED, 309 checks
- New e2e module 53 with 13 checks, all with the real mouse. Expected
  values come from its own Bezier evaluation.
- Counter-checks bite: without Bezier evaluation 4 unit tests fail,
  without handle clamping 2. In the browser, a key that cannot find its
  curve, a click that sets no point and a handle drag that moves the
  point all turn checks red.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

README.md

@@ -43,7 +43,7 @@ npm run build        # writes dist/ and regenerates index.html; the folder is wh
 The browser suite and the three example games need a machine with a GPU:
 
 ```bash
-node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1459 checks (GM_STEPS=20 for one step)
+node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1472 checks (GM_STEPS=20 for one step)
                                                    #   every tool signs in first – see the Accounts page
 node tools/seed-jumprun.mjs && node tools/smoke-jumprun.mjs
 node tools/seed-tetris.mjs && node tools/smoke-tetris.mjs
@@ -72,6 +72,7 @@ CI. Details, the GPU requirement and the detached runner are in
 | [Fonts](https://git.nockal.com/meleki/game-maker/wiki/Fonts) | Font assets, the picker, what a text falls back to |
 | [Sounds](https://git.nockal.com/meleki/game-maker/wiki/Sounds) | Sound assets and `Play sound` |
 | [Animations](https://git.nockal.com/meleki/game-maker/wiki/Animations) | Animation assets and the Animation tab |
+| [Curves](https://git.nockal.com/meleki/game-maker/wiki/Curves) | Easings drawn by hand, the Curve tab, using one on a key or a `Lerp` |
 | [Shaders](https://git.nockal.com/meleki/game-maker/wiki/Shaders) | Shader graphs a sprite wears, their node set, the properties they declare |
 | [Particles](https://git.nockal.com/meleki/game-maker/wiki/Particles) | Particle graphs: a particle as a function of its age |
 | [State machines](https://git.nockal.com/meleki/game-maker/wiki/State-machines) | The asset, named transitions, `State branch`, `Set state` and `State transition` |

src/core/commands/animationCommands.ts

@@ -13,6 +13,7 @@ import {
   trackValueAt,
 } from '../model/animation';
 import type { AnimationAsset, AnimationKey, AnimationTrack, KeyInterpolation } from '../model/Asset';
+import { curveLookup } from '../model/curve';
 import { findAsset, type Project } from '../model/Project';
 import type { PropertyValue } from '../model/Properties';
 import { coerceValue } from '../properties/PropertySchema';
@@ -233,7 +234,7 @@ export class SetAnimationKeyCommand extends TimelineCommand {
     requireFrame(this.frame, 'A key sits on a whole frame from 0');
     const def = trackDef(project, asset, track);
     if (!def) throw new CommandError('The row aims at something that is gone');
-    const current = trackValueAt(track.keys, def.kind, this.frame);
+    const current = trackValueAt(track.keys, def.kind, this.frame, false, curveLookup(project));
     const raw = this.value ?? current ?? (track.relative ? 0 : def.default);
     const key: AnimationKey = { frame: this.frame, value: coerceValue(def, raw) };
     const interpolation = track.keys.find((k) => k.frame === this.frame)?.interpolation;

src/core/commands/assetCommands.ts

@@ -9,6 +9,7 @@ import type {
   VariablesAsset,
 } from '../model/Asset';
 import type { AssetType } from '../model/AssetTypes';
+import { linearCurve } from '../model/curve';
 import { isFontFile } from '../model/font';
 import { DEFAULT_PALETTE, PIXEL_CANVAS_DEFAULT } from '../model/pixelart';
 import { isSoundFile } from '../model/sound';
@@ -71,6 +72,9 @@ export function buildAsset(type: AssetType, name: string, id = newId()): Asset {
       return { ...base, type: 'palette', colors: [...DEFAULT_PALETTE] };
     case 'animation':
       return { ...base, type: 'animation', root: '', tracks: [] };
+    // Linear until someone bends it: a key that picks a new curve still moves as it did.
+    case 'curve':
+      return { ...base, type: 'curve', points: linearCurve() };
     case 'tile':
       return { ...base, type: 'tile', pictures: [] };
     // A tilemap without a layer could not be painted on, so it starts with one.

src/core/commands/curveCommands.ts

@@ -0,0 +1,39 @@
+/**
+ * Editing the points of a Curve asset (#247). One gesture is one command, as with a vector art ring:
+ * the whole point list is written once when the pointer lets go, so an undo takes the drag back.
+ * Whatever is written is held to the curve's rules first (`sanitizedCurve`), so no command – and no
+ * hand-made list from a preset – can leave a curve that runs backwards in `t`.
+ */
+import type { CurveAsset, VectorPoint } from '../model/Asset';
+import { sanitizedCurve } from '../model/curve';
+import type { Project } from '../model/Project';
+import type { Command } from './Command';
+import { requireCurve } from './require';
+
+export class SetCurvePointsCommand implements Command {
+  readonly label: string;
+  private previous: VectorPoint[] = [];
+
+  constructor(
+    private readonly assetId: string,
+    private readonly points: readonly VectorPoint[],
+    label = 'Edit curve',
+  ) {
+    this.label = label;
+  }
+
+  /** Nothing to do when the curve already reads exactly like this – no empty undo step. */
+  static changes(asset: CurveAsset, points: readonly VectorPoint[]): boolean {
+    return JSON.stringify(asset.points) !== JSON.stringify(sanitizedCurve(points));
+  }
+
+  execute(project: Project): void {
+    const asset = requireCurve(project, this.assetId);
+    this.previous = asset.points;
+    asset.points = sanitizedCurve(this.points);
+  }
+
+  undo(project: Project): void {
+    requireCurve(project, this.assetId).points = this.previous;
+  }
+}

src/core/commands/require.ts

@@ -3,6 +3,7 @@ import { findNode, type Graph, type GraphEdge, type GraphNode } from '../graph/G
 import { type NodeDef, nodeDef } from '../graph/NodeRegistry';
 import type {
   Asset,
+  CurveAsset,
   TileAsset,
   BehaviorAsset,
   StateMachineAsset,
@@ -121,6 +122,12 @@ export function requireVectorShape(project: Project, assetId: string, shapeId: s
   return shape;
 }
 
+export function requireCurve(project: Project, assetId: string): CurveAsset {
+  const asset = findAssetOf(project, assetId, 'curve');
+  if (!asset) throw new CommandError(`Curve ${assetId} not found`);
+  return asset;
+}
+
 export function requireStateMachine(project: Project, assetId: string): StateMachineAsset {
   const asset = findAssetOf(project, assetId, 'statemachine');
   if (!asset) throw new CommandError(`State machine ${assetId} not found`);

src/core/graph/lookup.ts

@@ -1,3 +1,4 @@
+import type { VectorPoint } from '../model/Asset';
 import type { PropertyBag } from '../model/Properties';
 import type { Graph } from './Graph';
 
@@ -35,12 +36,14 @@ export interface StateMachine {
 }
 
 /**
- * What a node may look up in the project around its graph: the behaviors it can run and the
- * state machines it can read. One handle, so no caller can resolve a node with half of it.
+ * What a node may look up in the project around its graph: the behaviors it can run, the state
+ * machines it can read and the curves a `Lerp` eases along (#247). One handle, so no caller can
+ * resolve a node with half of it.
  */
 export interface GraphLookup {
   behavior(assetId: string): BehaviorProgram | null;
   machine(assetId: string): StateMachine | null;
+  curve(assetId: string): readonly VectorPoint[] | null;
 }
 
-export const NO_LOOKUP: GraphLookup = { behavior: () => null, machine: () => null };
+export const NO_LOOKUP: GraphLookup = { behavior: () => null, machine: () => null, curve: () => null };

src/core/graph/nested.ts

@@ -13,6 +13,7 @@ import {
 } from './Graph';
 import type { GraphLookup } from './lookup';
 import { nodeDef, type NodeDef, type PortDef } from './NodeRegistry';
+import { lerpProblem } from './nodes/data/Lerp';
 import { agreedType, type SharedPortGroup } from './portTypes';
 
 export const BEHAVIOR_START = 'BehaviorStart';
@@ -273,10 +274,11 @@ export function ghostProblem(node: GraphNode, graph: Graph, def: NodeDef): strin
 
 /**
  * Why this call cannot do anything, or null if it can. A call is the one node that depends on a
- * *different* graph, so it is the one node that can look perfectly healthy and still be dead.
+ * *different* graph, so it is the one node that can look perfectly healthy and still be dead. A
+ * `Lerp` depends on another asset as well, the curve it eases along (#247), and says so here too.
  */
 export function callProblem(node: GraphNode, lookup: GraphLookup, ownerId = ''): string | null {
-  if (node.type !== RUN_BEHAVIOR) return null;
+  if (node.type !== RUN_BEHAVIOR) return lerpProblem(node, lookup);
   const id = textOf(node.params[BEHAVIOR_PARAM] ?? '');
   if (!id) return 'No behavior picked';
   if (id === ownerId) return 'A behavior cannot run itself';

src/core/graph/nodes/data/Lerp.ts

@@ -1,7 +1,10 @@
+import type { GraphNode } from '../../Graph';
+import type { GraphLookup } from '../../lookup';
 import type { NodeDef } from '../../NodeRegistry';
 import { asNumber } from '../../values';
 import { num, withDefault } from '../shared';
 
+import { curveValue, LERP, LERP_CURVE } from '../../../model/curve';
 import { textOf } from '../../../model/Properties';
 
 /** Quadratic curves over t in 0…1, each running from 0 to 1. */
@@ -13,10 +16,12 @@ const EASES: Record<string, (t: number) => number> = {
 };
 
 export const Lerp: NodeDef = {
-  type: 'Lerp',
+  type: LERP,
   label: 'Lerp',
   category: 'data',
-  description: 'Blends from a to b as t runs from 0 to 1, along the chosen ease. t is held in 0…1.',
+  description:
+    'Blends from a to b as t runs from 0 to 1, along the chosen ease. t is held in 0…1. With Ease ' +
+    'set to Curve it follows the Curve asset picked below, and may overshoot b.',
   inputs: [withDefault(num('a'), 0), withDefault(num('b'), 1), withDefault(num('t'), 0)],
   outputs: [num('result')],
   params: [
@@ -30,13 +35,26 @@ export const Lerp: NodeDef = {
         { value: 'in', label: 'In' },
         { value: 'out', label: 'Out' },
         { value: 'inOut', label: 'In-out' },
+        { value: 'curve', label: 'Curve' },
       ],
     },
+    { key: LERP_CURVE, label: 'Curve', kind: 'asset', default: '', assetTypes: ['curve'] },
   ],
-  run: (_ctx, inputs, params) => {
+  hiddenParams: (params) => (textOf(params.ease) === 'curve' ? [] : [LERP_CURVE]),
+  run: (_ctx, inputs, params, _def, _entry, lookup) => {
     const a = asNumber(inputs.a);
     const t = Math.min(Math.max(asNumber(inputs.t), 0), 1);
-    const ease = EASES[textOf(params.ease)] ?? EASES.linear!;
-    return { outputs: { result: a + (asNumber(inputs.b) - a) * ease(t) } };
+    const ease = textOf(params.ease);
+    const points = ease === 'curve' ? lookup.curve(textOf(params[LERP_CURVE] ?? '')) : null;
+    const share = points ? curveValue(points, t) : (EASES[ease] ?? EASES.linear!)(t);
+    return { outputs: { result: a + (asNumber(inputs.b) - a) * share } };
   },
 };
+
+/** Why a Lerp set to Curve runs linear instead, or null when it eases as it says. */
+export function lerpProblem(node: GraphNode, lookup: GraphLookup): string | null {
+  if (node.type !== LERP || textOf(node.params.ease) !== 'curve') return null;
+  const id = textOf(node.params[LERP_CURVE] ?? '');
+  if (!id) return 'No curve picked – runs linear';
+  return lookup.curve(id) ? null : 'That curve is gone – runs linear';
+}

src/core/model/Asset.ts

@@ -160,9 +160,14 @@ export type EasingDirection = 'in' | 'out' | 'in-out';
 /**
  * How a key blends into the next one (#101); absent is `linear`. `step` holds until the next key. A
  * curve is stored as `<curve>-<direction>`, except quad, which keeps its first name `ease-<direction>`.
+ * `curve:<id>` blends along a Curve asset (#247); an empty id is "Curve" with none picked yet.
  */
 export type KeyInterpolation =
-  'linear' | 'step' | `ease-${EasingDirection}` | `${Exclude<EasingCurve, 'quad'>}-${EasingDirection}`;
+  | 'linear'
+  | 'step'
+  | `ease-${EasingDirection}`
+  | `${Exclude<EasingCurve, 'quad'>}-${EasingDirection}`
+  | `curve:${string}`;
 
 /**
  * A value on a whole frame. Its interpolation rules the way to the next key. A value that cannot
@@ -424,6 +429,18 @@ export interface PaletteAsset extends AssetBase {
   colors: number[];
 }
 
+/**
+ * An easing drawn by hand (#247). The points are those of an open vector art line, read as a graph:
+ * `x` is the share of the time (`t`, 0…1) and `y` the share of the way (`v`), which may leave 0…1 to
+ * overshoot. The first point sits at `t` 0 and the last at 1, the points never overtake each other
+ * in `t` and a handle never reaches past a neighbour – so the curve has one value for every `t`.
+ * `sanitizedCurve` holds every stored curve to that.
+ */
+export interface CurveAsset extends AssetBase {
+  type: 'curve';
+  points: VectorPoint[];
+}
+
 /**
  * The graph is the motion of one particle: every output of its `Output` node is a function of the
  * particle's age and its own random number (see `core/particles/compile.ts`). A placed object is
@@ -449,6 +466,7 @@ export type Asset =
   | PixelArtAsset
   | PaletteAsset
   | AnimationAsset
+  | CurveAsset
   | TileAsset
   | TilemapAsset
   | StateMachineAsset

src/core/model/AssetTypes.ts

@@ -13,6 +13,7 @@ export const ASSET_TYPES = [
   'pixelart',
   'palette',
   'animation',
+  'curve',
   'tile',
   'tilemap',
   'statemachine',
@@ -39,6 +40,7 @@ export const ASSET_TYPE_LABELS: Record<AssetType, string> = {
   pixelart: 'Pixel art',
   palette: 'Palette',
   animation: 'Animation',
+  curve: 'Curve',
   tile: 'Tile',
   tilemap: 'Tilemap',
   statemachine: 'State machine',
@@ -54,7 +56,7 @@ export const ASSET_TYPE_LABELS: Record<AssetType, string> = {
  * a behavior refers to it by id, and a Variables asset is declarations a graph reads by id. A
  * sound is nowhere on screen at all – a graph plays it, so there is nothing to place. A tile is
  * what a tilemap draws with, so it is placed no more directly than a texture is – what is placed
- * is the tilemap.
+ * is the tilemap. A curve is the way a key or a `Lerp` blends, picked by id like a state machine.
  */
 export type PlaceableAssetType = Exclude<
   AssetType,
@@ -64,6 +66,7 @@ export type PlaceableAssetType = Exclude<
   | 'pixelart'
   | 'palette'
   | 'animation'
+  | 'curve'
   | 'tile'
   | 'statemachine'
   | 'shader'
@@ -79,6 +82,7 @@ const NOT_PLACEABLE: ReadonlySet<AssetType> = new Set([
   'pixelart',
   'palette',
   'animation',
+  'curve',
   'tile',
   'statemachine',
   'shader',

src/core/model/animation.ts

@@ -11,6 +11,7 @@ import type {
   KeyInterpolation,
 } from './Asset';
 import type { AssetType } from './AssetTypes';
+import { type CurveLookup, curveValue, NO_CURVES } from './curve';
 import { treeOrder } from './hierarchy';
 import { instanceChildId, resolveObjects } from './instance';
 import { findAsset, type Project } from './Project';
@@ -115,7 +116,7 @@ export function blends(kind: string): boolean {
   return kind === 'number' || kind === 'color';
 }
 
-export type EasingShape = 'linear' | 'step' | EasingCurve;
+export type EasingShape = 'linear' | 'step' | EasingCurve | 'curve';
 
 /** The inspector's first easing field, in the order it offers them; `linear` is what an absent field means. */
 export const EASING_SHAPES: readonly { value: EasingShape; label: string }[] = [
@@ -131,6 +132,7 @@ export const EASING_SHAPES: readonly { value: EasingShape; label: string }[] = [
   { value: 'back', label: 'Back' },
   { value: 'elastic', label: 'Elastic' },
   { value: 'bounce', label: 'Bounce' },
+  { value: 'curve', label: 'Curve' },
 ];
 
 /** The second field, for a curve only. */
@@ -170,12 +172,18 @@ function isCurve(value: string): value is EasingCurve {
   return Object.hasOwn(EASE_IN, value);
 }
 
-/** A stored interpolation split into the inspector's two fields; unknown text reads as `linear`. */
+/**
+ * A stored interpolation split into the inspector's fields; unknown text reads as `linear`. `curve`
+ * is the id of the Curve asset (#247), `''` while none is picked.
+ */
 export function easingOf(interpolation: KeyInterpolation): {
   shape: EasingShape;
   direction?: EasingDirection;
+  curve?: string;
 } {
   if (interpolation === 'linear' || interpolation === 'step') return { shape: interpolation };
+  if (interpolation.startsWith(CURVE_PREFIX))
+    return { shape: 'curve', curve: interpolation.slice(CURVE_PREFIX.length) };
   const match = /^([a-z]+)-(in|out|in-out)$/.exec(interpolation);
   if (!match) return { shape: 'linear' };
   const curve = match[1]!;
@@ -184,16 +192,23 @@ export function easingOf(interpolation: KeyInterpolation): {
   return isCurve(curve) && curve !== 'quad' ? { shape: curve, direction } : { shape: 'linear' };
 }
 
-/** The stored form of the two fields; a curve without a direction eases both ways. */
-export function easingValue(shape: EasingShape, direction: EasingDirection = 'in-out'): KeyInterpolation {
+const CURVE_PREFIX = 'curve:';
+
+/** The stored form of the fields; a curve without a direction eases both ways. */
+export function easingValue(
+  shape: EasingShape,
+  direction: EasingDirection = 'in-out',
+  curve = '',
+): KeyInterpolation {
   if (shape === 'linear' || shape === 'step') return shape;
+  if (shape === 'curve') return `${CURVE_PREFIX}${curve}`;
   return shape === 'quad' ? `ease-${direction}` : `${shape}-${direction}`;
 }
 
 export function isKeyInterpolation(value: unknown): value is KeyInterpolation {
   if (typeof value !== 'string') return false;
-  const { shape, direction } = easingOf(value as KeyInterpolation);
-  return easingValue(shape, direction) === value;
+  const { shape, direction, curve } = easingOf(value as KeyInterpolation);
+  return easingValue(shape, direction, curve) === value;
 }
 
 export function interpolationOf(key: AnimationKey): KeyInterpolation {
@@ -203,11 +218,20 @@ export function interpolationOf(key: AnimationKey): KeyInterpolation {
 /**
  * How far along the way to the next key a value is, `t` the share of the time passed. Quad, the eases
  * of old, reaches 0.25 at half the time going in, 0.75 going out, and 0.125 at a quarter going both.
+ * A Curve asset that is gone, or none picked, blends linearly.
  */
-export function easedShare(interpolation: KeyInterpolation, t: number): number {
-  const { shape, direction } = easingOf(interpolation);
+export function easedShare(
+  interpolation: KeyInterpolation,
+  t: number,
+  curves: CurveLookup = NO_CURVES,
+): number {
+  const { shape, direction, curve } = easingOf(interpolation);
   if (shape === 'linear') return t;
   if (shape === 'step') return 0;
+  if (shape === 'curve') {
+    const points = curves(curve ?? '');
+    return points ? curveValue(points, t) : t;
+  }
   const easeIn = EASE_IN[shape];
   switch (direction ?? 'in-out') {
     case 'in':
@@ -234,13 +258,15 @@ export function blendValue(kind: string, a: PropertyValue, b: PropertyValue, t:
  * A row's value at a (fractional) frame: the first value before the first key, the last after the
  * last one. Between two keys the earlier one's interpolation decides the way. A value that jumps –
  * one that cannot blend, or a `step` key – holds until the next key in the direction of play: played
- * in `reverse`, that is the key above. `undefined` only for a row without keys.
+ * in `reverse`, that is the key above. `undefined` only for a row without keys. `curves` finds the
+ * Curve assets a key may blend along.
  */
 export function trackValueAt(
   keys: readonly AnimationKey[],
   kind: string,
   frame: number,
   reverse = false,
+  curves: CurveLookup = NO_CURVES,
 ): PropertyValue | undefined {
   const first = keys[0];
   if (!first) return undefined;
@@ -253,7 +279,7 @@ export function trackValueAt(
     if (!blends(kind) || interpolation === 'step')
       return reverse && frame > prev.frame ? next.value : prev.value;
     const t = (frame - prev.frame) / (next.frame - prev.frame);
-    return blendValue(kind, prev.value, next.value, easedShare(interpolation, t));
+    return blendValue(kind, prev.value, next.value, easedShare(interpolation, t, curves));
   }
   return keys[keys.length - 1]!.value;
 }
@@ -270,8 +296,9 @@ export function trackWriteAt(
   frame: number,
   base: PropertyValue | undefined,
   reverse = false,
+  curves: CurveLookup = NO_CURVES,
 ): PropertyValue | undefined {
-  const value = trackValueAt(track.keys, def.kind, frame, reverse);
+  const value = trackValueAt(track.keys, def.kind, frame, reverse, curves);
   if (value === undefined) return undefined;
   if (def.kind !== 'number') return value;
   const offset = track.relative && typeof base === 'number';

src/core/model/animationPreview.ts

@@ -14,6 +14,7 @@ import {
   trackWriteAt,
 } from './animation';
 import type { AnimationAsset, AnimationTrack, Asset } from './Asset';
+import { type CurveLookup, curveLookup } from './curve';
 import { instanceChildId, objectRef } from './instance';
 import { findAsset, type ObjectHolder, type Project } from './Project';
 import { resolveSceneObjectProps } from '../properties/resolve';
@@ -37,9 +38,10 @@ export function previewHolder(
   if (!root) return undefined;
   const reset = playbackOf(animation) === 'once-reset' && frame >= frameCount(animation);
   const holder = root.type === 'scene' ? sceneCopy(root) : placedHolder(root);
+  const at: ReadAt = { frame, reverse, curves: curveLookup(project) };
   for (const track of reset ? [] : animation.tracks) {
-    if (root.type === 'scene' && track.target === '') writeScene(holder, track, frame, reverse);
-    else writeObject(project, holder, previewObjectId(root, track.target), track, frame, reverse);
+    if (root.type === 'scene' && track.target === '') writeScene(holder, track, at);
+    else writeObject(project, holder, previewObjectId(root, track.target), track, at);
   }
   return holder;
 }
@@ -68,11 +70,19 @@ function placedHolder(root: Asset): ObjectHolder {
   return { id: PLACED_ROOT_ID, type: 'container', name: root.name, props: {}, objects: [placedRoot(root)] };
 }
 
+/** Where on the timeline a row is read, and the Curve assets its keys may blend along. */
+interface ReadAt {
+  frame: number;
+  reverse: boolean;
+  curves: CurveLookup;
+}
+
 /** A row on the scene itself: its value goes into the copy's own properties. */
-function writeScene(holder: ObjectHolder, track: AnimationTrack, frame: number, reverse: boolean): void {
+function writeScene(holder: ObjectHolder, track: AnimationTrack, at: ReadAt): void {
   const def = animatableDefs('scene').find((d) => d.key === track.property);
   if (!def) return;
-  const value = trackWriteAt(track, def, frame, holder.props[track.property] ?? def.default, reverse);
+  const base = holder.props[track.property] ?? def.default;
+  const value = trackWriteAt(track, def, at.frame, base, at.reverse, at.curves);
   if (value !== undefined) holder.props[track.property] = value;
 }
 
@@ -81,8 +91,7 @@ function writeObject(
   holder: ObjectHolder,
   id: string,
   track: AnimationTrack,
-  frame: number,
-  reverse: boolean,
+  at: ReadAt,
 ): void {
   const ref = objectRef(project, holder, id);
   const asset = ref && findAsset(project, ref.object.assetId);
@@ -93,10 +102,10 @@ function writeObject(
   if (!def) return;
   const key = track.property;
   if (isPositionRow(asset.type, key)) {
-    const value = trackWriteAt(track, def, frame, ref.object.position[key], reverse);
+    const value = trackWriteAt(track, def, at.frame, ref.object.position[key], at.reverse, at.curves);
     if (value !== undefined) ref.setPosition({ ...ref.object.position, [key]: Number(value) });
     return;
   }
-  const value = trackWriteAt(track, def, frame, props[key], reverse);
+  const value = trackWriteAt(track, def, at.frame, props[key], at.reverse, at.curves);
   if (value !== undefined) ref.setOverride(key, value);
 }

src/core/model/curve.ts

@@ -0,0 +1,151 @@
+/**
+ * Curve assets (#247): an easing drawn by hand, read wherever a key or a `Lerp` node picks one.
+ * One pure function evaluates it for the Curve tab, the animation player and the graph alike.
+ *
+ * A segment is a cubic Bezier from one point to the next, a line where neither end has a handle –
+ * the same rule vector art draws by. It is solved for `t` like CSS `cubic-bezier`: with both inner
+ * control points between the ends in `t`, `t` rises monotonically along the segment, so bisection
+ * finds the one place a `t` is reached.
+ */
+import { isGraphAsset, type VectorPoint } from './Asset';
+import { findAssetOf, type Project } from './Project';
+import type { Vec2 } from './Properties';
+import { cloneVectorPoint } from './vectorart';
+
+/** The node type that eases along a curve, and its setting naming the curve. */
+export const LERP = 'Lerp';
+export const LERP_CURVE = 'curve';
+
+/** How many animation keys and `Lerp` nodes ease along a curve – what deleting it has to warn about. */
+export function curveUsages(project: Project, curveId: string): { keys: number; nodes: number } {
+  let keys = 0;
+  let nodes = 0;
+  for (const asset of project.assets) {
+    if (asset.type === 'animation')
+      for (const track of asset.tracks)
+        keys += track.keys.filter((key) => key.interpolation === `curve:${curveId}`).length;
+    if (isGraphAsset(asset))
+      nodes += asset.graph.nodes.filter((n) => n.type === LERP && n.params[LERP_CURVE] === curveId).length;
+  }
+  return { keys, nodes };
+}
+
+/** The points of the curve an id names; undefined once it is gone. */
+export type CurveLookup = (curveId: string) => readonly VectorPoint[] | undefined;
+
+export const NO_CURVES: CurveLookup = () => undefined;
+
+export function curveLookup(project: Project): CurveLookup {
+  return (curveId) => (curveId ? findAssetOf(project, curveId, 'curve')?.points : undefined);
+}
+
+/** What a new curve is: a straight line from (0, 0) to (1, 1), the same as `linear`. */
+export function linearCurve(): VectorPoint[] {
+  return [
+    { x: 0, y: 0 },
+    { x: 1, y: 1 },
+  ];
+}
+
+/** Halvings of the segment; 2^-40 of a segment is far below anything a value could show. */
+const BISECTIONS = 40;
+
+/**
+ * The value at `t`, held to 0…1. Between two points the segment decides; a segment without width –
+ * two points on one `t` – is a jump, and the later point's value wins from there on.
+ */
+export function curveValue(points: readonly VectorPoint[], t: number): number {
+  const first = points[0];
+  if (!first) return t;
+  const at = Math.min(Math.max(Number.isFinite(t) ? t : 0, 0), 1);
+  if (at <= first.x) return first.y;
+  for (let i = 1; i < points.length; i++) {
+    const to = points[i]!;
+    if (at > to.x) continue;
+    return segmentValue(points[i - 1]!, to, at);
+  }
+  return points[points.length - 1]!.y;
+}
+
+function segmentValue(from: VectorPoint, to: VectorPoint, t: number): number {
+  const span = to.x - from.x;
+  if (span <= 0) return to.y;
+  if (!from.out && !to.in) return from.y + ((to.y - from.y) * (t - from.x)) / span;
+  // Held between the ends in `t`, whatever is stored: that is what keeps the solve unique.
+  const c1x = clamp(from.x + (from.out?.x ?? 0), from.x, to.x);
+  const c2x = clamp(to.x + (to.in?.x ?? 0), from.x, to.x);
+  const c1y = from.y + (from.out?.y ?? 0);
+  const c2y = to.y + (to.in?.y ?? 0);
+  let lo = 0;
+  let hi = 1;
+  for (let step = 0; step < BISECTIONS; step++) {
+    const mid = (lo + hi) / 2;
+    if (cubic(from.x, c1x, c2x, to.x, mid) < t) lo = mid;
+    else hi = mid;
+  }
+  return cubic(from.y, c1y, c2y, to.y, (lo + hi) / 2);
+}
+
+function cubic(a: number, b: number, c: number, d: number, s: number): number {
+  const u = 1 - s;
+  return u * u * u * a + 3 * u * u * s * b + 3 * u * s * s * c + s * s * s * d;
+}
+
+function clamp(value: number, min: number, max: number): number {
+  return Math.min(Math.max(value, min), max);
+}
+
+/**
+ * The curve as the rules want it, whatever was handed in. At least two points; sorted by `t`, `t`
+ * held to 0…1, the first at 0 and the last at 1. The first point has no handle in and the last none
+ * out. A handle pointing backwards in `t` is turned upright, and one reaching past its neighbour is
+ * shortened along its own direction, so a smooth point stays smooth. What does not come out a number
+ * is dropped; with fewer than two points left the curve is linear.
+ */
+export function sanitizedCurve(points: readonly VectorPoint[]): VectorPoint[] {
+  const kept = points
+    .filter((p) => Number.isFinite(p.x) && Number.isFinite(p.y))
+    .map((p) => ({ ...cloneVectorPoint(p), x: clamp(p.x, 0, 1) }))
+    .sort((a, b) => a.x - b.x);
+  if (kept.length < 2) return linearCurve();
+  kept[0]!.x = 0;
+  kept[kept.length - 1]!.x = 1;
+  for (const [i, point] of kept.entries()) {
+    const before = kept[i - 1];
+    const after = kept[i + 1];
+    const handleIn = before && point.in ? heldHandle(point.in, before.x - point.x) : undefined;
+    const handleOut = after && point.out ? heldHandle(point.out, after.x - point.x) : undefined;
+    if (handleIn) point.in = handleIn;
+    else delete point.in;
+    if (handleOut) point.out = handleOut;
+    else delete point.out;
+    if (!point.in && !point.out) delete point.mode;
+  }
+  return kept;
+}
+
+/** A handle kept on its own side of the point, reaching `reach` in `t` at most (negative for `in`). */
+function heldHandle(handle: Vec2, reach: number): Vec2 | undefined {
+  const finite = Number.isFinite(handle.x) && Number.isFinite(handle.y);
+  if (!finite) return undefined;
+  let { x, y } = handle;
+  if (x * reach < 0) x = 0;
+  if (Math.abs(x) > Math.abs(reach)) {
+    const scale = Math.abs(reach) / Math.abs(x);
+    x *= scale;
+    y *= scale;
+  }
+  return Math.hypot(x, y) < 1e-9 ? undefined : { x, y };
+}
+
+/** The lowest and highest value the curve can reach – its points and handles – and never less than 0…1. */
+export function curveExtent(points: readonly VectorPoint[]): { min: number; max: number } {
+  let min = 0;
+  let max = 1;
+  for (const point of points)
+    for (const y of [point.y, point.y + (point.in?.y ?? 0), point.y + (point.out?.y ?? 0)]) {
+      min = Math.min(min, y);
+      max = Math.max(max, y);
+    }
+  return { min, max };
+}

src/core/model/curvePresets.ts

@@ -0,0 +1,111 @@
+/**
+ * The built-in eases as starting points for a Curve asset (#247). Each is traced by a few Bezier
+ * segments: the points sit on the ease, and each handle points along the ease's slope on its side, a
+ * third of the way to the neighbour (a cubic Hermite piece). A segment that strays more than
+ * `TOLERANCE` from the ease is halved, and only that one – so a quad keeps its single segment, and
+ * circ gets ever shorter ones only towards its upright end.
+ */
+import type { EasingDirection, VectorPoint } from './Asset';
+import type { Vec2 } from './Properties';
+import { EASING_DIRECTIONS, EASING_SHAPES, easedShare, type EasingShape, easingValue } from './animation';
+import { curveValue, linearCurve } from './curve';
+
+export interface CurvePreset {
+  label: string;
+  /** The ease it traces; presets of one shape share it, so a menu can group them. */
+  shape: EasingShape;
+  build(): VectorPoint[];
+}
+
+const TOLERANCE = 0.004;
+/** Enough for a bounce; a curve with more points than this is no longer one to edit by hand. */
+const MAX_POINTS = 64;
+const MAX_ROUNDS = 16;
+/** Where each segment is compared with the ease. */
+const SAMPLES = 24;
+/** The step of the one-sided slopes: small, and never onto the point itself, where expo jumps to 0. */
+const H = 1e-6;
+
+export function curvePresets(): CurvePreset[] {
+  const presets: CurvePreset[] = [{ label: 'Linear', shape: 'linear', build: linearCurve }];
+  for (const { value: shape, label } of EASING_SHAPES) {
+    if (shape === 'linear' || shape === 'step' || shape === 'curve') continue;
+    for (const direction of EASING_DIRECTIONS)
+      presets.push({
+        label: `${label} ${direction.label.toLowerCase()}`,
+        shape,
+        build: () => easeCurve(shape, direction.value),
+      });
+  }
+  return presets;
+}
+
+export function easeCurve(shape: EasingShape, direction: EasingDirection): VectorPoint[] {
+  const interpolation = easingValue(shape, direction);
+  return curveFromEase((t) => easedShare(interpolation, t));
+}
+
+export function curveFromEase(ease: (t: number) => number): VectorPoint[] {
+  let at = [0, 1];
+  let points = traced(ease, at);
+  for (let round = 0; round < MAX_ROUNDS; round++) {
+    const next = [0];
+    for (let i = 1; i < at.length; i++) {
+      const strays = segmentGap(points[i - 1]!, points[i]!, ease) > TOLERANCE;
+      if (strays && next.length + at.length - i < MAX_POINTS) next.push((at[i - 1]! + at[i]!) / 2);
+      next.push(at[i]!);
+    }
+    if (next.length === at.length) break;
+    at = next;
+    points = traced(ease, at);
+  }
+  return points;
+}
+
+function traced(ease: (t: number) => number, at: readonly number[]): VectorPoint[] {
+  const value = (x: number) => clean(ease(x));
+  return at.map((x, i) => {
+    const point: VectorPoint = { x, y: value(x) };
+    const before = at[i - 1];
+    const after = at[i + 1];
+    const slopeIn = before === undefined ? null : (ease(x - H) - ease(x - 2 * H)) / H;
+    const slopeOut = after === undefined ? null : (ease(x + 2 * H) - ease(x + H)) / H;
+    if (before !== undefined && slopeIn !== null)
+      point.in = handle((before - x) / 3, slopeIn, point.y - value(before));
+    if (after !== undefined && slopeOut !== null)
+      point.out = handle((after - x) / 3, slopeOut, value(after) - point.y);
+    if (
+      slopeIn !== null &&
+      slopeOut !== null &&
+      Math.abs(slopeIn - slopeOut) < 1e-3 * Math.max(1, Math.abs(slopeOut))
+    )
+      point.mode = 'smooth';
+    return point;
+  });
+}
+
+/**
+ * A handle along `slope`, reaching `reach` in `t`. Where the ease stands upright – circ at its steep
+ * end – the slope is huge, so the handle is held to the rise of its segment plus one step, keeping
+ * its direction: nearly vertical, as the ease is there, instead of shooting off the graph.
+ */
+function handle(reach: number, slope: number, rise: number): Vec2 {
+  const y = slope * reach;
+  const most = Math.abs(rise) + Math.abs(reach) * 3;
+  const scale = Math.abs(y) > most ? most / Math.abs(y) : 1;
+  return { x: reach * scale, y: y * scale };
+}
+
+/** Rounding noise off, so an ease that starts at 0 starts at 0 and not at 2e-16. */
+function clean(value: number): number {
+  return Math.round(value * 1e12) / 1e12;
+}
+
+function segmentGap(from: VectorPoint, to: VectorPoint, ease: (t: number) => number): number {
+  let gap = 0;
+  for (let i = 1; i < SAMPLES; i++) {
+    const t = from.x + ((to.x - from.x) * i) / SAMPLES;
+    gap = Math.max(gap, Math.abs(curveValue([from, to], t) - ease(t)));
+  }
+  return gap;
+}

src/core/model/graphLookup.ts

@@ -29,5 +29,6 @@ export function graphLookup(project: Project): GraphLookup {
         start: startStateOf(asset.graph, asset.start),
       };
     },
+    curve: (assetId) => findAssetOf(project, assetId, 'curve')?.points ?? null,
   };
 }

src/core/properties/PropertySchema.ts

@@ -405,6 +405,8 @@ const ASSET_SCHEMAS: Record<AssetType, PropertySchema> = {
   ],
   // The colours are intrinsic data on the asset (see PaletteAsset).
   palette: [],
+  // The points are intrinsic data on the asset (see CurveAsset).
+  curve: [],
   // The root and the rows are intrinsic data on the asset (see AnimationAsset).
   animation: [
     { key: 'fps', label: 'Frames per second', kind: 'number', default: 10, min: 0.1, max: 120, step: 1 },

src/core/store/serialize.ts

@@ -68,6 +68,7 @@ import { canvasSide, PALETTE_MAX } from '../model/pixelart';
 import { isCelFile } from '../model/pixelCel';
 import { newId } from '../ids';
 import { SHAPE_FILL_DEFAULT } from '../model/vectorart';
+import { sanitizedCurve } from '../model/curve';
 import { hasParentCycle } from '../model/walk';
 import {
   DECLARED_PORT_KINDS,
@@ -230,6 +231,8 @@ export function deserializeProject(raw: unknown, fallbackId = ''): Project {
       assets.push({ id, type, name, props, ...normalizePixelArt(a, takenIds) });
     } else if (type === 'palette') {
       assets.push({ id, type, name, props, colors: normalizePalette(a.colors) });
+    } else if (type === 'curve') {
+      assets.push({ id, type, name, props, points: sanitizedCurve(normalizePoints(a.points)) });
     } else if (type === 'animation') {
       // A root or row aiming at something gone is kept: it reads as missing and keeps its keys.
       const root = typeof a.root === 'string' ? a.root : '';
@@ -702,22 +705,8 @@ function normalizeShapes(raw: unknown): VectorShape[] {
     const rings: VectorRing[] = [];
     for (const r of Array.isArray(s.rings) ? s.rings : []) {
       const ring = asRecord(r);
-      const points: VectorPoint[] = [];
-      for (const p of Array.isArray(ring.points) ? ring.points : []) {
-        const point = asRecord(p);
-        const x = asFinite(point.x);
-        const y = asFinite(point.y);
-        if (x === null || y === null) continue;
-        const kept: VectorPoint = { x, y };
-        for (const side of ['in', 'out'] as const) {
-          const handle = normalizeHandle(point[side]);
-          if (handle) kept[side] = handle;
-        }
-        if (point.mode === 'smooth' || point.mode === 'symmetric') kept.mode = point.mode;
-        points.push(kept);
-      }
       // Closed is what a shape usually is, and what every ring written by the editor says.
-      rings.push({ points, closed: ring.closed !== false });
+      rings.push({ points: normalizePoints(ring.points), closed: ring.closed !== false });
     }
     const shape: VectorShape = {
       id: s.id,
@@ -740,6 +729,25 @@ function normalizeShapes(raw: unknown): VectorShape[] {
   return shapes;
 }
 
+/** The points of a ring or of a curve (#247); the rules are those of `normalizeShapes`. */
+function normalizePoints(raw: unknown): VectorPoint[] {
+  const points: VectorPoint[] = [];
+  for (const p of Array.isArray(raw) ? raw : []) {
+    const point = asRecord(p);
+    const x = asFinite(point.x);
+    const y = asFinite(point.y);
+    if (x === null || y === null) continue;
+    const kept: VectorPoint = { x, y };
+    for (const side of ['in', 'out'] as const) {
+      const handle = normalizeHandle(point[side]);
+      if (handle) kept[side] = handle;
+    }
+    if (point.mode === 'smooth' || point.mode === 'symmetric') kept.mode = point.mode;
+    points.push(kept);
+  }
+  return points;
+}
+
 /**
  * A number as written, or null – unlike `toNumber`, which reads anything unusable as 0. A coordinate
  * of 0 is a place on the canvas, so "broken" and "the left edge" must not come out the same.

src/editor/Editor.ts

@@ -70,6 +70,7 @@ import type { EditorState } from './state';
 import { copySelection } from './clipboard';
 import { PixelArtEditor } from './pixelart/PixelArtEditor';
 import { VectorArtEditor } from './vectorart/VectorArtEditor';
+import { CurveEditor } from './curve/CurveEditor';
 import { TextureEditor } from './texture/TextureEditor';
 import { installFileImport } from './fileImport';
 import type { PluginManager } from './plugins/loader';
@@ -88,6 +89,7 @@ export type CentreTab =
   | 'vectorart'
   | 'pixelart'
   | 'animation'
+  | 'curve'
   | 'tile'
   | 'container'
   | 'list'
@@ -134,6 +136,7 @@ const PANE_ORDER = [
   'vectorart',
   'pixelart',
   'animation',
+  'curve',
   'tile',
   'container',
   'list',
@@ -152,6 +155,7 @@ const TAB_LABELS: Record<CentreTab, string> = {
   vectorart: 'Vector art',
   pixelart: 'Pixel art',
   animation: 'Animation',
+  curve: 'Curve',
   tile: 'Tile',
   container: 'Container',
   list: 'List',
@@ -197,6 +201,7 @@ export class Editor implements PlayHost {
   readonly vectorArtEditor: VectorArtEditor;
   readonly pixelArtEditor: PixelArtEditor;
   readonly animationEditor: AnimationEditor;
+  readonly curveEditor: CurveEditor;
   readonly tileEditor: TileEditor;
   readonly containerEditor: ContainerEditor;
   readonly listEditor: ListEditor;
@@ -276,6 +281,7 @@ export class Editor implements PlayHost {
     this.vectorArtEditor = new VectorArtEditor(state);
     this.pixelArtEditor = new PixelArtEditor(state);
     this.animationEditor = new AnimationEditor(state);
+    this.curveEditor = new CurveEditor(state);
     this.tileEditor = new TileEditor(state);
     this.containerEditor = new ContainerEditor(state);
     this.listEditor = new ListEditor(state);
@@ -380,6 +386,7 @@ export class Editor implements PlayHost {
       vectorart: this.vectorArtEditor,
       pixelart: this.pixelArtEditor,
       animation: this.animationEditor,
+      curve: this.curveEditor,
       tile: this.tileEditor,
       container: this.containerEditor,
     };
@@ -814,6 +821,8 @@ export class Editor implements PlayHost {
     this.console.refresh();
     if (this.tab === 'animation') this.animationEditor.tick(step);
     if (this.tab === 'tile') this.tileEditor.tick(step);
+    // The preview is the editor's own, so it runs on while the game is paused.
+    if (this.tab === 'curve') this.curveEditor.tick(dt);
     // Play repaints the machine tab itself (see `PlaySession.tick`); an editor run has no session
     // to do it, and its states move just the same.
     if (this.tab === 'statemachine' && this.editorRun.isRunning) this.stateMachineEditor.canvas.redraw();
@@ -837,7 +846,8 @@ export class Editor implements PlayHost {
       this.tab === 'pixelart' ||
       (this.tab === 'shader' && this.shaderEditor.animates) ||
       (this.tab === 'animation' && this.animationEditor.isPlaying) ||
-      (this.tab === 'tile' && this.tileEditor.isPlaying)
+      (this.tab === 'tile' && this.tileEditor.isPlaying) ||
+      (this.tab === 'curve' && this.curveEditor.isPlaying)
     );
   }
 

src/editor/actions.ts

@@ -15,6 +15,7 @@ import { CreateContainerCommand } from '../core/commands/containerCommands';
 import { RemoveNodeCommand } from '../core/commands/graphCommands';
 import { RemoveSceneObjectsCommand } from '../core/commands/sceneObjectCommands';
 import type { AssetType } from '../core/model/AssetTypes';
+import { curveUsages } from '../core/model/curve';
 import { generatesPictures } from '../core/model/generated';
 import { isTemplateContent } from '../core/model/instance';
 import type { Command } from '../core/commands/Command';
@@ -131,16 +132,19 @@ export function confirmDeleteAsset(state: EditorState, assetId: string): void {
   const picture = asset.type === 'texture' || generatesPictures(asset.type);
   const animations = picture ? animationsUsing(state.project, ids).length : 0;
   const tiles = picture ? tilesUsing(state.project, ids).length : 0;
+  const eased = asset.type === 'curve' ? curveUsages(state.project, assetId) : { keys: 0, nodes: 0 };
   const detail =
     asset.type === 'scene'
       ? `The scene and its ${asset.objects.length} object(s) are removed.`
-      : references > 0 || animations > 0 || tiles > 0
-        ? wornDetail(references, animations, tiles, asset.type)
-        : usages === 0
-          ? 'This cannot be undone with Ctrl+Z after reload.'
-          : asset.type === 'container'
-            ? `${usages} placed container(s) are removed together with their content.`
-            : `${usages} placed instance(s) are removed as well (scenes and container templates).`;
+      : eased.keys > 0 || eased.nodes > 0
+        ? `${eased.keys} animation key(s) and ${eased.nodes} Lerp node(s) use it and blend linearly instead.`
+        : references > 0 || animations > 0 || tiles > 0
+          ? wornDetail(references, animations, tiles, asset.type)
+          : usages === 0
+            ? 'This cannot be undone with Ctrl+Z after reload.'
+            : asset.type === 'container'
+              ? `${usages} placed container(s) are removed together with their content.`
+              : `${usages} placed instance(s) are removed as well (scenes and container templates).`;
   new Dialog(`Delete "${asset.name}"?`, detail, [
     { label: 'Cancel' },
     { label: 'Delete', danger: true, onClick: () => state.execute(new DeleteAssetCommand(assetId)) },

src/editor/animation/TimelineCanvas.ts

@@ -702,7 +702,7 @@ export class TimelineCanvas extends Widget {
 /**
  * A key's outline tells its easing: the right half is the start of the way to the next key, the left
  * half its end, and a round half is a slow one. Linear is the diamond, any curve in-out the circle, a
- * step – which holds – the square.
+ * step – which holds – the square. A Curve asset (#247) may do anything, so it is drawn round both ways.
  */
 function drawKeyShape(
   g: Graphics,
@@ -712,9 +712,9 @@ function drawKeyShape(
   half: number,
 ): Graphics {
   if (interpolation === 'step') return g.rect(x - half * 0.75, y - half * 0.75, half * 1.5, half * 1.5);
-  const { direction } = easingOf(interpolation);
-  const slowStart = direction === 'in' || direction === 'in-out';
-  const slowEnd = direction === 'out' || direction === 'in-out';
+  const { shape, direction } = easingOf(interpolation);
+  const slowStart = shape === 'curve' || direction === 'in' || direction === 'in-out';
+  const slowEnd = shape === 'curve' || direction === 'out' || direction === 'in-out';
   g.moveTo(x, y - half);
   if (slowStart) g.arc(x, y, half, -Math.PI / 2, Math.PI / 2);
   else g.lineTo(x + half, y).lineTo(x, y + half);

src/editor/assetTabs.ts

@@ -12,6 +12,7 @@ export const TAB_OF_ASSET: Partial<Record<AssetType, CentreTab>> = {
   vectorart: 'vectorart',
   pixelart: 'pixelart',
   animation: 'animation',
+  curve: 'curve',
   tile: 'tile',
   container: 'container',
 };

src/editor/curve/CurveCanvas.ts

@@ -0,0 +1,424 @@
+/**
+ * The Curve tab's canvas (#247): the curve as a graph, `t` to the right and `v` up, with guides at
+ * 0 and 1. Points and handles are edited with the vector art gestures (see `curveView.ts` for how
+ * the curve is laid onto a picture for them), and a gesture writes the model as a preview and puts
+ * it back on release, so one drag is one undo step.
+ *
+ * The line is drawn from `curveValue`, not from the Bezier segments: what the tab shows is exactly
+ * what a key or a `Lerp` reads. A dot runs along it as a preview, and a second one beside the graph
+ * moves only up and down – the motion the curve gives a value.
+ */
+import { type FederatedPointerEvent, Graphics, Text } from 'pixi.js';
+import { SetCurvePointsCommand } from '../../core/commands/curveCommands';
+import type { CurveAsset, VectorPoint, VectorRing } from '../../core/model/Asset';
+import { curveValue, sanitizedCurve } from '../../core/model/curve';
+import { findAssetOf } from '../../core/model/Project';
+import type { Vec2 } from '../../core/model/Properties';
+import { handleAt } from '../../core/model/vectorart';
+import { cancelFrameWork, onFrame, pressCount, Theme, textStyle } from '../../ui';
+import {
+  type PointKind,
+  pointKind,
+  ringGripAt,
+  withHandleMoved,
+  withoutPoint,
+  withPointKind,
+  withPointOnSegment,
+  withSmoothToggled,
+} from '../polygonEdit';
+import type { EditorState } from '../state';
+import { SheetCanvas } from '../texture/SheetCanvas';
+import { fitView, imageToLocal, localToImage } from '../texture/sheetView';
+import {
+  curveFrame,
+  curveToImage,
+  imageToCurve,
+  isCurveEnd,
+  previewShare,
+  toImage,
+  withCurvePointAt,
+  withCurvePointMoved,
+} from './curveView';
+
+/** Side of a point handle in screen pixels – constant, so a point stays grabbable at any zoom. */
+const POINT_SIZE = 8;
+const HANDLE_RADIUS = 4;
+const DRAG_THRESHOLD = 3;
+/** Steps the drawn line is walked in; a bounce needs this many to keep its corners. */
+const LINE_STEPS = 240;
+/** Where the preview's second dot runs, in units of `t` right of the graph. */
+const BAR_AT = 1.08;
+const DOT_RADIUS = 5;
+
+/** A gesture in progress. `before` is what the curve read when it began – the undo step's other side. */
+interface CurveDrag {
+  kind: 'point' | 'handle';
+  before: VectorPoint[];
+  ring: VectorRing;
+  points: VectorPoint[];
+  index: number;
+  side: 'in' | 'out';
+  pointer: Vec2;
+  moved: boolean;
+  label: string;
+}
+
+let instances = 0;
+
+export class CurveCanvas extends SheetCanvas<CurveAsset> {
+  private readonly guides = new Graphics();
+  private readonly line = new Graphics();
+  private readonly overlay = new Graphics();
+  private readonly labels = ['0', '1', '0', '1'].map((text) => new Text({ text, style: textStyle('muted') }));
+  private drag: CurveDrag | null = null;
+  /** The point last pressed or put down – the one the header's point type is about; -1 for none. */
+  private picked = -1;
+  onPointPicked: () => void = () => {};
+  /** Seconds the preview has run; it only moves while `previewing` is on. */
+  private previewTime = 0;
+  private previewOn = true;
+  private readonly frameKey = `curve:${(instances += 1)}`;
+
+  constructor(private readonly state: EditorState) {
+    super();
+    this.content.addChild(this.guides, this.line, this.overlay, ...this.labels);
+    for (const label of this.labels) label.eventMode = 'none';
+    state.on('project', () => this.redraw());
+    state.on('load', () => {
+      this.needsFit = true;
+      this.pick(-1);
+      this.redraw();
+    });
+  }
+
+  show(assetId: string): void {
+    if (this.assetId === assetId) return;
+    this.assetId = assetId;
+    this.needsFit = true;
+    this.pick(-1);
+    this.redraw();
+  }
+
+  /** Moves the preview on; only called while the tab is visible. */
+  tick(dt: number): void {
+    if (!this.previewOn || !this.asset()) return;
+    this.previewTime += dt;
+    this.redraw();
+  }
+
+  get previewing(): boolean {
+    return this.previewOn;
+  }
+
+  setPreviewing(on: boolean): void {
+    this.previewOn = on;
+    this.redraw();
+  }
+
+  /** Where the preview stands: the share of time, the value the curve gives it, and its two dots. */
+  previewState(): { t: number; v: number; dot: Vec2; bar: Vec2 } | null {
+    const asset = this.asset();
+    if (!asset) return null;
+    const t = previewShare(this.previewTime);
+    const v = curveValue(asset.points, t);
+    return { t, v, dot: this.graphToScreen(t, v), bar: this.graphToScreen(BAR_AT, v) };
+  }
+
+  /** For the check scripts: stops the preview at `seconds` into its pass. */
+  setPreviewTime(seconds: number): void {
+    this.previewTime = seconds;
+    this.redraw();
+  }
+
+  /** Where a place on the graph sits on screen – the check scripts aim with it. */
+  graphToScreen(t: number, v: number): Vec2 {
+    const at = toImage({ x: t, y: v });
+    return this.imageToScreen(at.x, at.y);
+  }
+
+  get pickedIndex(): number {
+    return this.picked;
+  }
+
+  /** The type of the picked point; null while none is picked or it has gone since (an undo). */
+  get pickedKind(): PointKind | null {
+    const point = this.asset()?.points[this.picked];
+    return point ? pointKind(point) : null;
+  }
+
+  setPickedKind(kind: PointKind): void {
+    const asset = this.asset();
+    if (!asset || !asset.points[this.picked]) return;
+    const points = imageToCurve(withPointKind(curveToImage(asset.points), this.picked, kind));
+    if (SetCurvePointsCommand.changes(asset, points))
+      this.state.execute(new SetCurvePointsCommand(asset.id, points, 'Point type'));
+  }
+
+  /** Replaces the whole curve – what a preset does. */
+  replace(points: readonly VectorPoint[], label: string): void {
+    const asset = this.asset();
+    if (!asset || !SetCurvePointsCommand.changes(asset, points)) return;
+    this.pick(-1);
+    this.state.execute(new SetCurvePointsCommand(asset.id, points, label));
+  }
+
+  private pick(index: number): void {
+    if (this.picked === index) return;
+    this.picked = index;
+    this.onPointPicked();
+  }
+
+  private asset(): CurveAsset | null {
+    return (this.assetId && findAssetOf(this.state.project, this.assetId, 'curve')) || null;
+  }
+
+  /** Delete takes the picked point away – never an end, which holds the curve at 0 or 1. */
+  override onKeyDown(event: KeyboardEvent): boolean {
+    const asset = this.asset();
+    if ((event.key !== 'Delete' && event.key !== 'Backspace') || !asset || this.picked < 0)
+      return super.onKeyDown(event);
+    this.removePoint(asset, this.picked);
+    return true;
+  }
+
+  private removePoint(asset: CurveAsset, index: number): void {
+    const ring = curveToImage(asset.points);
+    const next = isCurveEnd(ring, index) ? null : withoutPoint(ring, index);
+    if (!next) return;
+    this.pick(-1);
+    this.state.execute(new SetCurvePointsCommand(asset.id, imageToCurve(next), 'Remove point'));
+  }
+
+  protected pressTarget(): CurveAsset | null {
+    return this.asset();
+  }
+
+  /**
+   * A press: on a handle it drags the handle, on a point the point – a double-click takes the point
+   * away, Alt makes it round or straight again. On the line it puts a point there that keeps the
+   * curve as it was, on free space a plain one at the pointer. Either way the new point follows the
+   * pointer until it lets go.
+   */
+  protected press(asset: CurveAsset, e: FederatedPointerEvent, local: Vec2): void {
+    e.stopPropagation();
+    const ring = curveToImage(asset.points);
+    const at = localToImage(this.view, local.x, local.y);
+    const grip = ringGripAt(ring, at, POINT_SIZE / this.view.zoom);
+    if (grip?.kind === 'point') {
+      this.pick(grip.index);
+      if (pressCount(e, `curve point ${asset.id} ${grip.index}`) === 2) {
+        this.removePoint(asset, grip.index);
+        return;
+      }
+      if (e.altKey) {
+        const points = imageToCurve(withSmoothToggled(ring, grip.index));
+        this.state.execute(new SetCurvePointsCommand(asset.id, points, 'Smooth point'));
+        return;
+      }
+      this.startDrag(asset, ring, grip.index, 'point', 'out', local, false, 'Move point');
+      return;
+    }
+    if (grip?.kind === 'handle') {
+      this.pick(grip.index);
+      this.startDrag(asset, ring, grip.index, 'handle', grip.side, local, false, 'Bend curve');
+      return;
+    }
+    const put =
+      grip?.kind === 'segment'
+        ? { ring: withPointOnSegment(ring, grip.index, grip.t), index: grip.index + 1 }
+        : withCurvePointAt(ring, at);
+    if (!put) {
+      this.pick(-1);
+      this.redraw();
+      return;
+    }
+    this.pick(put.index);
+    this.startDrag(asset, put.ring, put.index, 'point', 'out', local, true, 'Add point');
+    this.preview();
+  }
+
+  private startDrag(
+    asset: CurveAsset,
+    ring: VectorRing,
+    index: number,
+    kind: CurveDrag['kind'],
+    side: 'in' | 'out',
+    pointer: Vec2,
+    moved: boolean,
+    label: string,
+  ): void {
+    this.drag = {
+      kind,
+      before: asset.points,
+      ring,
+      points: sanitizedCurve(imageToCurve(ring)),
+      index,
+      side,
+      pointer: { x: pointer.x, y: pointer.y },
+      moved,
+      label,
+    };
+    this.redraw();
+  }
+
+  protected move(local: Vec2): void {
+    const drag = this.drag;
+    if (!drag) {
+      this.updateCursor(local);
+      return;
+    }
+    if (!drag.moved && Math.hypot(local.x - drag.pointer.x, local.y - drag.pointer.y) < DRAG_THRESHOLD)
+      return;
+    drag.moved = true;
+    const to = localToImage(this.view, local.x, local.y);
+    drag.ring =
+      drag.kind === 'handle'
+        ? withHandleMoved(drag.ring, drag.index, drag.side, to)
+        : withCurvePointMoved(drag.ring, drag.index, to);
+    drag.points = sanitizedCurve(imageToCurve(drag.ring));
+    this.preview();
+  }
+
+  /** Once per frame, not once per pointer move – the reason is the one `VectorArtCanvas.preview` gives. */
+  private preview(): void {
+    onFrame(this.frameKey, () => {
+      const asset = this.asset();
+      if (this.destroyed || !this.drag || !asset) return;
+      asset.points = this.drag.points;
+      this.state.preview();
+    });
+  }
+
+  protected release(): void {
+    const drag = this.drag;
+    this.drag = null;
+    cancelFrameWork(this.frameKey);
+    const asset = this.asset();
+    if (!drag || !asset) return;
+    asset.points = drag.before;
+    if (drag.moved && SetCurvePointsCommand.changes(asset, drag.points))
+      this.state.execute(new SetCurvePointsCommand(asset.id, drag.points, drag.label));
+    else this.state.preview();
+  }
+
+  private updateCursor(local: Vec2): void {
+    const asset = this.asset();
+    if (!asset) {
+      this.cursor = 'default';
+      return;
+    }
+    const at = localToImage(this.view, local.x, local.y);
+    const grip = ringGripAt(curveToImage(asset.points), at, POINT_SIZE / this.view.zoom);
+    this.cursor = grip ? 'pointer' : 'crosshair';
+  }
+
+  override redraw(): void {
+    this.drawGround();
+    const asset = this.asset();
+    if (asset && this.needsFit && this.w > 0 && this.h > 0) {
+      const frame = curveFrame(asset.points);
+      const view = fitView(frame.w, frame.h, this.w, this.h);
+      this.view = { ...view, panX: view.panX - frame.x * view.zoom, panY: view.panY - frame.y * view.zoom };
+      this.needsFit = false;
+    }
+    this.checker.clear();
+    this.guides.clear();
+    this.line.clear();
+    this.overlay.clear();
+    for (const label of this.labels) label.visible = asset !== null;
+    if (asset) {
+      this.drawGuides();
+      this.drawLine(asset.points);
+      // Under the points: resting at the end, the dot would hide the last one.
+      this.drawPreview(asset.points);
+      this.drawPoints(asset.points);
+    }
+    this.syncHint(asset);
+  }
+
+  private local(t: number, v: number): Vec2 {
+    const at = toImage({ x: t, y: v });
+    return imageToLocal(this.view, at.x, at.y);
+  }
+
+  /** The unit square, its sides at 0 and 1 carried across the whole view, and their numbers. */
+  private drawGuides(): void {
+    const origin = this.local(0, 0);
+    const corner = this.local(1, 1);
+    this.guides
+      .rect(origin.x, corner.y, corner.x - origin.x, origin.y - corner.y)
+      .fill({ color: Theme.colors.panel, alpha: 0.5 });
+    for (const y of [origin.y, corner.y]) this.guides.moveTo(0, y).lineTo(this.w, y);
+    for (const x of [origin.x, corner.x]) this.guides.moveTo(x, 0).lineTo(x, this.h);
+    this.guides.stroke({ width: 1, color: Theme.colors.border });
+    const [v0, v1, t0, t1] = this.labels as [Text, Text, Text, Text];
+    const gap = Theme.gap;
+    v0.position.set(origin.x - v0.width - gap, origin.y - v0.height / 2);
+    v1.position.set(origin.x - v1.width - gap, corner.y - v1.height / 2);
+    t0.position.set(origin.x - t0.width / 2, origin.y + gap);
+    t1.position.set(corner.x - t1.width / 2, origin.y + gap);
+  }
+
+  private drawLine(points: readonly VectorPoint[]): void {
+    const walked: number[] = [];
+    for (let step = 0; step <= LINE_STEPS; step++) {
+      const t = step / LINE_STEPS;
+      const at = this.local(t, curveValue(points, t));
+      walked.push(at.x, at.y);
+    }
+    this.line.poly(walked, false).stroke({ width: 2, color: Theme.colors.accent });
+  }
+
+  /** Every point with its handles, in widget pixels so they keep their size. */
+  private drawPoints(points: readonly VectorPoint[]): void {
+    const half = POINT_SIZE / 2;
+    for (const [index, point] of points.entries()) {
+      const at = this.local(point.x, point.y);
+      for (const side of ['in', 'out'] as const) {
+        const handle = handleAt(point, side);
+        if (!handle) continue;
+        const tip = this.local(handle.x, handle.y);
+        this.overlay
+          .moveTo(at.x, at.y)
+          .lineTo(tip.x, tip.y)
+          .stroke({ width: 1, color: Theme.colors.marquee });
+        this.overlay
+          .circle(tip.x, tip.y, HANDLE_RADIUS)
+          .fill(Theme.colors.viewport)
+          .stroke({ width: 1, color: Theme.colors.marquee });
+      }
+      const isPicked = index === this.picked;
+      this.overlay
+        .rect(at.x - half, at.y - half, POINT_SIZE, POINT_SIZE)
+        .fill(isPicked ? Theme.colors.accent : Theme.colors.accentText)
+        .stroke({ width: 1, color: isPicked ? Theme.colors.accentText : Theme.colors.accent });
+    }
+  }
+
+  /** A dot on the line at the preview's `t`, and its twin on a rail beside the graph. */
+  private drawPreview(points: readonly VectorPoint[]): void {
+    const t = previewShare(this.previewTime);
+    const v = curveValue(points, t);
+    const dot = this.local(t, v);
+    const bar = this.local(BAR_AT, v);
+    const top = this.local(BAR_AT, 1);
+    const bottom = this.local(BAR_AT, 0);
+    this.overlay
+      .moveTo(dot.x, dot.y)
+      .lineTo(bar.x, bar.y)
+      .stroke({ width: 1, color: Theme.colors.hot, alpha: 0.4 });
+    this.overlay
+      .moveTo(top.x, top.y)
+      .lineTo(bottom.x, bottom.y)
+      .stroke({ width: 2, color: Theme.colors.border });
+    for (const at of [dot, bar]) this.overlay.circle(at.x, at.y, DOT_RADIUS).fill(Theme.colors.hot);
+  }
+
+  private syncHint(asset: CurveAsset | null): void {
+    this.hint.text = asset
+      ? 'Click the line or free space to add a point, drag handles to bend, double-click a point to remove it.'
+      : 'No curve selected – pick one in the Assets panel.';
+    this.hint.visible = true;
+    this.hint.position.set(Theme.padding * 2, Theme.padding * 2);
+  }
+}

src/editor/curve/CurveEditor.ts

@@ -0,0 +1,112 @@
+import type { Asset, CurveAsset } from '../../core/model/Asset';
+import { curvePresets } from '../../core/model/curvePresets';
+import { Button, Dropdown, Menu, type MenuEntry } from '../../ui';
+import { AssetTabEditor } from '../AssetTabEditor';
+import { POINT_KINDS, type PointKind } from '../polygonEdit';
+import type { EditorState } from '../state';
+import { CurveCanvas } from './CurveCanvas';
+
+const INFO_WIDTH = 90;
+/** Fixed, so the header does not shift when "Point: Symmetric" becomes "Point: Corner". */
+const POINT_WIDTH = 150;
+
+const POINT_KIND_LABELS: Record<PointKind, string> = {
+  straight: 'Straight',
+  corner: 'Corner',
+  smooth: 'Smooth',
+  symmetric: 'Symmetric',
+};
+
+function pointLabel(kind: PointKind | null): string {
+  return `Point: ${kind ? POINT_KIND_LABELS[kind] : '–'}`;
+}
+
+/**
+ * The Curve tab (#247): the canvas edits the curve, the header starts it over from a built-in ease,
+ * sets the picked point's type as in the Vector art tab, and runs the preview or holds it.
+ */
+export class CurveEditor extends AssetTabEditor<CurveAsset, CurveCanvas> {
+  /** Public for the check scripts. */
+  readonly presetButton = new Dropdown('Preset');
+  readonly pointButton = new Dropdown(pointLabel(null), { width: POINT_WIDTH });
+  readonly previewButton: Button;
+
+  constructor(state: EditorState) {
+    super(state, { infoWidth: INFO_WIDTH });
+    this.presetButton.onClick = () => this.openPresetMenu();
+    this.pointButton.onClick = () => this.openPointMenu();
+    this.previewButton = new Button('Preview', {
+      toggle: true,
+      onClick: () => this.setPreviewing(!this.canvas.previewing),
+    });
+    const canvas = new CurveCanvas(state);
+    canvas.onPointPicked = () => this.syncPoint();
+    this.mount(canvas, [this.presetButton, this.pointButton, this.previewButton]);
+    this.setPreviewing(true);
+  }
+
+  /** Only called while the tab is visible. */
+  tick(dt: number): void {
+    this.canvas.tick(dt);
+  }
+
+  /** Whether the preview moves by itself – nothing else would wake the tab for it. */
+  get isPlaying(): boolean {
+    return this.canvas.previewing && this.asset() !== null;
+  }
+
+  setPreviewing(on: boolean): void {
+    this.canvas.setPreviewing(on);
+    this.previewButton.setToggled(on);
+  }
+
+  /** The built-in eases, one group per shape; picking one replaces the curve in one undo step. */
+  private openPresetMenu(): void {
+    const entries: MenuEntry[] = [];
+    let shape = '';
+    for (const preset of curvePresets()) {
+      if (entries.length > 0 && preset.shape !== shape) entries.push({ separator: true });
+      shape = preset.shape;
+      entries.push({
+        label: preset.label,
+        onSelect: () => this.canvas.replace(preset.build(), `Curve preset "${preset.label}"`),
+      });
+    }
+    new Menu(entries, { searchable: true }).openBelow(this.presetButton);
+  }
+
+  private openPointMenu(): void {
+    const items = POINT_KINDS.map((kind) => ({
+      label: POINT_KIND_LABELS[kind],
+      checked: () => this.canvas.pickedKind === kind,
+      onSelect: () => this.canvas.setPickedKind(kind),
+    }));
+    new Menu(items).openBelow(this.pointButton);
+  }
+
+  private syncPoint(): void {
+    const kind = this.canvas.pickedKind;
+    this.pointButton.setText(pointLabel(kind));
+    this.pointButton.setEnabled(kind !== null);
+  }
+
+  override selectedId(): string {
+    return this.state.selectedCurveId ?? '';
+  }
+
+  override isMine(asset: Asset): asset is CurveAsset {
+    return asset.type === 'curve';
+  }
+
+  protected override infoText(asset: CurveAsset): string {
+    const count = asset.points.length;
+    return `${count} ${count === 1 ? 'point' : 'points'}`;
+  }
+
+  protected override syncExtras(asset: CurveAsset | null): void {
+    this.fitButton.setEnabled(asset !== null);
+    this.presetButton.setEnabled(asset !== null);
+    this.previewButton.setEnabled(asset !== null);
+    this.syncPoint();
+  }
+}

src/editor/curve/curveView.ts

@@ -0,0 +1,109 @@
+/**
+ * The rules of the Curve tab (#247), apart from its widget so they are testable without a view.
+ *
+ * The tab edits a curve with the vector art gestures (`polygonEdit.ts`), which work on a ring in
+ * picture pixels with `y` pointing down. So the curve is laid onto such a picture: `t` 0…1 runs over
+ * `CURVE_SCALE` pixels to the right and `v` 0…1 as many pixels up. The gestures move points there,
+ * and `imageToCurve` reads the result back.
+ */
+import type { VectorPoint, VectorRing } from '../../core/model/Asset';
+import { curveExtent } from '../../core/model/curve';
+import type { Vec2 } from '../../core/model/Properties';
+import { cloneVectorPoint } from '../../core/model/vectorart';
+
+/** Picture pixels per unit of `t` and of `v`. */
+export const CURVE_SCALE = 256;
+
+/** Room around the curve when it is fitted, in units of `t`. */
+const FIT_MARGIN = 0.12;
+
+/** One pass of the preview: the dot runs `PREVIEW_RUN` seconds, then rests at the end. */
+export const PREVIEW_RUN = 1;
+const PREVIEW_REST = 0.5;
+
+export function curveToImage(points: readonly VectorPoint[]): VectorRing {
+  return { closed: false, points: points.map((p) => mapPoint(p, toImage, toImageOffset)) };
+}
+
+export function imageToCurve(ring: VectorRing): VectorPoint[] {
+  return ring.points.map((p) => mapPoint(p, fromImage, fromImageOffset));
+}
+
+/** A place on the graph, `t` right and `v` up, in picture pixels. */
+export function toImage(at: Vec2): Vec2 {
+  return { x: at.x * CURVE_SCALE, y: (1 - at.y) * CURVE_SCALE };
+}
+
+export function fromImage(at: Vec2): Vec2 {
+  return { x: at.x / CURVE_SCALE, y: 1 - at.y / CURVE_SCALE };
+}
+
+function toImageOffset(offset: Vec2): Vec2 {
+  return { x: offset.x * CURVE_SCALE, y: -offset.y * CURVE_SCALE };
+}
+
+function fromImageOffset(offset: Vec2): Vec2 {
+  return { x: offset.x / CURVE_SCALE, y: -offset.y / CURVE_SCALE };
+}
+
+function mapPoint(point: VectorPoint, place: (at: Vec2) => Vec2, offset: (at: Vec2) => Vec2): VectorPoint {
+  const copy = cloneVectorPoint(point);
+  const at = place(point);
+  copy.x = at.x;
+  copy.y = at.y;
+  if (copy.in) copy.in = offset(copy.in);
+  if (copy.out) copy.out = offset(copy.out);
+  return copy;
+}
+
+/** The part of the picture Fit frames: 0…1 in `t`, and in `v` whatever the curve reaches, plus room. */
+export function curveFrame(points: readonly VectorPoint[]): { x: number; y: number; w: number; h: number } {
+  const { min, max } = curveExtent(points);
+  const top = toImage({ x: -FIT_MARGIN, y: max + FIT_MARGIN });
+  const bottom = toImage({ x: 1 + FIT_MARGIN, y: min - FIT_MARGIN });
+  return { x: top.x, y: top.y, w: bottom.x - top.x, h: bottom.y - top.y };
+}
+
+/**
+ * Point `index` of a picture ring moved to `to`. It stays between its neighbours in `t`, so points
+ * never overtake one another, and the two ends move only up and down.
+ */
+export function withCurvePointMoved(ring: VectorRing, index: number, to: Vec2): VectorRing {
+  const last = ring.points.length - 1;
+  const points = ring.points.map((point, i) => {
+    const copy = cloneVectorPoint(point);
+    if (i !== index) return copy;
+    const before = ring.points[i - 1];
+    const after = ring.points[i + 1];
+    const x = i === 0 || i === last ? point.x : Math.min(Math.max(to.x, before?.x ?? to.x), after?.x ?? to.x);
+    return { ...copy, x, y: to.y };
+  });
+  return { closed: false, points };
+}
+
+/**
+ * A plain point put down at `at`, between the points it falls between in `t`; null outside the
+ * curve's `t` range or on an end. It carries no handles: a press on free space sets a corner, and
+ * pulling handles out is for the handles.
+ */
+export function withCurvePointAt(ring: VectorRing, at: Vec2): { ring: VectorRing; index: number } | null {
+  const first = ring.points[0];
+  const last = ring.points[ring.points.length - 1];
+  if (!first || !last || at.x <= first.x || at.x >= last.x) return null;
+  const index = ring.points.findIndex((p) => p.x > at.x);
+  const points = ring.points.map(cloneVectorPoint);
+  points.splice(index, 0, { x: at.x, y: at.y });
+  return { ring: { closed: false, points }, index };
+}
+
+/** Whether a point may be taken away: the two ends hold the curve at `t` 0 and 1. */
+export function isCurveEnd(ring: VectorRing, index: number): boolean {
+  return index === 0 || index === ring.points.length - 1;
+}
+
+/** Where the preview's dot is after `seconds` of running: `t` climbs for a second, then rests at 1. */
+export function previewShare(seconds: number): number {
+  const cycle = PREVIEW_RUN + PREVIEW_REST;
+  const into = ((seconds % cycle) + cycle) % cycle;
+  return Math.min(into / PREVIEW_RUN, 1);
+}

src/editor/debug/curveHooks.ts

@@ -0,0 +1,36 @@
+import { findAssetOf } from '../../core/model/Project';
+import { centreOf, type HookContext } from './hookHelpers';
+
+/** The Curve tab (#247). */
+export function curveHooks({ state, editor }: HookContext) {
+  const { curveEditor } = editor;
+  return {
+    curve: {
+      current: () => curveEditor.currentAssetId,
+      info: () => curveEditor.shownInfo,
+      rect: () => curveEditor.canvasRect(),
+      /** Where a place on the graph (`t` right, `v` up) sits on screen. */
+      at: (t: number, v: number) => curveEditor.canvas.graphToScreen(t, v),
+      /** The points as the model holds them, handles as offsets in `t` and `v`. */
+      points: (assetId: string) => {
+        const asset = findAssetOf(state.project, assetId, 'curve');
+        return asset ? (JSON.parse(JSON.stringify(asset.points)) as unknown) : null;
+      },
+      picked: () => curveEditor.canvas.pickedIndex,
+      pointButton: () => ({
+        ...centreOf(curveEditor.pointButton),
+        text: curveEditor.pointButton.text,
+        enabled: curveEditor.pointButton.enabled,
+      }),
+      presetButton: () => centreOf(curveEditor.presetButton),
+      fitAt: () => centreOf(curveEditor.fitButton),
+      previewButton: () => ({
+        ...centreOf(curveEditor.previewButton),
+        toggled: curveEditor.previewButton.toggled,
+      }),
+      /** The preview as drawn: the share of time, the value, and where its two dots are. */
+      preview: () => curveEditor.canvas.previewState(),
+      setPreviewTime: (seconds: number) => curveEditor.canvas.setPreviewTime(seconds),
+    },
+  };
+}

src/editor/debugHook.ts

@@ -1,6 +1,7 @@
 import type { Application } from 'pixi.js';
 import { physicsStatus } from '../runtime/physics/engine';
 import { soundLibrary } from '../viewport/SoundLibrary';
+import { curveHooks } from './debug/curveHooks';
 import { documentHooks } from './debug/documentHooks';
 import { graphHooks } from './debug/graphHooks';
 import { centreOf, type HookContext } from './debug/hookHelpers';
@@ -30,6 +31,7 @@ export function installDebugHook(app: Application, state: EditorState, editor: E
     ...documentHooks(context),
     ...pixelArtHooks(context),
     ...vectorArtHooks(context),
+    ...curveHooks(context),
     ...renderHooks(context),
     /**
      * Voices started, stopped and in flight. CI runs the browser with `--mute-audio`, so nothing

src/editor/inspector/trackSection.ts

@@ -26,6 +26,8 @@ import type {
   KeyInterpolation,
 } from '../../core/model/Asset';
 import { findAssetOf, type Project } from '../../core/model/Project';
+import { textOf } from '../../core/model/Properties';
+import type { PropertyDef } from '../../core/properties/PropertySchema';
 import { Button } from '../../ui';
 import { openRowDialog, RowDialog } from '../animation/RowDialog';
 import { createFieldRow } from './fieldFactory';
@@ -45,9 +47,33 @@ export function trackSignature(
   if (!asset || !track) return 'missing';
   const kind = kindOf(project, asset, track) ?? 'missing';
   const key = keys.length === 1 ? `${keys[0]!.trackId}@${keys[0]!.frame}` : String(keys.length);
-  return `${track.id}|${track.target}|${track.property}|${kind}|${track.relative ? 'rel' : 'abs'}|${key}`;
+  return `${track.id}|${track.target}|${track.property}|${kind}|${track.relative ? 'rel' : 'abs'}|${key}|${curveState(
+    project,
+    asset,
+    keys,
+  )}`;
 }
 
+/**
+ * Which curve the shown easing picks and whether it is there (#247): the Curve row and its warning
+ * come and go with it, so a change here has to rebuild the section.
+ */
+function curveState(project: Project, asset: AnimationAsset, keys: readonly KeyRef[]): string {
+  const key = easingKey(project, asset, keys);
+  const easing = key && easingOf(interpolationOf(key));
+  if (easing?.shape !== 'curve') return '';
+  const found = findAssetOf(project, easing.curve ?? '', 'curve');
+  return `curve:${easing.curve ?? ''}:${found ? 'here' : 'gone'}`;
+}
+
+const CURVE_ROW: PropertyDef = {
+  key: 'curve',
+  label: 'Curve',
+  kind: 'asset',
+  default: '',
+  assetTypes: ['curve'],
+};
+
 /**
  * A row of the timeline: what it aims at, whether it is relative, and – with one key picked – the
  * key's value. Several keys show their count and the way to delete them at once.
@@ -160,11 +186,17 @@ function buildEasing(host: InspectorHost, asset: AnimationAsset, keys: readonly
     easing.shape,
     {
       onInput: () => {},
-      onChange: (value) => set(easingValue(value as EasingShape, current().direction)),
+      onChange: (value) => {
+        const now = current();
+        // Switched to Curve, a key takes the curve it had, else the first one there is.
+        const curve = now.curve || firstCurveId(host.state.project);
+        set(easingValue(value as EasingShape, now.direction, curve));
+      },
     },
   );
   host.fields.set('easing', shape);
   host.body.add(shape.row);
+  if (easing.shape === 'curve') buildCurveRow(host, easing.curve ?? '', set);
   if (easing.direction) {
     const direction = createFieldRow(
       host,
@@ -187,6 +219,23 @@ function buildEasing(host: InspectorHost, asset: AnimationAsset, keys: readonly
   addNote(host, 'Easing: the way from this key to the next one.', 'small');
 }
 
+/** The Curve asset the keys blend along, and why they blend linearly when there is none. */
+function buildCurveRow(host: InspectorHost, curveId: string, set: (value: KeyInterpolation) => void): void {
+  const row = createFieldRow(host, CURVE_ROW, curveId, {
+    onInput: () => {},
+    onChange: (value) => set(easingValue('curve', undefined, textOf(value))),
+  });
+  host.fields.set('curve', row);
+  host.body.add(row.row);
+  if (!curveId) addNote(host, 'No curve picked – the key blends linearly.', 'warning');
+  else if (!findAssetOf(host.state.project, curveId, 'curve'))
+    addNote(host, 'That curve is gone – the key blends linearly.', 'warning');
+}
+
+function firstCurveId(project: Project): string {
+  return project.assets.find((a) => a.type === 'curve')?.id ?? '';
+}
+
 /** The last picked key on a row that blends; undefined when none of them can ease. */
 function easingKey(
   project: Project,
@@ -226,6 +275,7 @@ export function refreshTrackSection(
   if (Boolean(easing.direction) !== host.fields.has('direction')) return false;
   host.fields.get('easing')?.setValue(easing.shape);
   if (easing.direction) host.fields.get('direction')?.setValue(easing.direction);
+  if (easing.shape === 'curve') host.fields.get('curve')?.setValue(easing.curve ?? '');
   return true;
 }
 

src/editor/panels/assetGroups.ts

@@ -23,6 +23,7 @@ export const ASSET_GROUP_LABELS: Record<AssetType, string> = {
   pixelart: 'Pixel drawings',
   palette: 'Palettes',
   animation: 'Animations',
+  curve: 'Curves',
   tile: 'Tiles',
   tilemap: 'Tilemaps',
   statemachine: 'State machines',

src/editor/panels/assetIcons.ts

@@ -8,6 +8,7 @@ import behavior from './icons/behavior.svg?raw';
 import camera from './icons/camera.svg?raw';
 import collider from './icons/collider.svg?raw';
 import container from './icons/container.svg?raw';
+import curve from './icons/curve.svg?raw';
 import font from './icons/font.svg?raw';
 import game from './icons/game.svg?raw';
 import group from './icons/group.svg?raw';
@@ -36,6 +37,7 @@ export const ASSET_ICON_SVG: Record<AssetType, string> = {
   camera,
   collider,
   container,
+  curve,
   font,
   palette,
   particles,

src/editor/panels/icons/curve.svg

@@ -0,0 +1,6 @@
+<svg xmlns="http://www.w3.org/2000/svg" viewBox="-8 -8 16 16" width="16" height="16">
+  <!-- An ease-in-out rising from the bottom left to the top right, over the two axes it is drawn on. -->
+  <path d="M-6.5 -7 L-6.5 6.5 L7 6.5" fill="none" stroke="currentColor" stroke-width="1" />
+  <path d="M-6.5 6.5 C0 6.5 0 -6.5 6.5 -6.5" fill="none" stroke="currentColor" stroke-width="1.75" />
+  <circle cx="0" cy="0" r="1.75" fill="currentColor" />
+</svg>

src/editor/state.ts

@@ -645,6 +645,13 @@ export class EditorState {
     return findAssetOf(this.project, s.assetId, 'tile')?.id ?? null;
   }
 
+  /** The curve the selection refers to (#247); only the asset itself, its points are picked in the tab. */
+  get selectedCurveId(): string | null {
+    const s = this.selection;
+    if (s?.kind !== 'asset') return null;
+    return findAssetOf(this.project, s.assetId, 'curve')?.id ?? null;
+  }
+
   /** The timeline row the selection is about; undefined when it is about something else. */
   get selectedTrackId(): string | undefined {
     return this.selection?.kind === 'track' ? this.selection.trackId : undefined;

src/runtime/systems/AnimationSystem.ts

@@ -12,6 +12,7 @@ import {
   trackWriteAt,
 } from '../../core/model/animation';
 import type { AnimationAsset, AnimationTrack } from '../../core/model/Asset';
+import { curveLookup } from '../../core/model/curve';
 import { instanceChildId, splitInstanceId } from '../../core/model/instance';
 import { findAsset, findAssetOf } from '../../core/model/Project';
 import type { PropertyValue } from '../../core/model/Properties';
@@ -52,6 +53,7 @@ export class AnimationSystem implements System {
     running.sort((a, b) => a.player.order - b.player.order);
     // What the players before this one wrote this tick – a blend mixes from that value, live.
     const written = new Set<string>();
+    const curves = curveLookup(world.project);
     for (const { entity, player } of running) {
       const asset = findAssetOf(world.project, player.animationId, 'animation');
       if (!asset) {
@@ -81,7 +83,7 @@ export class AnimationSystem implements System {
       const fade = player.fade;
       const fadeShare = fade ? blendShare(fade) : 0;
       for (const b of bindings) {
-        let value = trackWriteAt(b.track, b.def, head.frame, player.bases[b.base], head.reverse);
+        let value = trackWriteAt(b.track, b.def, head.frame, player.bases[b.base], head.reverse, curves);
         if (value === undefined) continue;
         const below = written.has(b.base) ? b.read() : undefined;
         if (share < 1 && blends(b.def.kind)) {

tests/core/curve.test.ts

@@ -0,0 +1,290 @@
+/**
+ * Curve assets (#247): an easing drawn by hand. One function evaluates it for the tab, the animation
+ * player and the `Lerp` node; every stored curve is held to the rules first, so it has exactly one
+ * value for every `t`.
+ */
+import { describe, expect, it } from 'vitest';
+import {
+  AddAnimationTrackCommand,
+  SetAnimationKeyCommand,
+  SetAnimationRootCommand,
+  SetKeyInterpolationCommand,
+} from '../../src/core/commands/animationCommands';
+import { CreateAssetCommand } from '../../src/core/commands/assetCommands';
+import { SetCurvePointsCommand } from '../../src/core/commands/curveCommands';
+import {
+  easedShare,
+  easingOf,
+  easingValue,
+  isKeyInterpolation,
+  playAnimation,
+  trackValueAt,
+} from '../../src/core/model/animation';
+import type { VectorPoint } from '../../src/core/model/Asset';
+import {
+  curveLookup,
+  curveUsages,
+  curveValue,
+  linearCurve,
+  sanitizedCurve,
+} from '../../src/core/model/curve';
+import { curvePresets, easeCurve } from '../../src/core/model/curvePresets';
+import { findAssetOf } from '../../src/core/model/Project';
+import { deserializeProject, serializeProject } from '../../src/core/store/serialize';
+import { AnimationSystem } from '../../src/runtime/systems/AnimationSystem';
+import { World } from '../../src/runtime/World';
+import { makeProject, makeSpriteScene, place, roundTrip } from '../helpers';
+
+/** Quad in, exactly: a cubic whose `t` runs evenly and whose value is s². */
+const QUAD_IN: VectorPoint[] = [
+  { x: 0, y: 0, out: { x: 1 / 3, y: 0 } },
+  { x: 1, y: 1, in: { x: -1 / 3, y: -2 / 3 } },
+];
+
+const steps = (count: number) => Array.from({ length: count + 1 }, (_, i) => i / count);
+
+describe('evaluating a curve', () => {
+  it('reads a new curve as linear', () => {
+    for (const t of steps(20)) expect(curveValue(linearCurve(), t)).toBeCloseTo(t, 12);
+  });
+
+  it('solves a Bezier segment for t', () => {
+    for (const t of steps(16)) expect(curveValue(QUAD_IN, t)).toBeCloseTo(t * t, 9);
+    // CSS `ease-in-out`: symmetric about the middle, and rising all the way.
+    const cssEaseInOut: VectorPoint[] = [
+      { x: 0, y: 0, out: { x: 0.42, y: 0 } },
+      { x: 1, y: 1, in: { x: -0.42, y: 0 } },
+    ];
+    expect(curveValue(cssEaseInOut, 0.5)).toBeCloseTo(0.5, 9);
+    expect(curveValue(cssEaseInOut, 0.25) + curveValue(cssEaseInOut, 0.75)).toBeCloseTo(1, 9);
+    const values = steps(100).map((t) => curveValue(cssEaseInOut, t));
+    for (let i = 1; i < values.length; i++) expect(values[i]!).toBeGreaterThanOrEqual(values[i - 1]!);
+  });
+
+  it('hits the ends exactly and holds t to 0…1', () => {
+    const back = easeCurve('back', 'out');
+    expect(curveValue(back, 0)).toBe(0);
+    expect(curveValue(back, 1)).toBe(1);
+    expect(curveValue(back, -3)).toBe(0);
+    expect(curveValue(back, 7)).toBe(1);
+  });
+
+  it('overshoots where the points go past 1', () => {
+    const overshoot: VectorPoint[] = [
+      { x: 0, y: 0 },
+      { x: 0.5, y: 1.5 },
+      { x: 1, y: 1 },
+    ];
+    expect(curveValue(overshoot, 0.25)).toBeCloseTo(0.75, 12);
+    expect(curveValue(overshoot, 0.5)).toBeCloseTo(1.5, 12);
+    expect(curveValue(overshoot, 0.75)).toBeCloseTo(1.25, 12);
+    expect(Math.max(...steps(100).map((t) => curveValue(easeCurve('back', 'out'), t)))).toBeGreaterThan(1.09);
+  });
+
+  it('keeps one value for every t even when the stored handles reach past a neighbour', () => {
+    const wild: VectorPoint[] = [
+      { x: 0, y: 0, out: { x: 5, y: 1 } },
+      { x: 1, y: 1, in: { x: -5, y: -1 } },
+    ];
+    const values = steps(200).map((t) => curveValue(wild, t));
+    for (let i = 1; i < values.length; i++) expect(values[i]!).toBeGreaterThanOrEqual(values[i - 1]! - 1e-12);
+  });
+});
+
+describe('the rules a stored curve is held to', () => {
+  it('sorts the points, pins the ends to t 0 and 1 and keeps t in 0…1', () => {
+    const held = sanitizedCurve([
+      { x: 0.9, y: 0.5 },
+      { x: 0.2, y: 2 },
+      { x: 1.4, y: 1 },
+      { x: -0.3, y: 0.1 },
+    ]);
+    expect(held.map((p) => [p.x, p.y])).toEqual([
+      [0, 0.1],
+      [0.2, 2],
+      [0.9, 0.5],
+      [1, 1],
+    ]);
+  });
+
+  it('drops what is no number, and falls back to linear below two points', () => {
+    expect(
+      sanitizedCurve([
+        { x: Number.NaN, y: 0 },
+        { x: 0.5, y: 0.5 },
+      ]),
+    ).toEqual(linearCurve());
+    expect(sanitizedCurve([])).toEqual(linearCurve());
+  });
+
+  it('shortens a handle reaching past its neighbour along its own direction', () => {
+    const [first, last] = sanitizedCurve([
+      { x: 0, y: 0, out: { x: 2, y: 1 } },
+      { x: 1, y: 1, in: { x: -4, y: -2 } },
+    ]);
+    expect(first!.out).toEqual({ x: 1, y: 0.5 });
+    expect(last!.in).toEqual({ x: -1, y: -0.5 });
+  });
+
+  it('turns a handle pointing backwards in t upright, and drops the ends outer handles', () => {
+    const [first, middle, last] = sanitizedCurve([
+      { x: 0, y: 0, in: { x: -0.1, y: 0 }, out: { x: 0.1, y: 0.2 } },
+      { x: 0.5, y: 0.5, in: { x: 0.2, y: 0.3 }, out: { x: -0.1, y: 0.4 }, mode: 'smooth' },
+      { x: 1, y: 1, out: { x: 0.2, y: 0 } },
+    ]);
+    expect(first!.in).toBeUndefined();
+    expect(middle!.in).toEqual({ x: 0, y: 0.3 });
+    expect(middle!.out).toEqual({ x: 0, y: 0.4 });
+    expect(middle!.mode).toBe('smooth');
+    expect(last!.out).toBeUndefined();
+  });
+});
+
+describe('a key and a Lerp that ease along a curve', () => {
+  it('stores the curve on the key and splits it back', () => {
+    expect(easingValue('curve', undefined, 'abc')).toBe('curve:abc');
+    expect(easingOf('curve:abc')).toEqual({ shape: 'curve', curve: 'abc' });
+    expect(isKeyInterpolation('curve:abc')).toBe(true);
+    expect(isKeyInterpolation('curve:')).toBe(true);
+    expect(easingOf('curve:')).toEqual({ shape: 'curve', curve: '' });
+  });
+
+  it('blends a row along the curve, and linearly once it is gone', () => {
+    const { project, stack } = makeProject();
+    const create = new CreateAssetCommand('curve', 'Quad');
+    stack.execute(create);
+    stack.execute(new SetCurvePointsCommand(create.asset.id, QUAD_IN));
+    const row = [
+      { frame: 0, value: 0, interpolation: easingValue('curve', undefined, create.asset.id) },
+      { frame: 10, value: 100 },
+    ];
+    expect(trackValueAt(row, 'number', 5, false, curveLookup(project))).toBeCloseTo(25, 6);
+    expect(trackValueAt(row, 'number', 5)).toBeCloseTo(50, 9);
+    expect(easedShare('curve:gone', 0.3, curveLookup(project))).toBe(0.3);
+    expect(easedShare('curve:', 0.3, curveLookup(project))).toBe(0.3);
+  });
+
+  it('plays a key along the curve in the running game', () => {
+    const f = makeSpriteScene();
+    const box = place(f, f.spriteId, { x: 0, y: 0 });
+    const curve = new CreateAssetCommand('curve', 'Quad');
+    f.stack.execute(curve);
+    f.stack.execute(new SetCurvePointsCommand(curve.asset.id, QUAD_IN));
+    const create = new CreateAssetCommand('animation', 'Slide', { fps: 10, playback: 'once' });
+    f.stack.execute(create);
+    f.stack.execute(new SetAnimationRootCommand(create.asset.id, f.spriteId));
+    const row = new AddAnimationTrackCommand(create.asset.id, '', 'x');
+    f.stack.execute(row);
+    f.stack.execute(new SetAnimationKeyCommand(create.asset.id, row.trackId, 0, 0));
+    f.stack.execute(new SetAnimationKeyCommand(create.asset.id, row.trackId, 10, 100));
+    const at = [{ trackId: row.trackId, frame: 0 }];
+    f.stack.execute(new SetKeyInterpolationCommand(create.asset.id, at, `curve:${curve.asset.id}`));
+
+    const world = World.instantiate(f.project, f.sceneId);
+    world.addSystem(new AnimationSystem());
+    const sprite = world.findByObjectId(box)!;
+    playAnimation(sprite, create.asset.id);
+    // The first tick takes the starting values and shows frame 0; five more reach frame 5, t = 0.5.
+    world.tick(0.1);
+    for (let i = 0; i < 5; i++) world.tick(0.1);
+    expect(sprite.x).toBeCloseTo(25, 4);
+  });
+
+  it('counts the keys and Lerp nodes using a curve, for the warning before deleting it', () => {
+    const f = makeSpriteScene();
+    const curve = new CreateAssetCommand('curve', 'Pop');
+    f.stack.execute(curve);
+    const create = new CreateAssetCommand('animation', 'Slide', {});
+    f.stack.execute(create);
+    f.stack.execute(new SetAnimationRootCommand(create.asset.id, f.spriteId));
+    const row = new AddAnimationTrackCommand(create.asset.id, '', 'x');
+    f.stack.execute(row);
+    for (const frame of [0, 5, 10])
+      f.stack.execute(new SetAnimationKeyCommand(create.asset.id, row.trackId, frame, 0));
+    const at = [0, 5].map((frame) => ({ trackId: row.trackId, frame }));
+    f.stack.execute(new SetKeyInterpolationCommand(create.asset.id, at, `curve:${curve.asset.id}`));
+    const behavior = new CreateAssetCommand('behavior', 'Mover');
+    f.stack.execute(behavior);
+    findAssetOf(f.project, behavior.asset.id, 'behavior')!.graph.nodes.push(
+      { id: 'l1', type: 'Lerp', x: 0, y: 0, params: { ease: 'curve', curve: curve.asset.id } },
+      { id: 'l2', type: 'Lerp', x: 0, y: 0, params: { ease: 'linear' } },
+    );
+    expect(curveUsages(f.project, curve.asset.id)).toEqual({ keys: 2, nodes: 1 });
+  });
+});
+
+describe('storing and editing a curve', () => {
+  it('starts as a straight line and keeps its points through a round trip', () => {
+    const { project, stack } = makeProject();
+    const create = new CreateAssetCommand('curve', 'Pop');
+    stack.execute(create);
+    expect(findAssetOf(project, create.asset.id, 'curve')!.points).toEqual(linearCurve());
+    stack.execute(new SetCurvePointsCommand(create.asset.id, easeCurve('elastic', 'out')));
+    const curve = findAssetOf(project, create.asset.id, 'curve')!;
+    expect(findAssetOf(roundTrip(project), create.asset.id, 'curve')).toEqual(curve);
+  });
+
+  it('holds a hand-written file to the rules on loading', () => {
+    const { project, stack } = makeProject();
+    const create = new CreateAssetCommand('curve', 'Pop');
+    stack.execute(create);
+    const raw = serializeProject(project) as { assets: { id: string; points?: unknown }[] };
+    raw.assets.find((a) => a.id === create.asset.id)!.points = [
+      { x: 1, y: 1 },
+      { x: 'far', y: 0 },
+      { x: 0.4, y: 0.8, out: { x: 3, y: 0 } },
+      { x: 0.2, y: 0 },
+    ];
+    const loaded = findAssetOf(deserializeProject(raw), create.asset.id, 'curve')!;
+    expect(loaded.points).toEqual([
+      { x: 0, y: 0 },
+      { x: 0.4, y: 0.8, out: { x: 0.6, y: 0 } },
+      { x: 1, y: 1 },
+    ]);
+  });
+
+  it('writes the curve in one undo step, held to the rules, and takes it back', () => {
+    const { project, stack } = makeProject();
+    const create = new CreateAssetCommand('curve', 'Pop');
+    stack.execute(create);
+    const curve = () => findAssetOf(project, create.asset.id, 'curve')!;
+    stack.execute(
+      new SetCurvePointsCommand(create.asset.id, [
+        { x: 0.3, y: 0 },
+        { x: 0.6, y: 1.2 },
+        { x: 0.8, y: 1 },
+      ]),
+    );
+    expect(curve().points.map((p) => p.x)).toEqual([0, 0.6, 1]);
+    expect(SetCurvePointsCommand.changes(curve(), curve().points)).toBe(false);
+    stack.undo();
+    expect(curve().points).toEqual(linearCurve());
+  });
+});
+
+describe('the built-in eases as presets', () => {
+  it('traces every ease to within half a percent, and each is a legal curve as it is', () => {
+    const presets = curvePresets();
+    expect(presets).toHaveLength(31);
+    expect(presets[0]!.build()).toEqual(linearCurve());
+    for (const preset of presets.slice(1)) {
+      const points = preset.build();
+      expect(sanitizedCurve(points), preset.label).toEqual(points);
+      const [shape, direction] = preset.label.toLowerCase().split(' ') as [string, string];
+      const interpolation = easingValue(
+        shape === 'quad' ? 'quad' : (shape as never),
+        direction as 'in' | 'out' | 'in-out',
+      );
+      for (const t of steps(97))
+        expect(
+          Math.abs(curveValue(points, t) - easedShare(interpolation, t)),
+          `${preset.label} at ${t}`,
+        ).toBeLessThan(0.005);
+    }
+  });
+
+  it('needs one segment for a quad, and more for what bounces', () => {
+    expect(easeCurve('quad', 'in')).toHaveLength(2);
+    expect(easeCurve('bounce', 'out').length).toBeGreaterThan(8);
+  });
+});

tests/core/easing-curves.test.ts

@@ -30,7 +30,10 @@ import { AnimationSystem } from '../../src/runtime/systems/AnimationSystem';
 import { World } from '../../src/runtime/World';
 import { makeSpriteScene, place, roundTrip } from '../helpers';
 
-const CURVES = EASING_SHAPES.filter((s) => s.value !== 'linear' && s.value !== 'step').map((s) => s.value);
+// A Curve asset (#247) is the last entry: drawn by hand, not one of the ten, and without directions.
+const CURVES = EASING_SHAPES.filter((s) => !['linear', 'step', 'curve'].includes(s.value)).map(
+  (s) => s.value,
+);
 const ALL = CURVES.flatMap((c) => EASING_DIRECTIONS.map((d) => easingValue(c, d.value)));
 
 describe('easing curves', () => {

tests/core/node-catalog.test.ts

@@ -52,6 +52,19 @@ const machineWithStates = (states: { id: string; name: string }[]): GraphLookup
   machine: (id) => (id === 'm' ? { name: 'M', states, start: '', transitions: [] } : null),
 });
 
+/** A lookup holding one curve "c" (#247): straight up to 1.5 at the middle, back down to 1 at the end. */
+const overshootingCurve: GraphLookup = {
+  ...NO_LOOKUP,
+  curve: (id) =>
+    id === 'c'
+      ? [
+          { x: 0, y: 0 },
+          { x: 0.5, y: 1.5 },
+          { x: 1, y: 1 },
+        ]
+      : null,
+};
+
 /** A lookup holding one machine "m" with the given transitions – what `State transition` reads. */
 const machineLookup = (transitions: { from: string; to: string; name?: string }[]): GraphLookup => ({
   ...NO_LOOKUP,
@@ -579,6 +592,20 @@ const CASES: Record<string, Case[]> = {
       params: { ease: 'out' },
       outputs: { result: 3 },
     },
+    {
+      name: 'along a Curve asset, overshooting b',
+      inputs: { a: 0, b: 8, t: 0.5 },
+      params: { ease: 'curve', curve: 'c' },
+      lookup: overshootingCurve,
+      outputs: { result: 12 },
+    },
+    {
+      name: 'along a Curve asset that is gone: linear',
+      inputs: { a: 0, b: 8, t: 0.25 },
+      params: { ease: 'curve', curve: 'gone' },
+      lookup: overshootingCurve,
+      outputs: { result: 2 },
+    },
   ],
   Floor: [
     { name: 'rounds down', inputs: { value: 2.9 }, outputs: { result: 2 } },

tests/editor/curve-view.test.ts

@@ -0,0 +1,89 @@
+/**
+ * The Curve tab's rules (#247): the curve is laid onto a picture for the vector art gestures and read
+ * back, a moved point stays between its neighbours, the ends move only up and down, and a press on
+ * free space puts a point where it falls in `t`.
+ */
+import { describe, expect, it } from 'vitest';
+import type { VectorPoint } from '../../src/core/model/Asset';
+import {
+  CURVE_SCALE,
+  curveFrame,
+  curveToImage,
+  imageToCurve,
+  isCurveEnd,
+  previewShare,
+  withCurvePointAt,
+  withCurvePointMoved,
+} from '../../src/editor/curve/curveView';
+
+const CURVE: VectorPoint[] = [
+  { x: 0, y: 0, out: { x: 0.1, y: 0.2 } },
+  { x: 0.5, y: 1.25, in: { x: -0.2, y: 0 }, out: { x: 0.2, y: 0 }, mode: 'smooth' },
+  { x: 1, y: 1 },
+];
+
+describe('the curve on the picture', () => {
+  it('lays t to the right and v upwards, and reads it back unchanged', () => {
+    const ring = curveToImage(CURVE);
+    expect(ring.closed).toBe(false);
+    expect(ring.points[0]).toMatchObject({
+      x: 0,
+      y: CURVE_SCALE,
+      out: { x: 0.1 * CURVE_SCALE, y: -0.2 * CURVE_SCALE },
+    });
+    expect(ring.points[1]).toMatchObject({ x: CURVE_SCALE / 2, y: -0.25 * CURVE_SCALE, mode: 'smooth' });
+    expect(imageToCurve(ring)).toEqual(CURVE);
+  });
+
+  it('frames 0…1 in t and everything the curve reaches in v', () => {
+    const frame = curveFrame(CURVE);
+    expect(frame.x).toBeLessThan(0);
+    expect(frame.x + frame.w).toBeGreaterThan(CURVE_SCALE);
+    // The top of the frame lies above v = 1.25, the bottom below v = 0.
+    expect(frame.y).toBeLessThan(-0.25 * CURVE_SCALE);
+    expect(frame.y + frame.h).toBeGreaterThan(CURVE_SCALE);
+  });
+});
+
+describe('moving and putting down points', () => {
+  const ring = curveToImage(CURVE);
+
+  it('keeps a moved point between its neighbours in t', () => {
+    const right = withCurvePointMoved(ring, 1, { x: 900, y: 10 });
+    expect(right.points[1]).toMatchObject({ x: CURVE_SCALE, y: 10 });
+    const left = withCurvePointMoved(ring, 1, { x: -50, y: 10 });
+    expect(left.points[1]!.x).toBe(0);
+    expect(withCurvePointMoved(ring, 1, { x: 64, y: 20 }).points[1]).toMatchObject({ x: 64, y: 20 });
+    // Handles ride along: they are offsets.
+    expect(right.points[1]!.out).toEqual(ring.points[1]!.out);
+  });
+
+  it('moves the two ends only up and down', () => {
+    expect(withCurvePointMoved(ring, 0, { x: 40, y: 30 }).points[0]).toMatchObject({ x: 0, y: 30 });
+    expect(withCurvePointMoved(ring, 2, { x: 10, y: 30 }).points[2]).toMatchObject({ x: CURVE_SCALE, y: 30 });
+  });
+
+  it('puts a point on free space where it falls in t, and none outside the curve', () => {
+    const put = withCurvePointAt(ring, { x: 200, y: 40 })!;
+    expect(put.index).toBe(2);
+    expect(put.ring.points.map((p) => p.x)).toEqual([0, CURVE_SCALE / 2, 200, CURVE_SCALE]);
+    expect(put.ring.points[2]).toEqual({ x: 200, y: 40 });
+    expect(withCurvePointAt(ring, { x: 20, y: 0 })!.index).toBe(1);
+    expect(withCurvePointAt(ring, { x: -1, y: 0 })).toBeNull();
+    expect(withCurvePointAt(ring, { x: CURVE_SCALE + 1, y: 0 })).toBeNull();
+    expect(withCurvePointAt(ring, { x: 0, y: 0 })).toBeNull();
+  });
+
+  it('knows the ends', () => {
+    expect([0, 1, 2].map((i) => isCurveEnd(ring, i))).toEqual([true, false, true]);
+  });
+});
+
+describe('the preview', () => {
+  it('climbs through t for a second, rests at the end, then starts over', () => {
+    expect(previewShare(0)).toBe(0);
+    expect(previewShare(0.25)).toBeCloseTo(0.25, 12);
+    expect(previewShare(1.2)).toBe(1);
+    expect(previewShare(1.75)).toBeCloseTo(0.25, 12);
+  });
+});

tools/e2e/04-assets.mjs

@@ -81,7 +81,7 @@ export async function assets(t) {
 
   // 4c. Create a new asset through the + menu. Since #43 the menu is two alphabetical groups –
   //     what can be placed in a scene, a line, then what only lives in the library – and it is
-  //     tall enough to show all twenty-one types without scrolling.
+  //     tall enough to show all twenty-two types without scrolling.
   await clickText('+');
   const rows = await json('__gm.menuRows()');
   const cut = rows.indexOf(null);
@@ -94,7 +94,7 @@ export async function assets(t) {
   );
   check(
     'every asset type is offered once, each group sorted by label',
-    placeable.length + library.length === 21 &&
+    placeable.length + library.length === 22 &&
       String(placeable) === String([...placeable].sort()) &&
       String(library) === String([...library].sort()),
     JSON.stringify({ placeable, library }),
@@ -453,7 +453,7 @@ export async function assets(t) {
 async function addMenuOnRightClick(t) {
   const { check, json, shot, click, clickText, press, undo, showTab } = t;
   const addRows = (rows) =>
-    Array.isArray(rows) && rows.filter(Boolean).length === 21 && rows.includes('Sprite');
+    Array.isArray(rows) && rows.filter(Boolean).length === 22 && rows.includes('Sprite');
   const heading = await json("__gm.assetRowShown('group:scene')");
   const sceneFolded = async () =>
     !(await json('__gm.assetGroups()')).find((g) => g.type === 'scene').expanded;

tools/e2e/25-animation.mjs

@@ -159,6 +159,7 @@ export async function animation(t) {
         'Back',
         'Elastic',
         'Bounce',
+        'Curve',
       ]) &&
       (await easingOf()) === 'cubic-in-out' &&
       Boolean(cubicDirection),

tools/e2e/53-curves.mjs

@@ -0,0 +1,328 @@
+import { edge, node } from '../lib/builders.mjs';
+
+/**
+ * Curve assets (#247): made from the + menu and opened by its row, bent in the Curve tab with the
+ * real mouse – a point put down on free space, turned smooth through the header, a handle pulled –
+ * and then picked where a built-in ease is picked, on an animation key and on a `Lerp` node. The
+ * values those two produce are compared with the curve worked out here, by walking its Bezier
+ * segments, not with the editor's own solver.
+ *
+ * Everything it adds carries a `cv-` id or is the curve it made, and goes again at the end.
+ */
+
+/** The curve's value at `t`, from its segments walked finely and read off in between. */
+function expectedAt(points, t) {
+  for (let i = 1; i < points.length; i++) {
+    const from = points[i - 1];
+    const to = points[i];
+    if (t > to.x) continue;
+    const c1 = { x: from.x + (from.out?.x ?? 0), y: from.y + (from.out?.y ?? 0) };
+    const c2 = { x: to.x + (to.in?.x ?? 0), y: to.y + (to.in?.y ?? 0) };
+    const at = (s, a, b, c, d) =>
+      (1 - s) ** 3 * a + 3 * (1 - s) ** 2 * s * b + 3 * (1 - s) * s * s * c + s ** 3 * d;
+    let previous = { x: from.x, y: from.y };
+    for (let step = 1; step <= 20000; step++) {
+      const s = step / 20000;
+      const here = { x: at(s, from.x, c1.x, c2.x, to.x), y: at(s, from.y, c1.y, c2.y, to.y) };
+      if (here.x >= t) {
+        const share = here.x > previous.x ? (t - previous.x) / (here.x - previous.x) : 1;
+        return previous.y + (here.y - previous.y) * share;
+      }
+      previous = here;
+    }
+    return to.y;
+  }
+  return points.at(-1).y;
+}
+
+export async function curves(t) {
+  const { check, json, evaluate, mutate, click, doubleClick, drag, settle, sleep, shot, showTab, undo } = t;
+  const inOverlay = async (text) => {
+    const box = await json('__gm.overlayRect()');
+    const hits = (await json(`__gm.locateAll(${JSON.stringify(text)})`)) ?? [];
+    return (
+      hits.find((h) => h.x >= box.x && h.x <= box.x + box.w && h.y >= box.y && h.y <= box.y + box.h) ?? null
+    );
+  };
+  const menuRow = async (label) => {
+    const rows = (await json('__gm.menuRows()')) ?? [];
+    const row = rows.find((r) => typeof r === 'string' && (r === label || r.endsWith(`  ${label}`)));
+    return row ? inOverlay(row) : null;
+  };
+  const pointsOf = (id) => json(`__gm.curve.points(${JSON.stringify(id)})`);
+
+  // 53a. The + menu makes one; its row opens the Curve tab on it, a straight line of two points.
+  await showTab('scene');
+  await t.clickText('+');
+  const offered = (await json('__gm.menuRows()')) ?? [];
+  const entry = await inOverlay('Curve');
+  check('the + menu offers Curve', offered.includes('Curve') && Boolean(entry), JSON.stringify(offered));
+  if (!entry) return;
+  await click(entry.x, entry.y);
+  await settle();
+  const curveId = (
+    await json("__gm.state.project.assets.filter((a) => a.type === 'curve').map((a) => a.id)")
+  ).at(-1);
+  // "Curve" is the new asset's name, the Easing value and the row label at once – a name of its own
+  // keeps `inspectorField('Curve')` on the row.
+  await mutate(
+    `__gm.state.project.assets.find((a) => a.id === ${JSON.stringify(curveId)}).name = 'Swoop 53'`,
+  );
+  const row = await json(`__gm.assetRow(${JSON.stringify(curveId)})`);
+  await doubleClick(row.x, row.y);
+  await settle();
+  const fresh = await pointsOf(curveId);
+  check(
+    'a double-click on the new curve opens the Curve tab on a straight line from (0, 0) to (1, 1)',
+    (await json('__gm.curve.current()')) === curveId &&
+      JSON.stringify(fresh) ===
+        JSON.stringify([
+          { x: 0, y: 0 },
+          { x: 1, y: 1 },
+        ]) &&
+      (await json('__gm.curve.info()')) === '2 points',
+    JSON.stringify({ current: await json('__gm.curve.current()'), fresh }),
+  );
+
+  // 53b. A click on free space puts a point there, and it is the picked one.
+  const spot = await json('__gm.curve.at(0.5, 0.9)');
+  await click(spot.x, spot.y);
+  await settle();
+  const put = await pointsOf(curveId);
+  const middle = put?.[1];
+  check(
+    'a click on free space puts a point where it was clicked, between the ends, and picks it',
+    put?.length === 3 &&
+      Math.abs(middle.x - 0.5) < 0.01 &&
+      Math.abs(middle.y - 0.9) < 0.01 &&
+      !middle.in &&
+      !middle.out &&
+      (await json('__gm.curve.picked()')) === 1,
+    JSON.stringify({ put, picked: await json('__gm.curve.picked()') }),
+  );
+
+  // 53c. Point: Smooth grows its handles, and pulling the right one up bends the curve – the left
+  //      handle turns with it, the other way round.
+  const pointButton = await json('__gm.curve.pointButton()');
+  await click(pointButton.x, pointButton.y);
+  await sleep(100);
+  const smooth = await menuRow('Smooth');
+  if (smooth) await click(smooth.x, smooth.y);
+  await settle();
+  const rounded = await pointsOf(curveId);
+  const grown = rounded?.[1];
+  check(
+    'Point: Smooth grows both handles of the picked point, in line',
+    grown?.mode === 'smooth' &&
+      Boolean(grown.in && grown.out) &&
+      Math.abs(grown.in.x * grown.out.y - grown.in.y * grown.out.x) < 1e-9,
+    JSON.stringify({ grown, button: pointButton }),
+  );
+  if (!grown?.out) return;
+  // The handle reaches above what the straight line was fitted to; Fit frames it again.
+  const fit = await json('__gm.curve.fitAt()');
+  await click(fit.x, fit.y);
+  await settle();
+  const tip = await json(`__gm.curve.at(${grown.x + grown.out.x}, ${grown.y + grown.out.y})`);
+  await drag(tip.x, tip.y, tip.x, tip.y - 60, { steps: 8 });
+  await settle();
+  const bent = await pointsOf(curveId);
+  const pulled = bent?.[1];
+  const across = pulled && pulled.in.x * pulled.out.y - pulled.in.y * pulled.out.x;
+  check(
+    'dragging the right handle up raises it, and the smooth point turns its left handle to match',
+    pulled?.out.y > grown.out.y + 0.1 && Math.abs(across) < 1e-6 && pulled.in.x < 0 && pulled.in.y < 0,
+    JSON.stringify({ before: grown, after: pulled }),
+  );
+  await shot('53-curve-tab');
+
+  // The preview runs by itself until its button holds it; held, it stands still.
+  // Three samples over 0.6 s: longer than the half second the dot rests at the end of each pass.
+  const running = [];
+  for (let i = 0; i < 3; i++) {
+    if (i > 0) await sleep(300);
+    running.push((await json('__gm.curve.preview()'))?.t);
+  }
+  const previewButton = await json('__gm.curve.previewButton()');
+  await click(previewButton.x, previewButton.y);
+  await settle();
+  const held = [(await json('__gm.curve.preview()'))?.t];
+  await sleep(250);
+  held.push((await json('__gm.curve.preview()'))?.t);
+  check(
+    'the preview runs by itself, and the Preview button holds it',
+    previewButton.toggled &&
+      new Set(running).size > 1 &&
+      !(await json('__gm.curve.previewButton()')).toggled &&
+      held[0] === held[1],
+    JSON.stringify({ previewButton, running, held }),
+  );
+
+  // The preview's dot sits on the line at its t, and its twin beside the graph at the same height.
+  await evaluate('__gm.curve.setPreviewTime(0.35)');
+  const preview = await json('__gm.curve.preview()');
+  const onLine = await json(`__gm.curve.at(${preview?.t}, ${expectedAt(bent, preview?.t ?? 0)})`);
+  check(
+    'the preview dot runs along the drawn curve, and its twin beside the graph at the same height',
+    Math.abs(preview?.t - 0.35) < 1e-9 &&
+      Math.abs(preview.v - expectedAt(bent, 0.35)) < 0.002 &&
+      Math.abs(preview.dot.x - onLine.x) < 1 &&
+      Math.abs(preview.dot.y - onLine.y) < 1 &&
+      Math.abs(preview.bar.y - preview.dot.y) < 1e-6 &&
+      preview.bar.x > preview.dot.x,
+    JSON.stringify({ preview, onLine }),
+  );
+
+  // 53d. An animation key picks the curve in the inspector, and the preview draws the value it gives.
+  await mutate(`
+    const p = __gm.state.project;
+    const sprite = p.assets.find((a) => a.type === 'sprite');
+    p.assets.push({ id: 'cv-anim', type: 'animation', name: 'Curve slide', props: { fps: 10, playback: 'once' },
+      root: sprite.id,
+      tracks: [{ id: 'cv-row', target: '', property: 'x', keys: [{ frame: 0, value: 0 }, { frame: 10, value: 100 }] }] });`);
+  await evaluate("__gm.openDocument('asset:cv-anim')");
+  await settle();
+  const cell = await json("__gm.animation.cellAt('cv-row', 0)");
+  await click(cell.x, cell.y);
+  await settle();
+  const easing = await json("__gm.inspectorField('Easing')");
+  if (easing) {
+    await click(easing.x, easing.y);
+    await sleep(100);
+    const curveEntry = await menuRow('Curve');
+    if (curveEntry) await click(curveEntry.x, curveEntry.y);
+    await settle();
+  }
+  const key = async () =>
+    (await json("__gm.state.project.assets.find((a) => a.id === 'cv-anim').tracks[0].keys[0]"))
+      ?.interpolation;
+  const curveRow = await json("__gm.inspectorField('Curve', true)");
+  check(
+    'Easing: Curve on the key takes the one curve there is and shows it in a Curve row',
+    (await key()) === `curve:${curveId}` && Boolean(curveRow),
+    JSON.stringify({ interpolation: await key(), curveRow, easing }),
+  );
+  const rootId = await json("__gm.animation.preview.objectId('')");
+  const drawnAt = async (frame) => {
+    await evaluate(`__gm.animation.scrub(${frame})`);
+    await sleep(100);
+    return (await json(`__gm.animation.preview.item(${JSON.stringify(rootId)})`))?.x;
+  };
+  const drawn = [await drawnAt(3), await drawnAt(5), await drawnAt(8)];
+  const wanted = [0.3, 0.5, 0.8].map((share) => 100 * expectedAt(bent, share));
+  check(
+    'the preview puts the sprite where the curve says, not where a straight line would',
+    drawn.every((x, i) => Math.abs(x - wanted[i]) < 0.05) && Math.abs(drawn[1] - 50) > 5,
+    JSON.stringify({ drawn, wanted }),
+  );
+  await shot('53-curve-key');
+
+  // 53e. A Lerp picks it too – Ease: Curve, then the curve in its row – and the game logs its value.
+  await mutate(`
+    const p = __gm.state.project;
+    p.assets.push({ id: 'cv-lerpy', type: 'behavior', name: 'Curve lerp', props: { enabled: true, runInEditor: false },
+      variables: [], graph: ${JSON.stringify({
+        nodes: [
+          node('cv-start', 'OnStart', 0, 0),
+          node('cv-lerp', 'Lerp', 0, 160, { a: 0, b: 100, t: 0.3 }),
+          node('cv-log', 'Log', 300, 0),
+        ],
+        edges: [
+          edge('cv-e1', 'cv-start', 'exec', 'cv-log', 'exec'),
+          edge('cv-e2', 'cv-lerp', 'result', 'cv-log', 'message'),
+        ],
+      })} });
+    const scene = __gm.state.activeScene;
+    const holder = structuredClone(scene.objects[0]);
+    Object.assign(holder, { id: 'cv-holder', assetId: 'cv-lerpy', parentId: '', name: 'Curve holder',
+      position: { x: 0, y: 0, z: 0 }, overrides: {}, instanceEdits: {} });
+    delete holder.groupId;
+    scene.objects.push(holder);
+    __gm.state.select({ kind: 'node', assetId: 'cv-lerpy', nodeId: 'cv-lerp', nodeIds: ['cv-lerp'], annotationIds: [] });`);
+  await showTab('graph');
+  await settle();
+  const pick = async (field, label) => {
+    const at = await json(`__gm.inspectorField(${JSON.stringify(field)}, true)`);
+    if (!at) return null;
+    await click(at.x, at.y);
+    await sleep(100);
+    const option = await menuRow(label);
+    if (option) await click(option.x, option.y);
+    else await t.press('Escape');
+    await settle();
+    return option;
+  };
+  await pick('Ease', 'Curve');
+  const unpicked = await json("__gm.graph.nodeSettings('cv-lerp')");
+  const name = await json(`__gm.state.project.assets.find((a) => a.id === ${JSON.stringify(curveId)}).name`);
+  const picked = await pick('Curve', `${name} (curve)`);
+  const params = await json(
+    "__gm.state.project.assets.find((a) => a.id === 'cv-lerpy').graph.nodes.find((n) => n.id === 'cv-lerp').params",
+  );
+  const settings = await json("__gm.graph.nodeSettings('cv-lerp')");
+  check(
+    'Ease: Curve brings the Curve row onto the node, and picking the curve there sets it',
+    params?.ease === 'curve' &&
+      params.curve === curveId &&
+      Boolean(picked) &&
+      unpicked?.length === 2 &&
+      settings?.some((s) => s.includes(name)),
+    JSON.stringify({ params, unpicked, settings, picked }),
+  );
+  await shot('53-curve-lerp');
+  const logFrom = t.consoleLog.length;
+  await t.play();
+  await sleep(600);
+  await t.stop();
+  const logged = t.consoleLog
+    .slice(logFrom)
+    .filter((line) => line.startsWith('[behavior Curve holder]'))
+    .map((line) => Number(line.split(']').pop()));
+  const lerpWanted = 100 * expectedAt(bent, 0.3);
+  check(
+    'the running Lerp gives what the curve says at t 0.3',
+    logged.length === 1 && Math.abs(logged[0] - lerpWanted) < 0.05 && Math.abs(logged[0] - 30) > 1,
+    JSON.stringify({ logged, lerpWanted }),
+  );
+
+  // 53f. Undo takes the pick back to the plain Lerp; then everything made here goes.
+  await showTab('graph');
+  await undo();
+  await settle();
+  const undone = await json(
+    "__gm.state.project.assets.find((a) => a.id === 'cv-lerpy').graph.nodes.find((n) => n.id === 'cv-lerp').params",
+  );
+  check('undo takes the picked curve back off the Lerp', !undone?.curve, JSON.stringify(undone));
+
+  // 53g. A preset starts the curve over from a built-in ease, and the key follows it at once.
+  await evaluate(`__gm.openDocument('asset:${curveId}')`);
+  await settle();
+  const presetButton = await json('__gm.curve.presetButton()');
+  await click(presetButton.x, presetButton.y);
+  await sleep(100);
+  const presets = (await json('__gm.menuRows()')) ?? [];
+  // Thirty-one entries run past the bottom of the popup; its search box is the way to the last ones.
+  await t.typeText('bounce out');
+  await t.press('Enter');
+  await settle();
+  const bounced = await pointsOf(curveId);
+  await evaluate("__gm.openDocument('asset:cv-anim')");
+  await settle();
+  const bouncedAt = await drawnAt(5);
+  check(
+    'Preset → Bounce out replaces the curve with the traced ease, and the key follows it (76.6 at the middle)',
+    presets.filter((r) => typeof r === 'string').length === 31 &&
+      bounced?.length > 8 &&
+      Math.abs(bouncedAt - 76.5625) < 0.4,
+    JSON.stringify({ presets: presets.length, points: bounced?.length, bouncedAt }),
+  );
+  await shot('53-curve-preset');
+
+  await mutate(`
+    const p = __gm.state.project;
+    const scene = __gm.state.activeScene;
+    scene.objects = scene.objects.filter((o) => !o.id.startsWith('cv-'));
+    p.assets = p.assets.filter((a) => !a.id.startsWith('cv-') && a.id !== ${JSON.stringify(curveId)});
+    __gm.state.select(null)`);
+  await showTab('scene');
+}

tools/e2e/index.mjs

@@ -55,6 +55,7 @@ import { users } from './49-users.mjs';
 import { snapshots } from './50-snapshots.mjs';
 import { clipboard } from './51-clipboard.mjs';
 import { hierarchyGroups } from './52-hierarchy-groups.mjs';
+import { curves } from './53-curves.mjs';
 
 export const STEPS = [
   hierarchy,
@@ -109,4 +110,5 @@ export const STEPS = [
   snapshots,
   clipboard,
   hierarchyGroups,
+  curves,
 ];

tools/e2e/lib/scaffold.mjs

@@ -118,6 +118,7 @@ export const TAB_LABELS = {
   vectorart: 'Vector art',
   pixelart: 'Pixel art',
   animation: 'Animation',
+  curve: 'Curve',
   tile: 'Tile',
   container: 'Container',
   list: 'List',
@@ -166,6 +167,7 @@ const DOCUMENT_KINDS = [
   'vectorart',
   'pixelart',
   'animation',
+  'curve',
   'tile',
   'container',
   'list',