Rumba skirt

Files

src

tools

LICENSE-Codim-IPC.txt

src/main.js

// A wooden mannequin dancing C-IPC's Rumba, its body parts the skirt's colliders.
//
// `rumba-track.json` is a rigid transform per body part per frame, derived from the mesh
// sequence C-IPC drives its garments with (see tools/derive_rumba_track.mjs). Each step
// `pose(dt)` samples it and places the parts. The parts the skirt can touch carry a Collider
// and a ClothCollider, so placing them moves the colliders: hips, abdomen and chest for the
// waist and torso, thighs, knees and shins for the legs, forearms and hands.
import { CapsuleShape3D } from "@woosh/meep-engine/src/core/geom/3d/shape/CapsuleShape3D.js";
import { SphereShape3D } from "@woosh/meep-engine/src/core/geom/3d/shape/SphereShape3D.js";
import { make_octahedron_geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/primitives/make_octahedron_geometry.js";
import { make_capsule_geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/primitives/make_capsule_geometry.js";
import track from "./rumba-track.json";

const FRAME = track.seconds_per_frame;
// The sequence lowers the arms from a T-pose (frames 0-40), dances a rumba step (40-104) and holds.
// The demo plays the lowering once, then repeats the step, blending its last frames into its first.
const LOOP_START = 40, LOOP_END = 104, BLEND = 8;

const chestCentre = track.points.chest_centre.rest, neck = track.joints.neck.rest;
track.points.neck_base = { part: "chest", rest: chestCentre.map((c, k) => (c + neck[k]) / 2) };

export function createDancer(scene) {
    const wood = scene.material("#d9b38c", { roughness: .55 });
    const joint = scene.material("#a9805c", { roughness: .5 });
    const part = (geometry, material) => scene.decor(geometry, material, 0, 0, 0);

    // Torso pieces lie across the body (along the part's x), limbs run joint to joint.
    const across = (radius, width) => ({ radius, length: Math.max(0, width - 2 * radius), mesh: part(make_capsule_geometry(radius, Math.max(0, width - 2 * radius), 8, 24), wood) });
    const limb = (radius, from, to, material = wood) => ({ radius, from, to, mesh: part(make_capsule_geometry(radius, length(from, to), 8, 20), material) });
    const ball = (radius, at, material = joint) => ({ radius, at, mesh: part(make_octahedron_geometry(radius, 4), material) });

    const torso = {
        pelvis: across(.088, .272), abdomen: across(.072, .186), chest: across(.1, .234),
    };
    const limbs = [
        // The neck rises from inside the chest, halfway to the neck joint, so it stays sunk in the
        // chest as the head moves; started at the joint, it only grazes the chest's rounded top.
        limb(.045, "neck_base", "head_centre", joint),
        ...["l", "r"].flatMap(s => [
            limb(.057, `hip_${s}`, `knee_${s}`), limb(.042, `knee_${s}`, `ankle_${s}`), limb(.03, `ankle_${s}`, `toe_${s}`, joint),
            limb(.034, `shoulder_${s}`, `elbow_${s}`), limb(.028, `elbow_${s}`, `wrist_${s}`), limb(.024, `wrist_${s}`, `hand_tip_${s}`, joint),
        ]),
    ];
    const balls = [
        ball(.09, "head_centre", wood),
        ...["l", "r"].flatMap(s => [ball(.05, `knee_${s}`), ball(.04, `shoulder_${s}`), ball(.033, `elbow_${s}`)]),
    ];

    // The cloth collides with the body below the shoulders.
    const collide = (item, shape) => { item.mesh = scene.collide(item.mesh, shape, { friction: .3 }); };
    for (const item of Object.values(torso)) collide(item, CapsuleShape3D.from(item.radius, item.length));
    for (const item of limbs) {
        if (/^(hip|knee|elbow|wrist)_/.test(item.from)) collide(item, CapsuleShape3D.from(item.radius, length(item.from, item.to)));
    }
    for (const item of balls) {
        if (/^knee_/.test(item.at)) collide(item, SphereShape3D.from(item.radius));
    }

    const sample = { t: [0, 0, 0], q: [0, 0, 0, 1] };
    const parts = track.parts.map(() => ({ t: [0, 0, 0], q: [0, 0, 0, 1] }));
    let time = 0;

    function point(name) {
        const p = track.joints[name] ?? track.points[name];
        const which = track.parts.indexOf(p.parts?.[1] ?? p.part);
        const pose = parts[which];
        return add(rotate(pose.q, p.rest), pose.t);
    }
    function length(a, b) {
        const pa = (track.joints[a] ?? track.points[a]).rest, pb = (track.joints[b] ?? track.points[b]).rest;
        return Math.max(0, Math.hypot(pa[0] - pb[0], pa[1] - pb[1], pa[2] - pb[2]) - .01);
    }
    function pose(dt) {
        time += dt;
        const frame = time / FRAME;
        const span = LOOP_END - LOOP_START;
        for (let i = 0; i < parts.length; i++) {
            if (frame < LOOP_START) {
                partAt(i, frame, parts[i]);
                continue;
            }
            const u = (frame - LOOP_START) % span;
            partAt(i, LOOP_START + u, parts[i]);
            if (u > span - BLEND) {
                // ease into the frames the loop is about to return to
                partAt(i, LOOP_START + u - span, sample);
                blend(parts[i], sample, smooth((u - span + BLEND) / BLEND));
            }
        }

        for (const [name, item] of Object.entries(torso)) {
            const pose = parts[track.parts.indexOf(name)];
            const centre = add(rotate(pose.q, track.points[`${name}_centre`].rest), pose.t);
            // the capsule's axis is y; the torso pieces lie along the part's x
            scene.move(item.mesh, ...centre, ...multiply(pose.q, [0, 0, Math.SQRT1_2, Math.SQRT1_2]));
        }
        for (const item of limbs) {
            const a = point(item.from), b = point(item.to);
            scene.move(item.mesh, ...scale(add(a, b), .5), ...alignY(sub(b, a)));
        }
        for (const item of balls) scene.move(item.mesh, ...point(item.at));
    }

    pose(0);
    // The abdomen is what holds the skirt's waistband.
    return { pose, abdomen: torso.abdomen.mesh };
}

function partAt(index, frame, out) {
    const frames = track.frames, last = frames.length - 1;
    const f = Math.min(Math.max(frame, 0), last), a = Math.floor(f), b = Math.min(a + 1, last), w = f - a;
    const o = index * 7, A = frames[a], B = frames[b];
    for (let k = 0; k < 3; k++) out.t[k] = A[o + k] + (B[o + k] - A[o + k]) * w;
    slerp(out.q, A.slice(o + 3, o + 7), B.slice(o + 3, o + 7), w);
}

function blend(into, other, w) {
    for (let k = 0; k < 3; k++) into.t[k] += (other.t[k] - into.t[k]) * w;
    slerp(into.q, into.q.slice(), other.q, w);
}

function slerp(out, a, b, w) {
    let d = a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
    const s = d < 0 ? -1 : 1;
    d *= s;
    let ka = 1 - w, kb = w * s;
    if (d < .9995) {
        const angle = Math.acos(d), sin = Math.sin(angle);
        ka = Math.sin((1 - w) * angle) / sin;
        kb = Math.sin(w * angle) / sin * s;
    }
    let l = 0;
    for (let k = 0; k < 4; k++) { out[k] = a[k] * ka + b[k] * kb; l += out[k] * out[k]; }
    l = Math.sqrt(l);
    for (let k = 0; k < 4; k++) out[k] /= l;
}

function smooth(x) {
    return x * x * (3 - 2 * x);
}

// The rotation taking +Y onto a direction.
function alignY(d) {
    const l = Math.hypot(d[0], d[1], d[2]) || 1, x = d[0] / l, y = d[1] / l, z = d[2] / l;
    if (y < -.999999) return [1, 0, 0, 0];
    const q = [z, 0, -x, 1 + y];
    const n = Math.hypot(...q);
    return q.map(c => c / n);
}

function add(a, b) { return [a[0] + b[0], a[1] + b[1], a[2] + b[2]]; }
function sub(a, b) { return [a[0] - b[0], a[1] - b[1], a[2] - b[2]]; }
function scale(a, s) { return [a[0] * s, a[1] * s, a[2] * s]; }

function multiply(a, b) {
    return [
        a[3] * b[0] + a[0] * b[3] + a[1] * b[2] - a[2] * b[1],
        a[3] * b[1] - a[0] * b[2] + a[1] * b[3] + a[2] * b[0],
        a[3] * b[2] + a[0] * b[1] - a[1] * b[0] + a[2] * b[3],
        a[3] * b[3] - a[0] * b[0] - a[1] * b[1] - a[2] * b[2],
    ];
}

function rotate(q, v) {
    const [x, y, z, w] = q;
    const tx = 2 * (y * v[2] - z * v[1]), ty = 2 * (z * v[0] - x * v[2]), tz = 2 * (x * v[1] - y * v[0]);
    return [v[0] + w * tx + y * tz - z * ty, v[1] + w * ty + z * tx - x * tz, v[2] + w * tz + x * ty - y * tx];
}

import { PlaneShape3D } from "@woosh/meep-engine/src/core/geom/3d/shape/PlaneShape3D.js";
import { ClothDynamics } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothDynamics.js";
import { ClothDynamicsFlags } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothDynamicsFlags.js";
import { ClothPin } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothPin.js";
import { createScene } from "./scene.js";
import { createSheet } from "./sheet.js";
import { createDancer } from "./dancer.js";

// A circle skirt is cut as a flat ring: the waistband on the inside, the hem outside. It sits at
// the mannequin's natural waist, 0.95 m up, just clear of the body.
const RINGS = 13;
const WAIST = [0, .95, -.012], WAIST_RADIUS = .1, SKIRT_LENGTH = .45;

// The mannequin faces +z; this yaw puts the camera in front of it.
const scene = await createScene({ distance: 2.6, yaw: Math.PI + .35, pitch: .12, focus: [0, .85, 0] });

// The ring is meshed as a near-square lattice: rings 37.5 mm apart, and on each ring as many
// vertices as make its edges about as long, 17 round the waistband and 92 at the hem. Cloth
// self-collision keeps vertices about one edge apart, so it wants edges of one length; with the
// same count on every ring, the waist's edges would be a quarter of the hem's. Two rings of
// unequal counts are joined by walking both in angle, each triangle advancing whichever ring's
// next vertex comes first.
const SPACING = SKIRT_LENGTH / (RINGS - 1);
const around = [], first = [0];
for (let k = 0; k < RINGS; k++) {
    around.push(Math.round(2 * Math.PI * (WAIST_RADIUS + SPACING * k) / SPACING));
    first.push(first[k] + around[k]);
}
const position = new Float32Array(first[RINGS] * 3), uv = new Float32Array(first[RINGS] * 2);
const triangle = [], waistband = [];
for (let k = 0; k < RINGS; k++) {
    const radius = WAIST_RADIUS + SPACING * k;
    for (let i = 0; i < around[k]; i++) {
        const v = first[k] + i, angle = i / around[k] * Math.PI * 2;
        position.set([WAIST[0] + radius * Math.cos(angle), WAIST[1], WAIST[2] + radius * Math.sin(angle)], v * 3);
        uv.set([i / around[k], k / (RINGS - 1)], v * 2);
        if (k === 0) waistband.push(v);
    }
}
for (let k = 0; k + 1 < RINGS; k++) {
    const n = around[k], m = around[k + 1];
    for (let i = 0, j = 0; i < n || j < m;) {
        const a = first[k] + i % n, c = first[k + 1] + j % m;
        if (j === m || (i < n && (i + 1) / n <= (j + 1) / m)) {
            triangle.push(a, first[k] + (i + 1) % n, c);
            i++;
        } else {
            triangle.push(a, first[k + 1] + (j + 1) % m, c);
            j++;
        }
    }
}

scene.collide(scene.point(), PlaneShape3D.GROUND, { friction: .5 });
const dancer = createDancer(scene);

// The rows take their rest lengths and their flat rest shape from the pattern. The skirt starts
// as the flat ring, in the mannequin's T-pose, and falls from its waistband; the hem has more
// fabric than the hanging skirt has room for, so it folds into flutes.
const sheet = createSheet(scene.ecd, {
    position, uv, triangle,
    material: scene.material("#ffffff", { texture: await scene.canvasTexture(skirtTexture()), roughness: .8 }),
    dynamics: ClothDynamics.from({
        bend: .63, damping: .0125, slack: 1, thickness: .006, substeps: 2, iterations: 4,
        flags: ClothDynamicsFlags.SelfCollision,
    }),
});

// The abdomen holds the waistband where it starts, and carries it through the dance.
scene.ecd.addComponentToEntity(dancer.abdomen.entity, ClothPin.from({ cloth: sheet.entity, particles: waistband }));

scene.onStep(dt => dancer.pose(dt));
await scene.start();
document.querySelector("fieldset").disabled = false;

// Panels of two reds, and a band at the hem, so the flutes and the swing read.
function skirtTexture() {
    const canvas = document.createElement("canvas");
    canvas.width = 1024;
    canvas.height = 256;
    const g = canvas.getContext("2d"), panels = 16;
    for (let i = 0; i < panels; i++) {
        g.fillStyle = i % 2 ? "#b8323f" : "#d4434f";
        g.fillRect(i * 1024 / panels, 0, 1024 / panels, 256);
    }
    g.fillStyle = "#f2c14e";
    g.fillRect(0, 226, 1024, 14);
    g.fillStyle = "#2a2230";
    g.fillRect(0, 0, 1024, 10);
    return canvas;
}

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import { EngineHarness } from "@woosh/meep-engine/src/engine/EngineHarness.js";
import TopDownCameraController from "@woosh/meep-engine/src/engine/graphics/ecs/camera/topdown/TopDownCameraController.js";
import Entity from "@woosh/meep-engine/src/engine/ecs/Entity.js";
import { ParentEntitySystem } from "@woosh/meep-engine/src/engine/ecs/parent/ParentEntitySystem.js";
import { Transform64 } from "@woosh/meep-engine/src/engine/ecs/transform/Transform64.js";
import { t64_announce_change } from "@woosh/meep-engine/src/engine/ecs/transform/t64_announce_change.js";
import { TRANSFORM64_EVENT_PLACED } from "@woosh/meep-engine/src/engine/ecs/transform/TRANSFORM64_EVENT_PLACED.js";
import { TransformAttachmentSystem } from "@woosh/meep-engine/src/engine/ecs/transform-attachment/TransformAttachmentSystem.js";
import { MeshSkinSystem } from "@woosh/meep-engine/src/engine/graphics3/MeshSkinSystem.js";
import { ShadedGeometry } from "@woosh/meep-engine/src/engine/graphics/ecs/mesh-v2/ShadedGeometry.js";
import { ShadedGeometrySystem } from "@woosh/meep-engine/src/engine/graphics3/ShadedGeometrySystem.js";
import { Light } from "@woosh/meep-engine/src/engine/graphics/ecs/light/Light.js";
import { LightType } from "@woosh/meep-engine/src/engine/graphics/ecs/light/LightType.js";
import { Collider } from "@woosh/meep-engine/src/engine/physics/ecs/Collider.js";
import { ClothCollider } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothCollider.js";
import { ClothColliderSystem } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothColliderSystem.js";
import { ClothPin } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothPin.js";
import { ClothRig } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothRig.js";
import { ClothSystem } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothSystem.js";
import { StandardShadeMaterial } from "@woosh/meep-engine/src/shade/renderer/material/StandardShadeMaterial.js";
import { ShadeDrawSide } from "@woosh/meep-engine/src/shade/renderer/material/ShadeDrawSide.js";
import { ColorSpace } from "@woosh/meep-engine/src/shade/renderer/texture/ColorSpace.js";
import { ShadeImage } from "@woosh/meep-engine/src/shade/renderer/texture/source/ShadeImage.js";
import { ShadeTexture } from "@woosh/meep-engine/src/shade/renderer/texture/ShadeTexture.js";
import { meshlet_geometry_build_from_geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/meshlet_geometry_build_from_geometry.js";
import { make_box_geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/primitives/make_box_geometry.js";
import { Color } from "@woosh/meep-engine/src/core/color/Color.js";
import Vector3 from "@woosh/meep-engine/src/core/geom/Vector3.js";

export async function createScene({ distance = 6.5, yaw = .25, pitch = .18, focus = [0, 1.5, 0], stepRate = 60 } = {}) {
    // Held until start(): see there.
    let tick = () => {}, playing = false;

    // Moves the example's holders and colliders, then steps every cloth, on the engine's fixed step.
    class ExampleClothSystem extends ClothSystem {
        fixedUpdate(dt) {
            if (!playing) return;
            tick(dt);
            super.fixedUpdate(dt);
        }
    }
    const cloth = new ExampleClothSystem();
    const colliders = new ClothColliderSystem();
    const engine = await EngineHarness.bootstrap({
        configuration(config, engine) {
            const scene = EngineHarness.shadeScene(engine);
            config.addSystem(new ShadedGeometrySystem(engine.graphics, scene));
            config.addSystem(new MeshSkinSystem(engine.graphics, scene));
            config.addSystem(new ParentEntitySystem());
            config.addSystem(new TransformAttachmentSystem());
            config.addSystem(colliders);
            config.addSystem(cloth);
        },
    });
    await EngineHarness.buildBasics({
        engine, enableTerrain: false, enableWater: false, enableLights: true,
        enableShadows: true, shadowmapResolution: 2048,
        focus: new Vector3(...focus), distance, pitch, yaw,
        // Shade spreads the sun's shadow cascades over the camera's whole near..far range, so
        // far is three opening distances and zooming out stops at two: the scene stays inside
        // far at any zoom, and the cascades are not stretched over empty floor.
        cameraFarDistance: distance * 3, showFps: false,
    });
    engine.entityManager.dataset.getAnyComponent(TopDownCameraController).component.distanceMax = distance * 2;
    engine.entityManager.fixedUpdateStepSize = 1 / stepRate;
    engine.graphics.renderer.feature_automatic_exposure_enabled = false;
    const ecd = engine.entityManager.dataset;
    ecd.registerManyComponentTypes([ClothRig, ClothPin]);
    ecd.traverseEntities([Light], light => {
        if (light.type.getValue() === LightType.DIRECTION) light.intensity.set(6);
    });

    function material(hex, { texture, roughness = .9 } = {}) {
        const m = new StandardShadeMaterial();
        m.diffuse_color.copy(Color.from_sRGB_to_linear(Color.parse(hex)));
        m.roughness_factor = roughness;
        m.draw_side = ShadeDrawSide.Double;
        if (texture) m.texture_albedo = texture;
        return m;
    }
    async function canvasTexture(canvas) {
        const image = ShadeImage.fromImageBitmap(await createImageBitmap(canvas));
        image.color_space = ColorSpace.SRGB;
        return ShadeTexture.from(image);
    }
    // An entity with nothing but a place: a holder, or the ground's collider.
    function point(x = 0, y = 0, z = 0) {
        const transform = new Transform64();
        transform.setTranslation(x, y, z);
        transform.updateMatrix();
        return { entity: new Entity().add(transform).build(ecd), transform };
    }
    function decor(geometry, color, x, y, z) {
        const transform = new Transform64();
        transform.setTranslation(x, y, z);
        const entity = new Entity().add(transform)
            .add(ShadedGeometry.from(meshlet_geometry_build_from_geometry(geometry), typeof color === "string" ? material(color) : color))
            .build(ecd);
        return { entity, transform };
    }
    function move(object, x, y, z, qx = 0, qy = 0, qz = 0, qw = 1) {
        object.transform.setTranslation(x, y, z);
        object.transform.setRotation(qx, qy, qz, qw);
        object.transform.updateMatrix();
        t64_announce_change(ecd, object.entity);
    }
    // A move that is a jump: colliders start again from here rather than sweeping across.
    function place(object, ...pose) {
        move(object, ...pose);
        ecd.sendEvent(object.entity, TRANSFORM64_EVENT_PLACED);
    }
    // Cloth collides with an entity that carries a Collider and a ClothCollider.
    function collide(object, shape, { friction = .5, inflation = 0 } = {}) {
        const collider = new Collider();
        collider.shape = shape;
        collider.friction = friction;
        ecd.addComponentToEntity(object.entity, collider);
        ecd.addComponentToEntity(object.entity, ClothCollider.from({ inflation }));
        return { ...object, collider };
    }

    decor(make_box_geometry(14, .2, 14), "#1b2433", 0, -.1, 0);
    const pause = document.getElementById("pause");
    pause.addEventListener("click", () => {
        playing = !playing;
        pause.textContent = playing ? "Pause" : "Resume";
        pause.setAttribute("aria-pressed", String(!playing));
    });
    // Start the cloth once a frame showing the scene has finished on the GPU. Shade builds the
    // scene's pipelines over its first frames, which take seconds; stepping through them would
    // bank those seconds as fixed steps the engine then has to catch up on.
    async function start() {
        await new Promise(resolve => {
            const rendered = () => {
                engine.graphics.on.postRender.remove(rendered);
                resolve();
            };
            engine.graphics.on.postRender.add(rendered);
        });
        await engine.graphics.renderer.device.queue.onSubmittedWorkDone();
        playing = true;
    }
    return {
        engine, ecd, cloth, colliders, material, canvasTexture, point, decor, move, place, collide, start,
        onStep: callback => { tick = callback; },
    };
}

// A sheet of cloth for ClothSystem: a triangle mesh skinned with one joint per vertex.
//
// The sheet is built here as a model, the way a loader describes one: the mesh, a root joint,
// and a joint per vertex hanging from the root at the vertex's rest position. Placed like any
// model, it becomes entities, and `cloth_proxy_from_mesh` reads its joints and triangles into a
// cloth: a hard stretch row per edge and a hinge per interior edge. ClothSystem then moves every
// joint, both its position and the turn of the surface around it, and GPU skinning moves and
// lights the mesh.
import Entity from "@woosh/meep-engine/src/engine/ecs/Entity.js";
import { Transform64 } from "@woosh/meep-engine/src/engine/ecs/transform/Transform64.js";
import { prefab_compile } from "@woosh/meep-engine/src/engine/graphics3/prefab/prefab_compile.js";
import { prefab_instantiate } from "@woosh/meep-engine/src/engine/graphics3/prefab/prefab_instantiate.js";
import { cloth_proxy_from_mesh } from "@woosh/meep-engine/src/engine/physics/cloth/build/cloth_proxy_from_mesh.js";
import { Cloth } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/Cloth.js";
import { ClothRig } from "@woosh/meep-engine/src/engine/physics/cloth/ecs/ClothRig.js";
import { Skin } from "@woosh/meep-engine/src/shade/renderer/animation/Skin.js";
import { Attribute } from "@woosh/meep-engine/src/shade/renderer/geometry/Attribute.js";
import { Geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/Geometry.js";
import { StandardAttributes } from "@woosh/meep-engine/src/shade/renderer/geometry/StandardAttributes.js";
import { meshlet_geometry_build_from_geometry } from "@woosh/meep-engine/src/shade/renderer/geometry/meshlet_geometry_build_from_geometry.js";
import { SceneBundle } from "@woosh/meep-engine/src/shade/renderer/loader/SceneBundle.js";
import { SceneNode } from "@woosh/meep-engine/src/shade/renderer/loader/SceneNode.js";

/**
 * @param {EntityComponentDataset} ecd
 * @param {object} options
 * @param {Float32Array} options.position rest positions, 3 per vertex, world space
 * @param {Float32Array} options.uv 2 per vertex
 * @param {number[]} options.triangle vertex triples; particle `i` of the cloth is vertex `i`
 * @param {StandardShadeMaterial} options.material
 * @param {ClothDynamics} options.dynamics
 * @returns {{entity: number, cloth: Cloth}} the entity carrying the cloth, which a `ClothPin` names
 */
export function createSheet(ecd, { position, uv, triangle, material, dynamics }) {
    const count = position.length / 3;

    // Vertex i is weighted wholly to joint i; the bind normals are the rest surface's.
    const joints = new Uint16Array(count * 4), weights = new Float32Array(count * 4);
    for (let i = 0; i < count; i++) {
        joints[i * 4] = i;
        weights[i * 4] = 1;
    }
    const geometry = new Geometry();
    geometry.addAttribute(Attribute.from(Float32Array.from(position), 3, StandardAttributes.Position));
    geometry.addAttribute(Attribute.from(restNormals(position, triangle), 3, StandardAttributes.Normal));
    geometry.addAttribute(Attribute.from(Float32Array.from(uv), 2, StandardAttributes.TextureCoordinates0));
    geometry.addAttribute(Attribute.from(joints, 4, StandardAttributes.SkinningJoints));
    geometry.addAttribute(Attribute.from(weights, 4, StandardAttributes.SkinningWeights));
    geometry.index = Attribute.from(Uint32Array.from(triangle), 1, "index");

    const bundle = new SceneBundle();
    const mesh = bundle.add_node(SceneNode.from({ name: "Sheet", geometry: meshlet_geometry_build_from_geometry(geometry), material }));
    const rig = bundle.add_node(SceneNode.from({ name: "Rig" }));
    const names = [], vertexJoints = [];
    for (let i = 0; i < count; i++) {
        names.push(`Vertex_${i}`);
        vertexJoints.push(bundle.add_node(SceneNode.from({
            name: names[i], parent: rig, translation: [position[i * 3], position[i * 3 + 1], position[i * 3 + 2]],
        })));
    }
    // The root joint comes last, so joint i stays vertex i. It is the frame the cloth is simulated in.
    const inverseBind = new Float32Array((count + 1) * 16);
    for (let j = 0; j <= count; j++) {
        const m = j * 16;
        inverseBind[m] = inverseBind[m + 5] = inverseBind[m + 10] = inverseBind[m + 15] = 1;
        if (j < count) for (let k = 0; k < 3; k++) inverseBind[m + 12 + k] = -position[j * 3 + k];
    }
    bundle.skins = [Skin.from({ joints: [...vertexJoints, rig], inverse_bind_matrices: inverseBind, meshes: [mesh] })];
    const prefab = prefab_compile(bundle);

    const { proxy, error } = cloth_proxy_from_mesh(prefab, prefab.skins[0], names, triangle, { name: "sheet" });
    if (proxy === null) throw new Error(error);

    const entity = new Entity().add(new Transform64()).build(ecd);
    const instance = prefab_instantiate(prefab, ecd, entity);
    const cloth = Cloth.from(dynamics);
    // The rig names the mesh whose MeshSkin the proxy's joints index.
    ecd.addComponentToEntity(entity, ClothRig.from(proxy, instance.mesh_entities[0]));
    ecd.addComponentToEntity(entity, cloth);
    return { entity, cloth };
}

// Area-weighted vertex normals of the rest surface.
function restNormals(p, triangle) {
    const normal = new Float32Array(p.length);
    for (let t = 0; t < triangle.length; t += 3) {
        const a = triangle[t] * 3, b = triangle[t + 1] * 3, c = triangle[t + 2] * 3;
        const ux = p[b] - p[a], uy = p[b + 1] - p[a + 1], uz = p[b + 2] - p[a + 2];
        const vx = p[c] - p[a], vy = p[c + 1] - p[a + 1], vz = p[c + 2] - p[a + 2];
        const nx = uy * vz - uz * vy, ny = uz * vx - ux * vz, nz = ux * vy - uy * vx;
        for (const v of [a, b, c]) {
            normal[v] += nx;
            normal[v + 1] += ny;
            normal[v + 2] += nz;
        }
    }
    for (let i = 0; i < normal.length; i += 3) {
        const l = Math.hypot(normal[i], normal[i + 1], normal[i + 2]) || 1;
        for (let k = 0; k < 3; k++) normal[i + k] /= l;
    }
    return normal;
}

// Derive a rigid-part joint track from C-IPC's Rumba mesh sequence.
//
//   node tools/derive_rumba_track.mjs <dir with shell0.obj … shell120.obj> > src/rumba-track.json
//
// Input: Projects/FEMShell/input/Rumba_Dancing from https://github.com/ipc-sim/Codim-IPC
// (Li, Kaufman and Jiang, "Codimensional Incremental Potential Contact", SIGGRAPH 2021):
// 121 frames, 0.04 s apart, of the wm2_15k mannequin, which starts in a T-pose facing +z.
//
// The mannequin is cut into body parts in the T-pose. Each part's rigid motion per frame is
// the best fit (Horn's quaternion method) of its vertices away from the cuts, and each joint
// is the point two neighbouring parts carry along together most closely over the whole
// sequence. What comes out is a transform per part per frame and a rest position per joint.
import { readFileSync, readdirSync } from "node:fs";

const dir = process.argv[2];
const count = readdirSync(dir).filter(f => /^shell\d+\.obj$/.test(f)).length;
const frames = Array.from({ length: count }, (_, i) => load(`${dir}/shell${i}.obj`));
const rest = frames[0];

// Body parts in the T-pose, by region; `core` keeps vertices clear of the cuts for fitting.
const side = (p, s) => Math.sign(p[0]) === s;
const PARTS = {
    pelvis: p => p[1] > .74 && p[1] <= .90 && Math.abs(p[0]) <= .16,
    abdomen: p => p[1] > .90 && p[1] <= 1.03 && Math.abs(p[0]) <= .16,
    chest: p => p[1] > 1.03 && p[1] <= 1.26 && Math.abs(p[0]) <= .15,
    head: p => p[1] > 1.26 && Math.abs(p[0]) <= .12,
    ...Object.fromEntries([[1, "l"], [-1, "r"]].flatMap(([s, n]) => [
        [`upper_arm_${n}`, p => side(p, s) && p[1] > 1.0 && Math.abs(p[0]) > .15 && Math.abs(p[0]) <= .34],
        [`forearm_${n}`, p => side(p, s) && p[1] > 1.0 && Math.abs(p[0]) > .34 && Math.abs(p[0]) <= .505],
        [`hand_${n}`, p => side(p, s) && p[1] > 1.0 && Math.abs(p[0]) > .505],
        [`thigh_${n}`, p => side(p, s) && p[1] > .44 && p[1] <= .74],
        [`shin_${n}`, p => side(p, s) && p[1] > .09 && p[1] <= .44],
        [`foot_${n}`, p => side(p, s) && p[1] <= .09],
    ])),
};
const MARGIN = .03;
const core = {};
for (const [name, test] of Object.entries(PARTS)) {
    const inside = rest.map((p, i) => test(p) ? i : -1).filter(i => i >= 0);
    // vertices whose neighbourhood (±margin along each axis) stays in the part
    const strict = inside.filter(i => {
        const p = rest[i];
        for (const d of [[MARGIN, 0, 0], [-MARGIN, 0, 0], [0, MARGIN, 0], [0, -MARGIN, 0]]) {
            if (!test([p[0] + d[0], p[1] + d[1], p[2] + d[2]])) return false;
        }
        return true;
    });
    core[name] = strict.length >= 20 ? strict : inside;
}

// Joints between parts, each with a guess the least-squares fit is pulled towards: hinges
// (knees, elbows) leave their position along the axis undetermined.
const JOINTS = {
    waist: ["pelvis", "abdomen", [0, .90, -.03]],
    ribs: ["abdomen", "chest", [0, 1.03, -.02]],
    neck: ["chest", "head", [0, 1.27, -.05]],
    ...Object.fromEntries([[1, "l"], [-1, "r"]].flatMap(([s, n]) => [
        [`shoulder_${n}`, ["chest", `upper_arm_${n}`, [s * .15, 1.22, -.07]]],
        [`elbow_${n}`, [`upper_arm_${n}`, `forearm_${n}`, [s * .34, 1.215, -.06]]],
        [`wrist_${n}`, [`forearm_${n}`, `hand_${n}`, [s * .505, 1.215, .025]]],
        [`hip_${n}`, ["pelvis", `thigh_${n}`, [s * .08, .80, -.04]]],
        [`knee_${n}`, [`thigh_${n}`, `shin_${n}`, [s * .055, .44, -.035]]],
        [`ankle_${n}`, [`shin_${n}`, `foot_${n}`, [s * .05, .08, -.03]]],
    ])),
};

const names = Object.keys(PARTS);
const motion = frames.map(frame => names.map(name => fit(core[name], rest, frame)));
const joints = {};
for (const [joint, [a, b, guess]] of Object.entries(JOINTS)) {
    joints[joint] = { parts: [a, b], rest: centre(names.indexOf(a), names.indexOf(b), guess) };
}
// Extra points along a part that the mannequin is drawn to: the head's crown, the hands' tips,
// and the middle of the toes (the front few centimetres of each foot).
const tip = (name, pick) => {
    const pts = core[name].map(i => rest[i]);
    return pts.reduce((best, p) => pick(p) > pick(best) ? p : best);
};
const front = (name, depth) => {
    const pts = core[name].map(i => rest[i]), z = Math.max(...pts.map(p => p[2]));
    const near = pts.filter(p => p[2] > z - depth);
    return [0, 1, 2].map(k => near.reduce((s, p) => s + p[k], 0) / near.length);
};
const centroid = name => [0, 1, 2].map(k => core[name].reduce((s, i) => s + rest[i][k], 0) / core[name].length);
const points = {
    crown: { part: "head", rest: [0, Math.max(...rest.map(p => p[1])), centroid("head")[2]] },
    pelvis_centre: { part: "pelvis", rest: centroid("pelvis") },
    abdomen_centre: { part: "abdomen", rest: centroid("abdomen") },
    chest_centre: { part: "chest", rest: centroid("chest") },
    head_centre: { part: "head", rest: centroid("head") },
    ...Object.fromEntries([[1, "l"], [-1, "r"]].flatMap(([s, n]) => [
        [`hand_tip_${n}`, { part: `hand_${n}`, rest: tip(`hand_${n}`, p => s * p[0]) }],
        [`toe_${n}`, { part: `foot_${n}`, rest: front(`foot_${n}`, .04) }],
    ])),
};

const round = x => Math.round(x * 1e4) / 1e4;
console.log(JSON.stringify({
    source: "C-IPC Rumba_Dancing (Li, Kaufman and Jiang 2021), github.com/ipc-sim/Codim-IPC, Apache-2.0; derived by tools/derive_rumba_track.mjs",
    seconds_per_frame: .04,
    parts: names,
    joints: Object.fromEntries(Object.entries(joints).map(([k, j]) => [k, { parts: j.parts, rest: j.rest.map(round) }])),
    points: Object.fromEntries(Object.entries(points).map(([k, p]) => [k, { part: p.part, rest: p.rest.map(round) }])),
    // per frame, per part: translation then rotation quaternion, taking rest-pose points to the frame
    frames: motion.map(parts => parts.flatMap(({ t, q }) => [...t, ...q].map(round))),
}));

function load(file) {
    const v = [];
    for (const line of readFileSync(file, "utf8").split("\n")) {
        if (line.startsWith("v ")) v.push(line.trim().split(/\s+/).slice(1, 4).map(Number));
    }
    return v;
}

// Rigid fit x' = R x + t of the indexed points, by Horn's closed form.
function fit(index, from, to) {
    const a = [0, 0, 0], b = [0, 0, 0];
    for (const i of index) for (let k = 0; k < 3; k++) { a[k] += from[i][k] / index.length; b[k] += to[i][k] / index.length; }
    const S = [[0, 0, 0], [0, 0, 0], [0, 0, 0]];
    for (const i of index) {
        for (let r = 0; r < 3; r++) for (let c = 0; c < 3; c++) S[r][c] += (from[i][r] - a[r]) * (to[i][c] - b[c]);
    }
    const [[xx, xy, xz], [yx, yy, yz], [zx, zy, zz]] = S;
    const N = [
        [xx + yy + zz, yz - zy, zx - xz, xy - yx],
        [yz - zy, xx - yy - zz, xy + yx, zx + xz],
        [zx - xz, xy + yx, -xx + yy - zz, yz + zy],
        [xy - yx, zx + xz, yz + zy, -xx - yy + zz],
    ];
    const [w, x, y, z] = largestEigenvector(N);
    const q = [x, y, z, w];
    const Ra = rotate(q, a);
    return { q, t: [b[0] - Ra[0], b[1] - Ra[1], b[2] - Ra[2]] };
}

// The rest-pose point both parts carry to the same place, over every frame, pulled towards a guess.
function centre(ia, ib, guess) {
    const M = [[0, 0, 0], [0, 0, 0], [0, 0, 0]], v = [0, 0, 0], lambda = .02 * frames.length;
    for (const parts of motion) {
        const A = matrix(parts[ia].q), B = matrix(parts[ib].q);
        const D = A.map((row, r) => row.map((x, c) => x - B[r][c]));
        const e = [0, 1, 2].map(k => parts[ib].t[k] - parts[ia].t[k]);
        for (let r = 0; r < 3; r++) for (let c = 0; c < 3; c++) {
            for (let k = 0; k < 3; k++) M[r][c] += D[k][r] * D[k][c];
        }
        for (let r = 0; r < 3; r++) for (let k = 0; k < 3; k++) v[r] += D[k][r] * e[k];
    }
    for (let k = 0; k < 3; k++) { M[k][k] += lambda; v[k] += lambda * guess[k]; }
    return solve3(M, v);
}

function largestEigenvector(N) {
    // Jacobi rotations on a symmetric 4x4
    const A = N.map(r => r.slice()), V = [[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]];
    for (let sweep = 0; sweep < 50; sweep++) {
        for (let p = 0; p < 3; p++) for (let q = p + 1; q < 4; q++) {
            if (Math.abs(A[p][q]) < 1e-15) continue;
            const theta = (A[q][q] - A[p][p]) / (2 * A[p][q]);
            const t = Math.sign(theta || 1) / (Math.abs(theta) + Math.sqrt(theta * theta + 1));
            const c = 1 / Math.sqrt(t * t + 1), s = t * c;
            for (let k = 0; k < 4; k++) {
                const akp = A[k][p], akq = A[k][q];
                A[k][p] = c * akp - s * akq; A[k][q] = s * akp + c * akq;
            }
            for (let k = 0; k < 4; k++) {
                const apk = A[p][k], aqk = A[q][k];
                A[p][k] = c * apk - s * aqk; A[q][k] = s * apk + c * aqk;
            }
            for (let k = 0; k < 4; k++) {
                const vkp = V[k][p], vkq = V[k][q];
                V[k][p] = c * vkp - s * vkq; V[k][q] = s * vkp + c * vkq;
            }
        }
    }
    let best = 0;
    for (let k = 1; k < 4; k++) if (A[k][k] > A[best][best]) best = k;
    const e = [V[0][best], V[1][best], V[2][best], V[3][best]];
    const l = Math.hypot(...e) * (e[0] < 0 ? -1 : 1);
    return e.map(x => x / l);
}

function rotate(q, v) {
    const [x, y, z, w] = q;
    const tx = 2 * (y * v[2] - z * v[1]), ty = 2 * (z * v[0] - x * v[2]), tz = 2 * (x * v[1] - y * v[0]);
    return [v[0] + w * tx + y * tz - z * ty, v[1] + w * ty + z * tx - x * tz, v[2] + w * tz + x * ty - y * tx];
}

function matrix(q) {
    return [[1, 0, 0], [0, 1, 0], [0, 0, 1]].map(axis => rotate(q, axis)).reduce((m, col, c) => {
        for (let r = 0; r < 3; r++) m[r][c] = col[r];
        return m;
    }, [[0, 0, 0], [0, 0, 0], [0, 0, 0]]);
}

function solve3(M, v) {
    const det = m => m[0][0] * (m[1][1] * m[2][2] - m[1][2] * m[2][1]) - m[0][1] * (m[1][0] * m[2][2] - m[1][2] * m[2][0]) + m[0][2] * (m[1][0] * m[2][1] - m[1][1] * m[2][0]);
    const d = det(M);
    return [0, 1, 2].map(k => det(M.map((row, r) => row.map((x, c) => c === k ? v[r] : x))) / d);
}

# Dance motion credits and terms

The dance is the **Rumba** sequence that C-IPC drives its garments with:

> Minchen Li, Danny M. Kaufman and Chenfanfu Jiang. *Codimensional Incremental Potential Contact.*
> ACM Transactions on Graphics 40(4), SIGGRAPH 2021. Figure 5.

The source is `Projects/FEMShell/input/Rumba_Dancing` in the Codim-IPC repository,
https://github.com/ipc-sim/Codim-IPC: 121 frames, 0.04 s apart, of the `wm2_15k` mannequin
mesh. The repository is licensed under the Apache License 2.0, included here as
`LICENSE-Codim-IPC.txt`. Neither the repository nor the paper says where the motion itself was
captured or authored.

**Changes.** `src/rumba-track.json` is not the mesh sequence. `tools/derive_rumba_track.mjs`
reduces it to a rigid transform per body part per frame, and a rest position per joint; no
mesh vertices are kept. The example draws its own wooden mannequin from those joints, and plays
frames 0-40 once and then repeats frames 40-104 with a blend at the seam.

<!doctype html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width, initial-scale=1">
  <meta name="robots" content="noindex">
  <link rel="icon" href="data:,">
  <title>Rumba skirt · Meep</title>
  <style>
    * { box-sizing: border-box; }
    html, body { margin: 0; width: 100%; height: 100%; overflow: hidden; background: #080c16; color: #edf3ff; font: 14px system-ui, sans-serif; }
    .panel { position: fixed; z-index: 100; left: 20px; bottom: 20px; padding: 12px; background: #080c16de; border: 1px solid #29344b; border-radius: 14px; backdrop-filter: blur(12px); }
    fieldset { border: 0; padding: 0; margin: 0; }
    button { background: #23314a; color: inherit; border: 1px solid #465675; padding: 7px 16px; border-radius: 8px; cursor: pointer; }
    button:focus-visible { outline: 2px solid #6bedc2; outline-offset: 3px; }
    :disabled { opacity: .5; }
    .hint { position: fixed; z-index: 100; bottom: 20px; right: 20px; margin: 0; color: #a8b6cd; font-size: 12px; pointer-events: none; }
    @media (max-width: 650px) { .panel { left: 10px; bottom: 10px; } .hint { display: none; } }
  </style>
</head>
<body>
  <section class="panel" aria-label="Rumba skirt controls">
    <fieldset disabled>
      <button id="pause" type="button" aria-pressed="false">Pause</button>
    </fieldset>
  </section>
  <p class="hint">Drag to orbit · Scroll to zoom</p>
  <script type="module" src="./src/main.js"></script>
</body>
</html>

{
  "name": "@meep-examples/cloth-skirt",
  "version": "0.1.0",
  "private": true,
  "type": "module",
  "description": "A circle skirt on a mannequin dancing the rumba step from the C-IPC garment tests.",
  "scripts": {
    "dev": "vite",
    "build": "vite build",
    "preview": "vite preview"
  },
  "dependencies": {
    "@woosh/meep-engine": "3.55.0"
  },
  "devDependencies": {
    "@rollup/plugin-strip": "^3.0.4",
    "vite": "^8.0.13"
  }
}

# Rumba skirt

A wooden mannequin dances the rumba step that C-IPC (Li, Kaufman and Jiang, SIGGRAPH 2021, Figure 5) drives its garments with, wearing a circle skirt. The skirt swings with the hips and flutes at the hem as the weight moves from foot to foot.

Run `npm ci` and `npm run dev`, then open `/demo.html`. Build with `npm run build`.

**The dance.** `src/rumba-track.json` holds a rigid transform per body part per frame, 25 frames a second, derived from C-IPC's mesh sequence by `tools/derive_rumba_track.mjs`; credits and terms are in `ASSET-LICENSES.md`. The sequence starts in the T-pose C-IPC drapes its garments on and lowers the arms (frames 0-40), then dances the step (40-104). The demo plays the lowering once and repeats the step, blending its last frames into its first.

**The skirt** is cut as a circle skirt: a flat ring of 13 rings from waistband to hem, 37.5 mm apart, and `ClothSystem` simulates it. The ring is meshed as a near-square lattice: each ring has as many vertices as make its edges about 37.5 mm long too, 17 round the waistband and 92 at the hem, 708 in all, and neighbouring rings are joined by triangles that walk both rings in angle. `src/sheet.js` builds it in code as a skinned model with one joint per vertex. `cloth_proxy_from_mesh` turns the joints and triangles into a cloth proxy: a hard stretch row per edge and a hinge per interior edge, with rest lengths and a flat rest shape taken from the pattern. A `Cloth` and a `ClothRig` go on the skirt's entity. The skirt starts as the flat ring, level with the natural waist, and falls from its waistband while the mannequin lowers its arms. The hem has more fabric than the hanging skirt has room for, so it falls into flutes. A `ClothPin` on the abdomen's collider entity holds the 17 waistband vertices where they start and carries them through the dance.

**Colliders** move with the body: capsules across the hips, abdomen and chest, so the skirt cannot pass through the waist or fold up into the torso; capsules along the thighs, shins, forearms and hands; spheres at the knees. Each is a mannequin part that also carries a `Collider` and a `ClothCollider`, so placing the part moves the collider, and `ClothSystem` sweeps it from its previous pose so a fast limb does not pass through the fabric.

The fabric is bend 0.63 and damping 0.0125 on `ClothDynamics`' normalised scales, 6 mm thick, 2 substeps × 4 iterations a step, self-collision on. Self-collision gives each vertex a radius of its own, half its shortest edge, capped below the closest vertex it shares no row with, and holds two vertices apart by the sum of their radii. That is why the lattice is near-square: on this one every edge is about 37.5 mm, so every vertex gets about 18 mm and the fabric is covered evenly. With the same count on every ring the cells would be long one way and short the other, a quarter as wide as they are tall at the waist, and a vertex's radius would follow its short edge and leave the long way open. Every particle has the same mass, and with cells of one size each one stands for the same area of fabric.

`src/dancer.js` samples the track and places the mannequin and its colliders. `src/main.js` sets up the scene. `src/scene.js` boots the engine, and holds the cloth until a frame showing the scene has finished on the GPU.

import { defineConfig } from "vite";
import { copyFileSync, existsSync, mkdirSync } from "node:fs";
import { fileURLToPath } from "node:url";
import { resolve, dirname } from "node:path";

import strip from "@rollup/plugin-strip";

const __dirname = dirname(fileURLToPath(import.meta.url));

export default defineConfig({
  root: __dirname,
  publicDir: false,
  // Keep the engine's imported asset URLs intact during development.
  optimizeDeps: {
    exclude: ["@woosh/meep-engine"],
    include: ["dat.gui", "opentype.js"],
  },
  plugins: [
    {
      name: "copy-thumbnail",
      apply: "build",
      closeBundle() {
        const thumb = resolve(__dirname, "thumbnail.png");
        const dst = resolve(__dirname, "../../public/examples/cloth-skirt");
        if (existsSync(thumb)) {
          mkdirSync(dst, { recursive: true });
          copyFileSync(thumb, resolve(dst, "thumbnail.png"));
        }
      },
    },
  ],
  base: "./",
  build: {
    outDir: resolve(__dirname, "../../public/examples/cloth-skirt"),
    emptyOutDir: false,
    rollupOptions: {
      input: resolve(__dirname, "demo.html"),
      plugins: [
        {
          ...strip(),
          apply: 'build'
        }
      ],
    },
    target: "es2022",
  },
});