Let a joint glide on a rail and drive it with a motor (#154)

Step 2 of the joints: a door that opens by itself, a lift and a
piston need a joint that slides along one line and a motor that turns
or pushes. A graph also needs to read how far such a joint stands.

- Slider: a fifth joint type on Rapier's prismatic joint. Its rail is
  the joint's own x axis, so turning the joint turns the rail. Joints
  now carry Scale, Rotation and Mirror like a sprite.
- Limit distance with Min and Max, in world units from where the
  object was placed.
- Motor on hinge and slider: Off, Speed or Target, with Motor speed,
  Motor target and Max force (0 = no limit). Target goes there at no
  more than the speed and slows down for the last stretch.
- Changing speed, target or force keeps the engine joint. Switching
  the motor on or off builds it again.
- New node Joint position: value and speed of a hinge (degrees,
  counting past a full round) or a slider (world units).
- Scene view draws a slider's rail dashed, with a tick at each limit.
- shownFor in the schema takes a list of choices that must all hold.

Findings, measured with a probe against Rapier 0.20:
- A prismatic joint holds both bodies at one angle. Held to the scene
  or to an object without a rigidbody, the joint's own anchor body is
  turned by the placed difference, so nothing jumps. Between two
  rigidbodies the held one is turned to match, and the console says
  so once.
- Rapier reads no joint angle back. The position is worked out from
  the two bodies.
- A hinge motor is weak on a small body at the end of a long arm
  (box 20 on an arm of 100 does not lift itself). More solver
  iterations would help but cost every scene. A door of 100 x 20
  reaches -90 and holds it. This is written in the wiki.

Tests:
- Unit: 16 new in joints.test.ts, 1 in joint-links, 3 catalog cases.
- e2e 41: 27 checks (25 + 2), block 41f with a real mouse in the
  inspector and the motor in play (59.1 of 60 units in 1 s).
- 9 of 9 unit counter-probes fail as they should.
- Gate: 220 files, 3436 tests (3416 + 20), CHECK EXIT 0.
- e2e total 1701 is counted (1699 + 2), the full suite did not run.

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

README.md

@@ -45,7 +45,7 @@ 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, 1699 checks (GM_STEPS=20 for one step)
+node tools/seed-e2e.mjs && node tools/e2e.mjs      # the editor, 1701 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

src/core/graph/NodeContext.ts

@@ -97,6 +97,11 @@ export interface PhysicsControl {
   applyImpulse(target: EntityHandle, x: number, y: number): boolean;
   /** World units per second squared, for the rest of the run. */
   setGravity(x: number, y: number): void;
+  /**
+   * How far a hinge has turned (degrees) or a slider has glided (world units) from how it was placed,
+   * and how fast; null for any other joint, for one that holds nothing, and for anything else (#154).
+   */
+  jointStateOf(target: EntityHandle): { value: number; speed: number } | null;
 }
 
 /**

src/core/graph/nodes/action/physicsNodes.ts

@@ -95,6 +95,24 @@ export const GetVelocity: NodeDef = {
   },
 };
 
+export const JointPosition: NodeDef = {
+  type: 'JointPosition',
+  label: 'Joint position',
+  category: 'data',
+  description:
+    'Where a hinge or a slider stands while the game is played: how far it has turned (degrees, ' +
+    'a wheel counts on past a full round) or glided (world units) from how it was placed, and how fast ' +
+    'that changes. 0 for a spring, a rope, a fixed joint, a joint that holds nothing, and in the editor run.',
+  inputs: [obj('joint')],
+  outputs: [num('value'), num('speed')],
+  params: [],
+  run: (ctx, inputs) => {
+    const joint = asEntity(inputs.joint);
+    const state = (joint && ctx.physics?.jointStateOf(joint)) || { value: 0, speed: 0 };
+    return { outputs: { value: state.value, speed: state.speed } };
+  },
+};
+
 export const SetGravity: NodeDef = {
   type: 'SetGravity',
   label: 'Set gravity',

src/core/graph/nodes/index.ts

@@ -12,6 +12,7 @@ import {
   ApplyForce,
   ApplyImpulse,
   GetVelocity,
+  JointPosition,
   SetAngularVelocity,
   SetGravity,
   SetVelocity,
@@ -277,6 +278,7 @@ export const BUILT_IN_NODES: readonly NodeDef[] = [
   Spawn,
   Destroy,
   AddJoint,
+  JointPosition,
   Emit,
   PlayAnimation,
   PauseAnimation,

src/core/model/joint.ts

@@ -1,10 +1,10 @@
 /**
  * A joint ties the object it is placed below to another one (#154): a hinge turns round one point, a
  * spring pulls towards a length, a rope allows no more than one, and a fixed joint keeps the two as
- * they were placed. These are the keys of its rows; what the engine reads off them is in
- * `properties/joint.ts`.
+ * they were placed, and a slider lets it glide along one axis only. These are the keys of its rows;
+ * what the engine reads off them is in `properties/joint.ts`.
  */
-export const JOINT_TYPES = ['hinge', 'spring', 'rope', 'fixed'] as const;
+export const JOINT_TYPES = ['hinge', 'spring', 'rope', 'fixed', 'slider'] as const;
 export type JointType = (typeof JOINT_TYPES)[number];
 
 export const JOINT_TYPE_LABELS: Record<JointType, string> = {
@@ -12,6 +12,7 @@ export const JOINT_TYPE_LABELS: Record<JointType, string> = {
   spring: 'Spring',
   rope: 'Rope',
   fixed: 'Fixed',
+  slider: 'Slider',
 };
 
 export const JOINT_TYPE_KEY = 'jointType';
@@ -24,8 +25,28 @@ export const JOINT_DAMPING_KEY = 'damping';
 export const JOINT_LIMIT_KEY = 'limitAngle';
 export const JOINT_MIN_ANGLE_KEY = 'minAngle';
 export const JOINT_MAX_ANGLE_KEY = 'maxAngle';
+export const JOINT_LIMIT_DISTANCE_KEY = 'limitDistance';
+export const JOINT_MIN_DISTANCE_KEY = 'minDistance';
+export const JOINT_MAX_DISTANCE_KEY = 'maxDistance';
+export const JOINT_MOTOR_KEY = 'motor';
+export const JOINT_MOTOR_SPEED_KEY = 'motorSpeed';
+export const JOINT_MOTOR_TARGET_KEY = 'motorTarget';
+export const JOINT_MAX_FORCE_KEY = 'maxForce';
 export const JOINT_COLLIDE_KEY = 'collideConnected';
 
+/** What a motor on a hinge or a slider does: nothing, turn or glide on, or go to a place and stay. */
+export const JOINT_MOTORS = ['off', 'speed', 'target'] as const;
+export type JointMotor = (typeof JOINT_MOTORS)[number];
+
+export const JOINT_MOTOR_LABELS: Record<JointMotor, string> = {
+  off: 'Off',
+  speed: 'Speed',
+  target: 'Target',
+};
+
+/** The types that move along one axis, which a motor can drive and a position can be read of. */
+export const AXIS_TYPES: readonly JointType[] = ['hinge', 'slider'];
+
 /** The types with a point of their own on the other end; a hinge and a fixed joint have the one they sit on. */
 export const TWO_ANCHOR_TYPES: readonly JointType[] = ['spring', 'rope'];
 

src/core/properties/PropertySchema.ts

@@ -41,15 +41,26 @@ import {
 } from '../model/tile';
 import { TILEMAP_COLUMNS_KEY, TILEMAP_MAX_CELLS, TILEMAP_ROWS_KEY, TILEMAP_TILE_KEY } from '../model/tilemap';
 import {
+  AXIS_TYPES,
   JOINT_ANCHOR_X_KEY,
   JOINT_ANCHOR_Y_KEY,
   JOINT_COLLIDE_KEY,
   JOINT_CONNECTED_KEY,
   JOINT_DAMPING_KEY,
   JOINT_LENGTH_KEY,
+  JOINT_LIMIT_DISTANCE_KEY,
   JOINT_LIMIT_KEY,
   JOINT_MAX_ANGLE_KEY,
+  JOINT_MAX_DISTANCE_KEY,
+  JOINT_MAX_FORCE_KEY,
   JOINT_MIN_ANGLE_KEY,
+  JOINT_MIN_DISTANCE_KEY,
+  JOINT_MOTOR_KEY,
+  JOINT_MOTOR_LABELS,
+  JOINT_MOTOR_SPEED_KEY,
+  JOINT_MOTOR_TARGET_KEY,
+  JOINT_MOTORS,
+  type JointMotor,
   JOINT_STIFFNESS_KEY,
   JOINT_TYPE_KEY,
   JOINT_TYPE_LABELS,
@@ -110,7 +121,8 @@ type Extras<K extends FlatKind> = K extends 'number'
  * object's: that default is no value of the kind but its tagged place (`ObjectDef`).
  * `shownWith` names a switch on the same bag; the inspector shows the row only while it is on
  * (see `isRowShown`), everything else – graph, defaults, files – always has it. `shownFor` does the
- * same by a choice: the row is shown while the enum under `key` holds one of `values` (#154).
+ * same by a choice: the row is shown while the enum under `key` holds one of `values` (#154); a
+ * list of such choices must all hold.
  */
 export type FlatDef<K extends FlatKind = FlatKind> = {
   [P in Exclude<K, 'object'>]: {
@@ -121,7 +133,7 @@ export type FlatDef<K extends FlatKind = FlatKind> = {
     /** What a new asset starts with when it differs from `default`, the value a missing key reads as. */
     initial?: ValueOf<P>;
     shownWith?: string;
-    shownFor?: { key: string; values: readonly string[] };
+    shownFor?: ShownFor | readonly ShownFor[];
   } & Extras<P>;
 }[Exclude<K, 'object'>];
 
@@ -130,15 +142,17 @@ export function initialOf(def: PropertyDef): PropertyValue {
   return 'initial' in def && def.initial !== undefined ? def.initial : def.default;
 }
 
+interface ShownFor {
+  key: string;
+  values: readonly string[];
+}
+
 /** Whether the inspector shows the row, given the values of the bag it is on. */
 export function isRowShown(def: PropertyDef, values: PropertyBag): boolean {
   if ('noRow' in def && def.noRow) return false;
-  if (
-    'shownFor' in def &&
-    def.shownFor &&
-    !def.shownFor.values.includes(textOf(values[def.shownFor.key] ?? ''))
-  )
-    return false;
+  const choices: readonly ShownFor[] =
+    'shownFor' in def && def.shownFor ? ('key' in def.shownFor ? [def.shownFor] : def.shownFor) : [];
+  if (choices.some(({ key, values: wanted }) => !wanted.includes(textOf(values[key] ?? '')))) return false;
   return !('shownWith' in def) || def.shownWith === undefined || values[def.shownWith] === true;
 }
 
@@ -190,6 +204,11 @@ const jointRows = (...values: JointType[]) => ({ shownFor: { key: JOINT_TYPE_KEY
 const JOINT_ENDS = jointRows(...TWO_ANCHOR_TYPES);
 const ONLY_SPRING = jointRows('spring');
 const ONLY_HINGE = jointRows('hinge');
+const ONLY_SLIDER = jointRows('slider');
+const ON_AXIS = jointRows(...AXIS_TYPES);
+const motorRows = (...values: JointMotor[]) => ({
+  shownFor: [ON_AXIS.shownFor, { key: JOINT_MOTOR_KEY, values }],
+});
 
 /** The inspector is generated from these entries, so a new property is one line in a schema below. */
 export type PropertyDef =
@@ -290,7 +309,10 @@ export const TRANSFORM_PROPS: PropertySchema = [
   { key: 'mirrorY', label: 'Mirror Y', kind: 'boolean', default: false },
 ];
 
-/** Cameras and behaviors are placed by the chain but have no look of their own to turn or size. */
+/**
+ * Cameras and behaviors are placed by the chain but have no look of their own to turn or size. A
+ * joint turns for a slider's sake, whose rail is its x axis (#154).
+ */
 const TRANSFORM_TYPES: ReadonlySet<AssetType> = new Set([
   'sprite',
   'text',
@@ -299,6 +321,7 @@ const TRANSFORM_TYPES: ReadonlySet<AssetType> = new Set([
   'clip',
   'particles',
   'tilemap',
+  'joint',
 ]);
 
 export function hasTransformProps(type: AssetType): boolean {
@@ -744,6 +767,68 @@ const ASSET_SCHEMAS: Record<AssetType, PropertySchema> = {
       shownWith: JOINT_LIMIT_KEY,
       ...ONLY_HINGE,
     },
+    // A slider glides along the joint's own x axis: turning the joint turns the rail.
+    {
+      key: JOINT_LIMIT_DISTANCE_KEY,
+      label: 'Limit distance',
+      kind: 'boolean',
+      default: false,
+      ...ONLY_SLIDER,
+    },
+    {
+      key: JOINT_MIN_DISTANCE_KEY,
+      label: 'Min distance',
+      kind: 'number',
+      default: -100,
+      max: 0,
+      step: 1,
+      shownWith: JOINT_LIMIT_DISTANCE_KEY,
+      ...ONLY_SLIDER,
+    },
+    {
+      key: JOINT_MAX_DISTANCE_KEY,
+      label: 'Max distance',
+      kind: 'number',
+      default: 100,
+      min: 0,
+      step: 1,
+      shownWith: JOINT_LIMIT_DISTANCE_KEY,
+      ...ONLY_SLIDER,
+    },
+    // Degrees for a hinge, world units for a slider, both counted from how it was placed.
+    {
+      key: JOINT_MOTOR_KEY,
+      label: 'Motor',
+      kind: 'enum',
+      default: 'off',
+      options: JOINT_MOTORS.map((value) => ({ value, label: JOINT_MOTOR_LABELS[value] })),
+      ...ON_AXIS,
+    },
+    {
+      key: JOINT_MOTOR_SPEED_KEY,
+      label: 'Motor speed',
+      kind: 'number',
+      default: 90,
+      step: 1,
+      ...motorRows('speed', 'target'),
+    },
+    {
+      key: JOINT_MOTOR_TARGET_KEY,
+      label: 'Motor target',
+      kind: 'number',
+      default: 0,
+      step: 1,
+      ...motorRows('target'),
+    },
+    {
+      key: JOINT_MAX_FORCE_KEY,
+      label: 'Max force (0 = no limit)',
+      kind: 'number',
+      default: 0,
+      min: 0,
+      step: 10,
+      ...motorRows('speed', 'target'),
+    },
     { key: JOINT_COLLIDE_KEY, label: 'Collide with connected', kind: 'boolean', default: false },
   ],
   // A container is pure structure: its content is the template, not a property.

src/core/properties/joint.ts

@@ -1,20 +1,29 @@
 /** What the physics engine and the scene view read off a joint (#154). */
 import {
+  AXIS_TYPES,
   hasConnectedAnchor,
   JOINT_ANCHOR_X_KEY,
   JOINT_ANCHOR_Y_KEY,
   JOINT_COLLIDE_KEY,
   JOINT_DAMPING_KEY,
   JOINT_LENGTH_KEY,
+  JOINT_LIMIT_DISTANCE_KEY,
   JOINT_LIMIT_KEY,
   JOINT_MAX_ANGLE_KEY,
+  JOINT_MAX_DISTANCE_KEY,
+  JOINT_MAX_FORCE_KEY,
   JOINT_MIN_ANGLE_KEY,
+  JOINT_MIN_DISTANCE_KEY,
+  JOINT_MOTOR_KEY,
+  JOINT_MOTOR_SPEED_KEY,
+  JOINT_MOTOR_TARGET_KEY,
+  type JointMotor,
   JOINT_STIFFNESS_KEY,
   JOINT_TYPE_KEY,
   JOINT_TYPES,
   type JointType,
 } from '../model/joint';
-import { apply, type Mat } from '../model/matrix';
+import { apply, applyVector, type Mat } from '../model/matrix';
 import type { PropertyBag, Vec2 } from '../model/Properties';
 import { defaultsFor } from './PropertySchema';
 
@@ -30,9 +39,22 @@ export interface JointSettings {
   damping: number;
   /** How far a hinge turns either way from how it was placed, in degrees; null for all the way round. */
   limits: { min: number; max: number } | null;
+  /** How far a slider glides either way from where it was placed, in world units; null for no end. */
+  distanceLimits: { min: number; max: number } | null;
+  /** What drives a hinge or a slider; null for every other type and with the motor off. */
+  motor: JointMotorSettings | null;
   collideConnected: boolean;
 }
 
+/** Degrees for a hinge, world units for a slider; positions count from how the joint was placed. */
+export interface JointMotorSettings {
+  mode: Exclude<JointMotor, 'off'>;
+  speed: number;
+  target: number;
+  /** World units × kg per second² – for a hinge, pushing 100 units from its pin; 0 for no limit. */
+  maxForce: number;
+}
+
 function num(value: unknown, fallback: unknown): number {
   const n = Number(value ?? fallback);
   return Number.isFinite(n) ? n : Number(fallback);
@@ -43,9 +65,21 @@ export function jointTypeOf(props: PropertyBag): JointType {
   return (JOINT_TYPES as readonly unknown[]).includes(type) ? (type as JointType) : 'hinge';
 }
 
+function motorOf(type: JointType, props: PropertyBag): JointMotorSettings | null {
+  const mode = props[JOINT_MOTOR_KEY];
+  if (!AXIS_TYPES.includes(type) || (mode !== 'speed' && mode !== 'target')) return null;
+  return {
+    mode,
+    speed: num(props[JOINT_MOTOR_SPEED_KEY], JOINT[JOINT_MOTOR_SPEED_KEY]),
+    target: num(props[JOINT_MOTOR_TARGET_KEY], JOINT[JOINT_MOTOR_TARGET_KEY]),
+    maxForce: Math.max(0, num(props[JOINT_MAX_FORCE_KEY], JOINT[JOINT_MAX_FORCE_KEY])),
+  };
+}
+
 export function jointSettings(props: PropertyBag): JointSettings {
   const type = jointTypeOf(props);
   const limited = type === 'hinge' && props[JOINT_LIMIT_KEY] === true;
+  const railed = type === 'slider' && props[JOINT_LIMIT_DISTANCE_KEY] === true;
   return {
     type,
     connectedAnchor: {
@@ -61,10 +95,47 @@ export function jointSettings(props: PropertyBag): JointSettings {
           max: Math.max(0, num(props[JOINT_MAX_ANGLE_KEY], JOINT[JOINT_MAX_ANGLE_KEY])),
         }
       : null,
+    distanceLimits: railed
+      ? {
+          min: Math.min(0, num(props[JOINT_MIN_DISTANCE_KEY], JOINT[JOINT_MIN_DISTANCE_KEY])),
+          max: Math.max(0, num(props[JOINT_MAX_DISTANCE_KEY], JOINT[JOINT_MAX_DISTANCE_KEY])),
+        }
+      : null,
+    motor: motorOf(type, props),
     collideConnected: props[JOINT_COLLIDE_KEY] === true,
   };
 }
 
+/** The direction a slider glides in: the x axis of the joint as it stands in the world. */
+export function sliderAxis(m: Mat): Vec2 {
+  const v = applyVector(m, { x: 1, y: 0 });
+  const length = Math.hypot(v.x, v.y) || 1;
+  return { x: v.x / length, y: v.y / length };
+}
+
+/** How far the scene view draws a slider's rail either way when it has no limits, in world units. */
+export const OPEN_RAIL = 60;
+
+/** The stretch of a slider's rail the scene view draws through `at`: its limits, or a piece of it. */
+export function sliderRail(settings: JointSettings, at: Vec2, axis: Vec2): { from: Vec2; to: Vec2 } {
+  const { min, max } = settings.distanceLimits ?? { min: -OPEN_RAIL, max: OPEN_RAIL };
+  const along = (d: number) => ({ x: at.x + axis.x * d, y: at.y + axis.y * d });
+  return { from: along(min), to: along(max) };
+}
+
+/** How quickly a motor going to its target slows down near it: the speed per unit still to go, per second. */
+export const MOTOR_GAIN = 10;
+
+/**
+ * The speed a motor asks for this frame: the one set, or towards its target at no more than that
+ * speed – slowing down for the last stretch, so it stops there rather than going past.
+ */
+export function motorSpeed(motor: JointMotorSettings, position: number): number {
+  if (motor.mode === 'speed') return motor.speed;
+  const most = Math.abs(motor.speed);
+  return Math.max(-most, Math.min(most, (motor.target - position) * MOTOR_GAIN));
+}
+
 /**
  * Where the joint's other end is in the world. A spring and a rope end at their connected anchor,
  * on the connected object or – without one – in the scene. A hinge and a fixed joint have no second

src/editor/viewport/SceneViewport.ts

@@ -997,8 +997,9 @@ export class SceneViewport extends FreeViewport {
       const link = jointLinkOf(item, byId);
       if (!link) continue;
       this.lastJointLinks.push(link);
-      const { from, to } = link;
+      const { from, to, rail } = link;
       this.links.circle(from.x, from.y, 4 / scale).stroke({ width: 1.5 / scale, color });
+      if (rail) this.drawRail(rail, scale, color);
       if (from.x === to.x && from.y === to.y) continue;
       this.links
         .moveTo(from.x, from.y)
@@ -1008,6 +1009,27 @@ export class SceneViewport extends FreeViewport {
     }
   }
 
+  /** A slider's rail, dashed so it reads apart from the line to what it holds on to; a tick at each limit. */
+  private drawRail(rail: NonNullable<JointLink['rail']>, scale: number, color: number): void {
+    const { from, to } = rail;
+    const length = Math.hypot(to.x - from.x, to.y - from.y);
+    if (length === 0) return;
+    const dir = { x: (to.x - from.x) / length, y: (to.y - from.y) / length };
+    const dash = 6 / scale;
+    for (let d = 0; d < length; d += 2 * dash) {
+      const end = Math.min(length, d + dash);
+      this.links
+        .moveTo(from.x + dir.x * d, from.y + dir.y * d)
+        .lineTo(from.x + dir.x * end, from.y + dir.y * end);
+    }
+    if (rail.limited) {
+      const tick = { x: (-dir.y * 6) / scale, y: (dir.x * 6) / scale };
+      for (const p of [from, to])
+        this.links.moveTo(p.x - tick.x, p.y - tick.y).lineTo(p.x + tick.x, p.y + tick.y);
+    }
+    this.links.stroke({ width: 1.5 / scale, color });
+  }
+
   /** The joints' lines as drawn, in world units, and the handle on the selected one's far end (test hook). */
   jointInfo(): { links: JointLink[]; handle: { objectId: string; x: number; y: number } | null } {
     return { links: this.lastJointLinks, handle: this.anchors.info() };

src/runtime/physics/PhysicsSystem.ts

@@ -63,7 +63,7 @@ import {
   samePose,
 } from './bodyGeometry';
 import { type Rapier, toMetres, toPixels } from './engine';
-import { type JointHost, JointSet, type RigidOwner } from './joints';
+import { type JointHost, JointSet, type JointState, type RigidOwner } from './joints';
 import { passesOneWay, reachOf } from './oneWay';
 
 /** The engine always steps this long, whatever the frame took. */
@@ -448,6 +448,11 @@ export class PhysicsSystem implements System, CollisionSource {
     return this.joints.holds(joint);
   }
 
+  /** Where a hinge or a slider stands (#154): degrees or world units from how it was placed. */
+  jointStateOf(joint: Entity): JointState | null {
+    return this.joints.stateOf(joint);
+  }
+
   /**
    * Every body the entities ask for, keyed by the entity that stands for it. A collider belongs to
    * the nearest object above it with a rigidbody switched on; without one it is a body of its own.

src/runtime/physics/joints.ts

@@ -1,20 +1,28 @@
 import type {
   ImpulseJoint,
   JointData,
-  RevoluteImpulseJoint,
   RigidBody,
+  UnitImpulseJoint,
   World as RapierWorld,
 } from '@dimforge/rapier2d-compat';
 import { isHandleEnabled, worldMatrixOf } from '../../core/graph';
 import { isEntity } from '../../core/graph/values';
-import { hasConnectedAnchor, JOINT_CONNECTED_KEY } from '../../core/model/joint';
+import { hasConnectedAnchor, JOINT_CONNECTED_KEY, type JointType } from '../../core/model/joint';
 import { referencedId } from '../../core/model/objectRefs';
 import type { PropertyValue, Vec2 } from '../../core/model/Properties';
-import { hingeLimits, jointFarEnd, jointLength, jointSettings } from '../../core/properties/joint';
+import {
+  hingeLimits,
+  jointFarEnd,
+  jointLength,
+  jointSettings,
+  type JointMotorSettings,
+  motorSpeed,
+  sliderAxis,
+} from '../../core/properties/joint';
 import type { Entity } from '../Entity';
 import type { World } from '../World';
 import { angleBetween, matrixPose, type Pose, round, samePose } from './bodyGeometry';
-import { type Rapier, toMetres } from './engine';
+import { type Rapier, toMetres, toPixels } from './engine';
 
 /** The body the engine moves for an object, and that object. */
 export interface RigidOwner {
@@ -39,12 +47,53 @@ interface Held {
   anchorPose: Pose | null;
   /** The length and the angle the two ends were placed at, kept while the same two bodies are held. */
   placed: { between: string; length: number; angle: number } | null;
+  /**
+   * How a slider's object was turned against its own anchor body when it was placed; that body
+   * is turned along by as much, since the engine holds a slider's two ends at one angle.
+   */
+  turn: number | null;
+  /** The held object's turn against the other end, counted on past a full round. */
+  wound: number;
+  /** What a slider's position is read off: the two points as placed and its axis, in the bodies' metres. */
+  rail: { onOther: Vec2; onOwn: Vec2; axis: Vec2 } | null;
+  type: JointType;
+  /** The speed and the force the motor was last asked for, so a sleeping body is woken on a change. */
+  motorCall: string;
   collide: boolean;
 }
 
+/** How a hinge or a slider stands: degrees or world units from how it was placed, and how fast that changes. */
+export interface JointState {
+  value: number;
+  speed: number;
+}
+
 const NO_RIGIDBODY = 'sits on an object without a rigidbody, so it holds nothing.';
 const GONE = 'lost its connected object, so it holds nothing.';
 const SAME_BODY = 'is connected to the object it sits on, so it holds nothing.';
+const TURNED_TO_MATCH =
+  'is a slider between two objects turned against each other; the engine keeps them at one angle, so it turns the object to match.';
+
+/** How hard a motor holds its speed; the engine's own unit, measured to reach it within a frame. */
+const MOTOR_FACTOR = 1000;
+/** What the engine takes for a motor without a limit. */
+const NO_FORCE_LIMIT = 1e30;
+const DEGREES = 180 / Math.PI;
+
+const rotate = (v: Vec2, angle: number): Vec2 => {
+  const cos = Math.cos(angle);
+  const sin = Math.sin(angle);
+  return { x: v.x * cos - v.y * sin, y: v.x * sin + v.y * cos };
+};
+
+/** Where a body's local point is in the world and how fast it moves there, in metres. */
+function pointOf(body: RigidBody, local: Vec2): { at: Vec2; velocity: Vec2 } {
+  const t = body.translation();
+  const r = rotate(local, body.rotation());
+  const v = body.linvel();
+  const w = body.angvel();
+  return { at: { x: t.x + r.x, y: t.y + r.y }, velocity: { x: v.x - w * r.y, y: v.y + w * r.x } };
+}
 
 /** The object a joint names: none (a point of the scene), one that is there, or one that is gone. */
 function connectedOf(world: World, joint: Entity): Entity | null | 'gone' {
@@ -71,6 +120,7 @@ const ORIGIN: Pose = { x: 0, y: 0, angle: 0 };
  * The joints of the played game (#154): one engine joint per joint entity whose object has a
  * rigidbody. The other end is the connected object's body, or – where that has none, or nothing is
  * connected – a body of the joint's own that goes wherever that end is and is pulled by nothing.
+ * The engine reads no angle or distance back, so a hinge's and a slider's are worked out here.
  */
 export class JointSet {
   private readonly held = new Map<Entity, Held>();
@@ -98,11 +148,62 @@ export class JointSet {
     return Boolean(this.held.get(entity)?.joint?.isValid());
   }
 
+  /** Where a hinge or a slider stands right now; null while it holds nothing or is of another type. */
+  stateOf(entity: Entity): JointState | null {
+    const held = this.held.get(entity);
+    return held?.joint?.isValid() ? this.measure(held) : null;
+  }
+
   /** The engine is freed as a whole; what was held in it is only forgotten. */
   clear(): void {
     this.held.clear();
   }
 
+  private measure(held: Held): JointState | null {
+    const joint = held.joint!;
+    const other = joint.body1();
+    const own = joint.body2();
+    if (held.type === 'hinge' && held.placed) {
+      held.wound += angleBetween(held.wound, angleBetween(other.rotation(), own.rotation()));
+      return {
+        value: (held.wound - held.placed.angle) * DEGREES,
+        speed: (own.angvel() - other.angvel()) * DEGREES,
+      };
+    }
+    if (held.type === 'slider' && held.rail) {
+      const a = pointOf(other, held.rail.onOther);
+      const b = pointOf(own, held.rail.onOwn);
+      const axis = rotate(held.rail.axis, other.rotation());
+      const along = (v: Vec2) => toPixels(v.x * axis.x + v.y * axis.y);
+      return {
+        value: along({ x: b.at.x - a.at.x, y: b.at.y - a.at.y }),
+        speed: along({ x: b.velocity.x - a.velocity.x, y: b.velocity.y - a.velocity.y }),
+      };
+    }
+    return null;
+  }
+
+  /**
+   * Asks the motor for this frame's speed – towards its target, that changes as it gets there – and
+   * wakes the bodies while it moves them or when it is asked for something new.
+   */
+  private drive(held: Held, motor: JointMotorSettings): void {
+    const state = this.measure(held);
+    if (!state) return;
+    const joint = held.joint as UnitImpulseJoint;
+    const speed = motorSpeed(motor, state.value);
+    const toEngine = held.type === 'hinge' ? 1 / DEGREES : toMetres(1);
+    // A hinge's force pushes 100 units – one of the engine's metres – from its pin.
+    const force = motor.maxForce > 0 ? toMetres(motor.maxForce) : NO_FORCE_LIMIT;
+    const call = `${round(speed)}|${force}`;
+    if (call === held.motorCall && Math.abs(speed) < 1e-6) return;
+    joint.configureMotorVelocity(speed * toEngine, MOTOR_FACTOR);
+    joint.setMotorMaxForce(force);
+    held.motorCall = call;
+    joint.body1().wakeUp();
+    joint.body2().wakeUp();
+  }
+
   private syncOne(world: World, engine: RapierWorld, host: JointHost, entity: Entity): void {
     let held = this.held.get(entity);
     if (!held) {
@@ -112,6 +213,11 @@ export class JointSet {
         anchor: null,
         anchorPose: null,
         placed: null,
+        turn: null,
+        wound: 0,
+        rail: null,
+        type: 'hinge',
+        motorCall: '',
         collide: false,
       };
       this.held.set(entity, held);
@@ -131,12 +237,16 @@ export class JointSet {
     if (!own.body.isEnabled() || (rigid && !rigid.body.isEnabled())) return idle();
 
     const settings = jointSettings(entity.props);
+    const slider = settings.type === 'slider';
     const ownPose = matrixPose(worldMatrixOf(own.entity));
-    const otherPose = rigid
+    const connectedPose = rigid
       ? matrixPose(worldMatrixOf(rigid.entity))
       : connected
         ? matrixPose(worldMatrixOf(connected))
         : ORIGIN;
+    if (!slider || rigid) held.turn = null;
+    else held.turn ??= angleBetween(connectedPose.angle, own.body.rotation());
+    const otherPose = { ...connectedPose, angle: connectedPose.angle + (held.turn ?? 0) };
     const other = rigid ? rigid.body : this.anchorAt(engine, held, otherPose);
     if (rigid) this.dropAnchor(engine, held);
 
@@ -145,44 +255,65 @@ export class JointSet {
     const far = jointFarEnd(settings, at, connected ? worldMatrixOf(connected) : null);
     const onOwn = inBody(ownPose, at);
     const twoEnds = hasConnectedAnchor(settings.type);
-    // A hinge's and a fixed joint's point on the other body is wherever the joint was when it was
-    // made, so it is no part of the key – the bodies move, and the point with them.
+    // Counted in the held object, which the joint sits on: the rail turns with it, not as it glides.
+    const axis = slider ? rotate(sliderAxis(m), -ownPose.angle) : null;
+    // A hinge's, a fixed joint's and a slider's point on the other body is wherever the joint was
+    // when it was made, so it is no part of the key – the bodies move, and the point with them.
     const key = JSON.stringify([
       settings.type,
       own.body.handle,
       other.handle,
       [round(onOwn.x), round(onOwn.y)],
       twoEnds ? [round(inBody(otherPose, far).x), round(inBody(otherPose, far).y)] : 0,
+      axis ? [round(axis.x), round(axis.y)] : 0,
       settings.length,
       settings.stiffness,
       settings.damping,
       settings.limits,
+      settings.distanceLimits,
+      // Switching the motor off is a joint without one; its speed and target change on the way.
+      Boolean(settings.motor),
     ]);
     if (!held.joint || key !== held.key) {
       this.release(engine, held);
       const between = `${settings.type}|${own.body.handle}|${other.handle}`;
-      if (held.placed?.between !== between)
+      if (held.placed?.between !== between) {
         held.placed = {
           between,
           length: Math.hypot(far.x - at.x, far.y - at.y),
           angle: angleBetween(other.rotation(), own.body.rotation()),
         };
-      const data = this.dataOf(settings, held.placed, inBody(otherPose, far), onOwn, other, own.body);
+        held.wound = held.placed.angle;
+        if (slider && rigid && Math.abs(held.placed.angle) > 1e-3) host.hint(world, entity, TURNED_TO_MATCH);
+      }
+      const onOther = inBody(otherPose, far);
+      // The engine reads a slider's axis in the other body; its turn is the held one's while it holds.
+      const railAxis = axis ? rotate(axis, ownPose.angle - otherPose.angle) : null;
+      held.rail = railAxis ? { onOther, onOwn, axis: railAxis } : null;
+      held.type = settings.type;
+      const data = this.dataOf(settings, held.placed, onOther, onOwn, railAxis, other, own.body);
       // The other end first: a hinge's angle is then the held object's turn against it.
       held.joint = engine.createImpulseJoint(data, other, own.body, true);
-      // Only a hinge has limits, and a hinge is the engine's revolute joint.
+      // Only a hinge and a slider have limits; they are the engine's revolute and prismatic joints.
       if (settings.limits)
-        (held.joint as RevoluteImpulseJoint).setLimits(...hingeLimits(settings.limits, held.placed.angle));
+        (held.joint as UnitImpulseJoint).setLimits(...hingeLimits(settings.limits, held.placed.angle));
+      if (settings.distanceLimits)
+        (held.joint as UnitImpulseJoint).setLimits(
+          toMetres(settings.distanceLimits.min),
+          toMetres(settings.distanceLimits.max),
+        );
       held.joint.setContactsEnabled(settings.collideConnected);
       held.key = key;
       held.collide = settings.collideConnected;
-      return;
-    }
-    if (held.collide !== settings.collideConnected) {
+      held.motorCall = '';
+    } else if (held.collide !== settings.collideConnected) {
       held.collide = settings.collideConnected;
       held.joint.setContactsEnabled(held.collide);
       own.body.wakeUp();
     }
+    if (settings.motor) this.drive(held, settings.motor);
+    // A hinge is followed every frame, so a wheel that turns on counts its rounds.
+    else if (held.type === 'hinge') this.measure(held);
   }
 
   private dataOf(
@@ -190,6 +321,7 @@ export class JointSet {
     placed: NonNullable<Held['placed']>,
     onOther: Vec2,
     onOwn: Vec2,
+    axis: Vec2 | null,
     other: RigidBody,
     own: RigidBody,
   ): JointData {
@@ -197,6 +329,8 @@ export class JointSet {
     switch (settings.type) {
       case 'hinge':
         return JointData.revolute(onOther, onOwn);
+      case 'slider':
+        return JointData.prismatic(onOther, onOwn, axis!);
       case 'spring':
         return JointData.spring(
           toMetres(jointLength(settings, placed.length)),
@@ -247,5 +381,6 @@ export class JointSet {
     engine.removeRigidBody(held.anchor);
     held.anchor = null;
     held.anchorPose = null;
+    held.turn = null;
   }
 }

src/runtime/systems/behaviorContext.ts

@@ -244,5 +244,9 @@ function physicsControl(
     setAngularVelocity: (handle, degrees) => act(handle, (e) => physics.setAngularVelocity(e, degrees)),
     applyImpulse: (handle, x, y) => act(handle, (e) => physics.applyImpulse(e, { x, y })),
     setGravity: (x, y) => physics.setGravity(world, { x, y }),
+    jointStateOf: (handle) => {
+      const found = resolve(handle);
+      return found?.type === 'joint' ? physics.jointStateOf(found) : null;
+    },
   };
 }

src/viewport/jointLinks.ts

@@ -2,7 +2,7 @@ import { hasConnectedAnchor, JOINT_CONNECTED_KEY } from '../core/model/joint';
 import type { Mat } from '../core/model/matrix';
 import { referenceCandidates, referencedId } from '../core/model/objectRefs';
 import type { Vec2 } from '../core/model/Properties';
-import { jointFarEnd, jointSettings } from '../core/properties/joint';
+import { jointFarEnd, jointSettings, sliderAxis, sliderRail } from '../core/properties/joint';
 import type { DrawItem } from './items';
 
 /** What the scene view draws of a joint (#154): from where it sits to what it holds on to. */
@@ -21,6 +21,8 @@ export interface JointLink {
   anchored: boolean;
   /** The frame the connected anchor is counted in; null for the scene's. */
   frame: Mat | null;
+  /** A slider's rail through where it sits; `limited` when its ends are the limits, which get a tick. */
+  rail: { from: Vec2; to: Vec2; limited: boolean } | null;
 }
 
 /** The item a joint's reference names, looked up from where the joint sits (see `objectRefs.ts`). */
@@ -45,5 +47,9 @@ export function jointLinkOf(item: DrawItem, byId: ReadonlyMap<string, DrawItem>)
     : connected
       ? { x: connected.x, y: connected.y }
       : from;
-  return { id: item.id, from, to, connectedId: connected?.id ?? '', anchored, frame };
+  const rail =
+    settings.type === 'slider'
+      ? { ...sliderRail(settings, from, sliderAxis(item.m)), limited: settings.distanceLimits !== null }
+      : null;
+  return { id: item.id, from, to, connectedId: connected?.id ?? '', anchored, frame, rail };
 }

tests/core/joints.test.ts

@@ -19,8 +19,18 @@ import { worldPositionOf } from '../../src/core/graph';
 import { objectReference } from '../../src/core/model/objectRefs';
 import type { PropertyValue } from '../../src/core/model/Properties';
 import { findAsset } from '../../src/core/model/Project';
-import { hingeLimits, jointFarEnd, jointLength, jointSettings } from '../../src/core/properties/joint';
-import { translation } from '../../src/core/model/matrix';
+import {
+  hingeLimits,
+  jointFarEnd,
+  jointLength,
+  jointSettings,
+  MOTOR_GAIN,
+  motorSpeed,
+  OPEN_RAIL,
+  sliderAxis,
+  sliderRail,
+} from '../../src/core/properties/joint';
+import { transformMatrix, translation } from '../../src/core/model/matrix';
 import { defaultsFor, isRowShown, schemaFor } from '../../src/core/properties/PropertySchema';
 import { loadPhysics } from '../../src/runtime/physics/engine';
 import type { PhysicsSystem } from '../../src/runtime/physics/PhysicsSystem';
@@ -213,6 +223,66 @@ describe('what a joint reads off its rows', () => {
     expect(shown({ jointType: 'rope' })).not.toContain('stiffness');
     expect(shown({ jointType: 'spring' })).toEqual(expect.arrayContaining(['stiffness', 'damping']));
   });
+
+  it('shows the limits of a slider with their switch, and the motor rows by its kind', () => {
+    const shown = (values: Values) =>
+      schemaFor('joint')
+        .filter((def) => isRowShown(def, { ...defaultsFor('joint'), ...values }))
+        .map((def) => def.key);
+    const motorRows = ['motorSpeed', 'motorTarget', 'maxForce'];
+    expect(shown({ jointType: 'slider' })).toEqual(expect.arrayContaining(['limitDistance', 'motor']));
+    expect(shown({ jointType: 'slider' })).not.toContain('minDistance');
+    expect(shown({ jointType: 'slider', limitDistance: true })).toEqual(
+      expect.arrayContaining(['minDistance', 'maxDistance']),
+    );
+    expect(shown({ jointType: 'hinge', limitDistance: true })).not.toContain('minDistance');
+    expect(shown({ jointType: 'slider' }).filter((k) => motorRows.includes(k))).toEqual([]);
+    expect(shown({ jointType: 'hinge', motor: 'speed' }).filter((k) => motorRows.includes(k))).toEqual([
+      'motorSpeed',
+      'maxForce',
+    ]);
+    expect(shown({ jointType: 'slider', motor: 'target' }).filter((k) => motorRows.includes(k))).toEqual(
+      motorRows,
+    );
+    expect(shown({ jointType: 'rope', motor: 'target' })).not.toContain('motor');
+    expect(shown({ jointType: 'rope', motor: 'target' })).not.toContain('motorTarget');
+  });
+
+  it('gives only a slider limits of distance, and only a hinge or a slider a motor', () => {
+    expect(jointSettings({ jointType: 'slider' })).toMatchObject({ distanceLimits: null, motor: null });
+    expect(
+      jointSettings({ jointType: 'slider', limitDistance: true, minDistance: 30, maxDistance: 70 })
+        .distanceLimits,
+    ).toEqual({ min: 0, max: 70 });
+    expect(jointSettings({ jointType: 'hinge', limitDistance: true }).distanceLimits).toBeNull();
+    expect(jointSettings({ jointType: 'hinge', motor: 'speed', motorSpeed: -45 }).motor).toEqual({
+      mode: 'speed',
+      speed: -45,
+      target: 0,
+      maxForce: 0,
+    });
+    expect(jointSettings({ jointType: 'slider', motor: 'target', maxForce: -5 }).motor?.maxForce).toBe(0);
+    expect(jointSettings({ jointType: 'rope', motor: 'speed' }).motor).toBeNull();
+    expect(jointSettings({ jointType: 'hinge', motor: 'nonsense' }).motor).toBeNull();
+  });
+
+  it('asks a motor for its speed, or towards its target at no more than it and slower near it', () => {
+    const motor = { mode: 'target' as const, speed: 90, target: 100, maxForce: 0 };
+    expect(motorSpeed({ ...motor, mode: 'speed' }, 40)).toBe(90);
+    expect(motorSpeed(motor, 0)).toBe(90);
+    expect(motorSpeed(motor, 200)).toBe(-90);
+    expect(motorSpeed(motor, 99)).toBeCloseTo(MOTOR_GAIN);
+    expect(motorSpeed(motor, 100)).toBe(0);
+    expect(motorSpeed({ ...motor, speed: -90 }, 0)).toBe(90);
+  });
+
+  it("runs a slider's rail along the joint's own x axis", () => {
+    const axis = sliderAxis(transformMatrix(5, 5, 90, 3, false, false));
+    expect(axis.x).toBeCloseTo(0);
+    expect(axis.y).toBeCloseTo(1);
+    const open = sliderRail(jointSettings({ jointType: 'slider' }), { x: 0, y: 0 }, { x: 1, y: 0 });
+    expect(open).toEqual({ from: { x: -OPEN_RAIL, y: 0 }, to: { x: OPEN_RAIL, y: 0 } });
+  });
 });
 
 describe('a rope', () => {
@@ -407,6 +477,178 @@ describe('a fixed joint', () => {
   });
 });
 
+describe('a slider', () => {
+  /** A box at the origin on a slider at its centre, held to the scene; the joint turned by `angle`. */
+  function railed(values: Values = {}, angle = 0, box: Thing = { w: 20, body: DYNAMIC }) {
+    const f = jointScene();
+    const id = f.add(0, 0, box);
+    const joint = f.joint(id, { x: 0, y: 0 }, null, { jointType: 'slider', ...values });
+    f.set(joint, 'rotation', angle);
+    return { f, box: id, joint };
+  }
+
+  it('holds the object on its rail, so it does not fall across it', () => {
+    const { f, box } = railed();
+    const r = run(f);
+    r.seconds(1);
+    expect(Math.abs(r.at(box).x)).toBeLessThan(0.5);
+    expect(Math.abs(r.at(box).y)).toBeLessThan(0.5);
+  });
+
+  it('lets it glide along the rail the joint is turned to, without turning it', () => {
+    const { f, box, joint } = railed({}, 45);
+    const r = run(f);
+    r.seconds(0.5);
+    const at = r.at(box);
+    expect(at.x).toBeGreaterThan(40);
+    expect(at.y).toBeCloseTo(at.x, 0);
+    expect(Math.abs(Number(r.entity(box).props.rotation ?? 0))).toBeLessThan(0.5);
+    // The box is drawn up to a step behind the engine, which glides 5.8 a step by now.
+    expect(Math.abs(r.physics.jointStateOf(r.entity(joint))!.value - Math.hypot(at.x, at.y))).toBeLessThan(7);
+  });
+
+  it('stops at its limits, counted from where it was placed', () => {
+    const { f, box } = railed({ limitDistance: true, minDistance: -10, maxDistance: 50 }, 90);
+    const r = run(f);
+    r.seconds(1.5);
+    expect(r.at(box).y).toBeGreaterThan(48);
+    expect(r.at(box).y).toBeLessThan(52);
+  });
+
+  it('keeps an object placed turned as it was when it is held to the scene', () => {
+    // The joint turns with the box it sits on: 30 and 60 make an upright rail.
+    const { f, box } = railed({}, 60);
+    f.set(box, 'rotation', 30);
+    const r = run(f);
+    r.seconds(1);
+    expect(Number(r.entity(box).props.rotation)).toBeCloseTo(30, 0);
+    expect(r.at(box).y).toBeGreaterThan(100);
+    expect(Math.abs(r.at(box).x)).toBeLessThan(0.5);
+  });
+
+  it('turns the object to match between two rigidbodies, and says so', () => {
+    const f = jointScene();
+    const wall = f.add(-100, 0, { w: 20, body: { bodyType: 'static' } });
+    const box = f.add(0, 0, { w: 20, body: DYNAMIC });
+    f.set(box, 'rotation', 30);
+    f.joint(box, { x: 0, y: 0 }, wall, { jointType: 'slider' });
+    const r = run(f);
+    r.seconds(1);
+    expect(Math.abs(Number(r.entity(box).props.rotation))).toBeLessThan(1);
+    expect(r.world.log.filter((line) => /keeps them at one angle/.test(line))).toHaveLength(1);
+  });
+});
+
+describe('a motor', () => {
+  /** A wheel turning about its own centre, pinned to the scene, with no gravity. */
+  function wheel(values: Values) {
+    const f = jointScene();
+    f.gravity(0, 0);
+    const id = f.add(0, 0, { w: 40, body: DYNAMIC });
+    const joint = f.joint(id, { x: 0, y: 0 }, null, { jointType: 'hinge', ...values });
+    return { f, wheel: id, joint };
+  }
+
+  /** A lift: a box on an upright rail held to the scene; the rail's x points down. */
+  function lift(values: Values) {
+    const f = jointScene();
+    const box = f.add(0, 0, { w: 20, body: DYNAMIC });
+    const joint = f.joint(box, { x: 0, y: 0 }, null, { jointType: 'slider', ...values });
+    f.set(joint, 'rotation', 90);
+    return { f, box, joint };
+  }
+
+  it('turns a hinge at its speed and counts on past a full round', () => {
+    const { f, wheel: id, joint } = wheel({ motor: 'speed', motorSpeed: 360 });
+    const r = run(f);
+    r.seconds(2.5);
+    const state = r.physics.jointStateOf(r.entity(joint))!;
+    expect(state.value).toBeGreaterThan(880);
+    expect(state.value).toBeLessThan(905);
+    expect(state.speed).toBeCloseTo(360, 0);
+    // Drawn up to a step – 6 degrees – behind the engine.
+    expect(Math.abs((Number(r.entity(id).props.rotation) % 360) - (state.value % 360))).toBeLessThan(7);
+  });
+
+  it('turns a hinge to its target and holds it there against the weight of the door', () => {
+    const f = jointScene();
+    const door = f.add(50, 0, { w: 100, h: 20, body: DYNAMIC });
+    const joint = f.joint(door, { x: -50, y: 0 }, null, {
+      jointType: 'hinge',
+      motor: 'target',
+      motorTarget: -90,
+      motorSpeed: 180,
+    });
+    const r = run(f);
+    r.seconds(0.25);
+    // On its way at 180 degrees a second, not there at once.
+    expect(r.physics.jointStateOf(r.entity(joint))!.value).toBeGreaterThan(-60);
+    expect(r.physics.jointStateOf(r.entity(joint))!.value).toBeLessThan(-20);
+    r.seconds(1.75);
+    expect(r.physics.jointStateOf(r.entity(joint))!.value).toBeCloseTo(-90, 0);
+    expect(r.at(door).x).toBeCloseTo(0, 0);
+    expect(r.at(door).y).toBeCloseTo(-50, 0);
+  });
+
+  it('glides a slider at its speed', () => {
+    const { f, box, joint } = lift({ motor: 'speed', motorSpeed: 50 });
+    f.gravity(0, 0);
+    const r = run(f);
+    r.seconds(2);
+    expect(Math.abs(r.at(box).y - 100)).toBeLessThan(1.5);
+    expect(r.physics.jointStateOf(r.entity(joint))!.speed).toBeCloseTo(50, 0);
+  });
+
+  it('lifts a box to its target, holds it there, and goes on to a target set while it runs', () => {
+    const { f, box, joint } = lift({ motor: 'target', motorTarget: -200, motorSpeed: 100 });
+    const r = run(f);
+    r.seconds(1);
+    expect(r.at(box).y).toBeGreaterThan(-110);
+    expect(r.at(box).y).toBeLessThan(-90);
+    r.seconds(2);
+    expect(r.at(box).y).toBeCloseTo(-200, 0);
+    expect(r.physics.jointStateOf(r.entity(joint))!.value).toBeCloseTo(-200, 0);
+    // What `Properties` writes: the target only, so the engine keeps the joint it has.
+    r.entity(joint).props.motorTarget = -50;
+    r.seconds(2.5);
+    expect(r.at(box).y).toBeCloseTo(-50, 0);
+  });
+
+  it('cannot lift more than its force allows', () => {
+    const weak = lift({ motor: 'speed', motorSpeed: -100, maxForce: 1 });
+    const r = run(weak.f);
+    r.seconds(0.5);
+    expect(r.at(weak.box).y).toBeGreaterThan(50);
+    const strong = lift({ motor: 'speed', motorSpeed: -100, maxForce: 100000 });
+    const s = run(strong.f);
+    s.seconds(0.5);
+    expect(s.at(strong.box).y).toBeLessThan(-45);
+  });
+
+  it('lets go once it is switched off while the game runs', () => {
+    const { f, box, joint } = lift({ motor: 'target', motorTarget: 0 });
+    const r = run(f);
+    r.seconds(0.5);
+    expect(Math.abs(r.at(box).y)).toBeLessThan(1);
+    r.entity(joint).props.motor = 'off';
+    r.seconds(0.5);
+    expect(r.at(box).y).toBeGreaterThan(100);
+    expect(r.physics.holdsJoint(r.entity(joint))).toBe(true);
+  });
+
+  it('reads no position off a rope, nor off a joint that holds nothing', () => {
+    const f = jointScene();
+    const box = f.add(0, 0, { w: 20, body: DYNAMIC });
+    const rope = f.joint(box, { x: 0, y: 0 }, null, { jointType: 'rope', connectedAnchorY: -50 });
+    const loose = f.add(100, 0, { w: 20 });
+    const idle = f.joint(loose, { x: 0, y: 0 }, null, { jointType: 'hinge' });
+    const r = run(f);
+    r.seconds(0.1);
+    expect(r.physics.jointStateOf(r.entity(rope))).toBeNull();
+    expect(r.physics.jointStateOf(r.entity(idle))).toBeNull();
+  });
+});
+
 describe('the other end of a joint', () => {
   it('follows a connected object without a rigidbody, which is pulled by nothing', () => {
     const f = jointScene();

tests/core/node-catalog.test.ts

@@ -135,6 +135,7 @@ const physicsDouble = (): PhysicsDouble => {
     ),
     applyImpulse: (target, x, y) => (calls.push(['applyImpulse', target.id, x, y]), has(target)),
     setGravity: (x, y) => void calls.push(['setGravity', x, y]),
+    jointStateOf: (target) => (target.id === 'hinge' ? { value: 30, speed: -12 } : null),
   };
 };
 const physicsCalls = (ctx: FakeContext) => (ctx.physics as PhysicsDouble).calls;
@@ -1462,6 +1463,25 @@ const CASES: Record<string, Case[]> = {
     },
     { name: 'without physics it reads 0', inputs: { object: crate }, outputs: { x: 0, y: 0, angular: 0 } },
   ],
+  JointPosition: [
+    {
+      name: 'reads how far the joint stands from where it was placed, and how fast',
+      inputs: { joint: fakeEntity('hinge') },
+      context: { physics: physicsDouble() },
+      outputs: { value: 30, speed: -12 },
+    },
+    {
+      name: 'a joint the engine does not read reads 0',
+      inputs: { joint: fakeEntity('rope') },
+      context: { physics: physicsDouble() },
+      outputs: { value: 0, speed: 0 },
+    },
+    {
+      name: 'without physics it reads 0',
+      inputs: { joint: fakeEntity('hinge') },
+      outputs: { value: 0, speed: 0 },
+    },
+  ],
   SetGravity: [
     {
       name: 'sets the scene gravity',

tests/viewport/joint-links.test.ts

@@ -67,6 +67,19 @@ describe('what the scene view draws of a joint', () => {
     expect(s.links()[0]).toMatchObject({ from: { x: 10, y: 0 }, to: { x: 10, y: 0 }, connectedId: '' });
   });
 
+  it('lays a slider rail along the joint as it is turned, between its limits once it has some', () => {
+    const open = scene({ jointType: 'slider', rotation: 90 });
+    const [link] = open.links();
+    expect(link!.to).toEqual({ x: 200, y: -100 });
+    expect(link!.rail!.limited).toBe(false);
+    expect(link!.rail!.from.x).toBeCloseTo(10);
+    expect(link!.rail!.from.y).toBeCloseTo(-60);
+    expect(link!.rail!.to.y).toBeCloseTo(60);
+    const limited = scene({ jointType: 'slider', limitDistance: true, minDistance: -20, maxDistance: 80 });
+    expect(limited.links()[0]!.rail).toEqual({ from: { x: -10, y: 0 }, to: { x: 90, y: 0 }, limited: true });
+    expect(scene({ jointType: 'hinge' }).links()[0]!.rail).toBeNull();
+  });
+
   it('has no link for anything but a joint', () => {
     const s = scene({});
     const { items } = collectHolderItems(s.f.project, s.f.sceneOf(), 0);

tools/e2e/41-physics.mjs

@@ -661,6 +661,61 @@ export async function physics(t) {
       hints: consoleLog.filter((line) => line.includes('[physics]')).slice(jointHints),
     }),
   );
+
+  // 41f. The same joint made a slider with a motor (#154, step 2): its rows follow the choices, its
+  //      rail is drawn along the joint as it is turned, and in play the motor drives the bob up it.
+  await selectObject(joint.id);
+  await pressAt(await inView(t, '__gm.inspectorRect()', "__gm.inspectorField('Type')"), 'the Type field');
+  await pressAt(await json("__gm.locate('Slider', true)"), 'Slider in the menu');
+  await pressAt(await inView(t, '__gm.inspectorRect()', "__gm.inspectorField('Motor')"), 'the Motor field');
+  await pressAt(await json("__gm.locate('Speed', true)"), 'Speed in the menu');
+  await mutate(`
+    const o = __gm.state.activeScene.objects.find((o) => o.id === '${joint.id}');
+    Object.assign(o.overrides, { rotation: 90, motorSpeed: -60 })`);
+  await settle();
+  const railLink = (await links()).links.find((l) => l.id === joint.id);
+  check(
+    'a slider with a speed motor shows its rows and draws its rail along the turned joint',
+    (await jointObject())?.overrides?.jointType === 'slider' &&
+      (await jointObject())?.overrides?.motor === 'speed' &&
+      (await has('Limit distance')) &&
+      (await has('Motor speed')) &&
+      (await has('Max force (0 = no limit)')) &&
+      !(await has('Motor target')) &&
+      !(await has('Connected anchor X')) &&
+      railLink?.rail?.limited === false &&
+      Math.abs(railLink.rail.from.x) < 0.01 &&
+      Math.abs(railLink.rail.to.y - railLink.rail.from.y - 120) < 0.01,
+    JSON.stringify({ railLink, overrides: (await jointObject())?.overrides }),
+  );
+  await select(null);
+  await play();
+  await evaluate(`(() => {
+    const out = (window.__sliderSamples = []);
+    const start = performance.now();
+    const sample = () => {
+      const w = __gm.world();
+      if (!w) return;
+      const bob = w.entities.find((e) => e.objectId === 'phys-bob');
+      out.push({ t: performance.now() - start, x: bob?.worldX, y: bob?.worldY });
+      if (performance.now() - start < 1000) requestAnimationFrame(sample);
+    };
+    requestAnimationFrame(sample);
+  })()`);
+  await sleep(1300);
+  const slid = await json('window.__sliderSamples');
+  await stop();
+  // From the first sample to the last, at 60 units a second up the rail.
+  const span = slid.length > 1 ? (slid.at(-1).t - slid[0].t) / 1000 : 0;
+  const climbed = slid.length > 1 ? slid[0].y - slid.at(-1).y : 0;
+  check(
+    'in the played scene the motor drives the bob up its rail at its speed, and not off it',
+    slid.length >= 5 &&
+      span > 0.8 &&
+      Math.abs(climbed - 60 * span) < 6 &&
+      slid.every((s) => Math.abs(s.x) < 0.5),
+    JSON.stringify({ frames: slid.length, span, climbed, first: slid[0], last: slid.at(-1) }),
+  );
   await mutate(`
     const p = __gm.state.project;
     const scene = __gm.state.activeScene;