README.md

@@ -10,7 +10,9 @@ A player emote library for Saturn Client, with limb bending.
   version with [Stonecutter](https://stonecutter.kikugie.dev/) and published as
   `org.saturnclient:emotes-fabric:<version>+<mc>`, with `core` bundled inside the jar.
 - `src/testmod/`: a dev-only tester mod that is never published. It adds `/emotes play <name>`,
-  `/emotes stop` and `/emotes info`. Press F5 to see yourself.
+  `/emotes stop` and `/emotes info`. Press F5 to see yourself. It also has a Fabric client gametest
+  that creates a world and screenshots each animation from the front and side, into
+  `versions/<mc>/build/run/clientGameTest/screenshots/`.
 
 Supported versions: 1.21.4 to 1.21.11, the same range as Saturn Client. Each version's Fabric API
 version is set in `stonecutter.properties.toml`. The code uses Mojang mappings.
@@ -22,22 +24,41 @@ version is set in `stonecutter.properties.toml`. The code uses Mojang mappings.
    and the armor layers both go through this method, so armor follows the pose.
 
 Both hook points exist unchanged in every supported version. Version-specific code goes behind
-Stonecutter comments:
+Stonecutter comments, like the vertex accessors in `BentCubeRenderer`:
 
 ```java
 //? if >=1.21.9 {
-import net.minecraft.client.renderer.entity.state.AvatarRenderState;
+return new float[] { vertex.x(), vertex.y(), vertex.z(), vertex.u(), vertex.v() };
 //?} else
-/*import net.minecraft.client.renderer.entity.state.PlayerRenderState;*/
+/*return new float[] { vertex.pos().x(), vertex.pos().y(), vertex.pos().z(), vertex.u(), vertex.v() };*/
 ```
 
-Bending (`BoneTransform.bend` / `bendAxis`) is part of the model but isn't rendered yet.
+## Bending
+
+Each limb bends along a single axis (`BoneTransform.bend`, `bendAxis`). It works like the cloak
+renderer: build a spine, put a ring of shared vertices along it, and draw the faces between the rings.
+
+- `LimbBend` (core) runs the spine along a cubic Bézier (`Bezier`). The control points are the rigid
+  "upper half, joint, lower half" shape, and `sharpness` goes from a round curve (0) to a tight joint
+  (1). The spine is cut into one ring per texture row (12 per limb), spaced evenly by arc length, so
+  the limb keeps its length. Each ring moves its cross-section rigidly, so neighbouring pieces share
+  vertices and the mesh stays closed.
+- `QuadSplitter` (core) cuts each vanilla face into strips at the rings and splits its UVs to match.
+  The texture is unchanged apart from the cuts.
+- `ModelPartMixin` swaps in `BentCubeRenderer` for any part with a bend. That renderer deforms
+  vanilla's own cubes, so slim arms, sleeves, pants and armor all work. Overlays and armor use the
+  limb's spine, not their own inflated box, so they stay attached.
+
+Axis 0 folds towards the front (-Z) and PI/2 towards +X, in the limb's own space. Knees fold back,
+so they use axis PI. The body bends too, but the head and arms don't follow its upper half yet.
+Held items still attach to the unbent arm.
 
 ## Commands
 
 ```sh
 ./gradlew :core:test                      # core unit tests
 ./gradlew :1.21.11:runTestmodClient       # launch the game with the tester (run dir: ./run)
+./gradlew :1.21.11:runClientGameTest      # screenshot each test animation, then quit
 ./gradlew :1.21.4:compileTestmodJava      # quick compile check for one version
 ./gradlew buildAll                        # every version's jar → build/libs/<version>/
 GITEA_TOKEN=... ./gradlew publish         # publish core + every version to Gitea

build.gradle.kts

@@ -33,6 +33,13 @@ loom {
         options.put("mark-corresponding-synthetics", "1") // Names lambdas, useful for mixins
     }
 
+    runConfigs.all {
+        preferGradleTask = true
+        generateRunConfig = true
+        runDirectory = rootProject.file("run") // Shared by every version
+        jvmArguments.add("-Dmixin.debug.export=true")
+    }
+
     runs {
         // ./gradlew :<mc>:runTestmodClient launches the game with the tester mod loaded.
         register("testmodClient") {
@@ -40,13 +47,15 @@ loom {
             name = "Testmod Client"
             source(testmod)
         }
-    }
 
-    runConfigs.all {
-        preferGradleTask = true
-        generateRunConfig = true
-        runDirectory = rootProject.file("run") // Shared by every version
-        jvmArguments.add("-Dmixin.debug.export=true")
+        // ./gradlew :<mc>:runClientGameTest screenshots the test animations, then quits.
+        register("clientGameTest") {
+            client()
+            name = "Client Game Test"
+            source(testmod)
+            vmArg("-Dfabric.client.gametest")
+            runDir = "build/run/clientGameTest"
+        }
     }
 }
 
@@ -65,7 +74,12 @@ dependencies {
     api(project(":core"))
     include(project(":core"))
 
-    "modTestmodImplementation"(fabricApi.module("fabric-command-api-v2", sc.properties["deps.fabric_api"]))
+    for (module in listOf("fabric-command-api-v2", "fabric-client-gametest-api-v1")) {
+        "modTestmodImplementation"(fabricApi.module(module, sc.properties["deps.fabric_api"]))
+    }
+    // Single modules don't bring their Fabric API dependencies (which differ between versions),
+    // so the tester runs with all of Fabric API.
+    "modTestmodRuntimeOnly"("net.fabricmc.fabric-api:fabric-api:${sc.properties.get<String>("deps.fabric_api")}")
 }
 
 java {

core/src/main/java/org/saturnclient/emotes/core/bend/Bezier.java

@@ -0,0 +1,51 @@
+package org.saturnclient.emotes.core.bend;
+
+import java.util.List;
+
+/** A Bézier curve of any degree, evaluated with De Casteljau's algorithm. */
+public final class Bezier {
+    private final Vec3[] points;
+
+    public Bezier(List<Vec3> controlPoints) {
+        if (controlPoints.size() < 2) {
+            throw new IllegalArgumentException("A Bézier curve needs at least two control points");
+        }
+        this.points = controlPoints.toArray(Vec3[]::new);
+    }
+
+    public static Bezier of(Vec3... controlPoints) {
+        return new Bezier(List.of(controlPoints));
+    }
+
+    public int degree() {
+        return points.length - 1;
+    }
+
+    public List<Vec3> controlPoints() {
+        return List.of(points);
+    }
+
+    /** The point at {@code t} in [0, 1]. */
+    public Vec3 point(float t) {
+        return deCasteljau(points, t);
+    }
+
+    /** The first derivative at {@code t}: the tangent, scaled by the curve's speed. */
+    public Vec3 derivative(float t) {
+        Vec3[] hodograph = new Vec3[points.length - 1];
+        for (int i = 0; i < hodograph.length; i++) {
+            hodograph[i] = points[i + 1].sub(points[i]).scale(degree());
+        }
+        return deCasteljau(hodograph, t);
+    }
+
+    private static Vec3 deCasteljau(Vec3[] controlPoints, float t) {
+        Vec3[] work = controlPoints.clone();
+        for (int level = work.length - 1; level > 0; level--) {
+            for (int i = 0; i < level; i++) {
+                work[i] = work[i].lerp(work[i + 1], t);
+            }
+        }
+        return work[0];
+    }
+}

core/src/main/java/org/saturnclient/emotes/core/bend/LimbBend.java

@@ -0,0 +1,195 @@
+package org.saturnclient.emotes.core.bend;
+
+/**
+ * Bends one limb along a single axis, the way an elbow or knee folds.
+ *
+ * <p>Coordinates are the limb's model space in pixels: the limb hangs along +Y from {@code start}
+ * to {@code end}, and its front faces -Z. At rest, the spine runs down the limb's center (x = z = 0).
+ * When bent, the spine follows a cubic Bézier curve whose control polygon is the rigid "upper half,
+ * joint, lower half" shape, so the upper and lower halves stay nearly straight and the joint curves.
+ *
+ * <p>The spine is split into {@code segments} rings, spaced evenly by arc length so the limb keeps its
+ * length and each piece covers the same texture rows as before. Each ring moves its cross-section
+ * rigidly, so neighbouring pieces share their vertices and the mesh stays closed however far it bends.
+ */
+public final class LimbBend {
+    /** Samples used to measure the curve's arc length. */
+    private static final int ARC_SAMPLES = 64;
+
+    private final float start;
+    private final float length;
+    private final int segments;
+    private final float angle;
+    /** Unit bend direction D in the XZ plane, and the rotation axis n = Y × D. */
+    private final float dirX, dirZ;
+    private final float axisX, axisZ;
+
+    /** Ring centers and their rotation around n, for rings 0..segments. */
+    private final float[] ringX, ringY, ringZ, ringAngle;
+
+    /**
+     * @param start     top of the limb (its pivot end), along Y
+     * @param end       bottom of the limb, along Y
+     * @param angle     how far the lower half folds, in radians
+     * @param axis      direction the limb folds towards, as an angle around the limb: 0 folds to the
+     *                  front (-Z) and PI/2 folds to +X
+     * @param sharpness 0 for a long, round curve (a quadratic Bézier) up to 1 for a tight joint
+     * @param segments  number of pieces the limb is divided into
+     */
+    public LimbBend(float start, float end, float angle, float axis, float sharpness, int segments) {
+        if (end <= start) {
+            throw new IllegalArgumentException("end must be below start");
+        }
+        if (segments < 1) {
+            throw new IllegalArgumentException("segments must be at least 1");
+        }
+        this.start = start;
+        this.length = end - start;
+        this.segments = segments;
+        this.angle = angle;
+        this.dirX = (float) Math.sin(axis);
+        this.dirZ = (float) -Math.cos(axis);
+        // n = Y × D = (0, 1, 0) × (dirX, 0, dirZ)
+        this.axisX = dirZ;
+        this.axisZ = -dirX;
+
+        ringX = new float[segments + 1];
+        ringY = new float[segments + 1];
+        ringZ = new float[segments + 1];
+        ringAngle = new float[segments + 1];
+
+        if (isStraight()) {
+            for (int i = 0; i <= segments; i++) {
+                ringY[i] = start + length * i / segments;
+            }
+            return;
+        }
+        buildRings(spine(Math.max(0, Math.min(1, sharpness))));
+    }
+
+    /** Whether the limb is (close enough to) unbent. Straight limbs can be drawn as they are. */
+    public boolean isStraight() {
+        return Math.abs(angle) < 1e-4f;
+    }
+
+    public int segments() {
+        return segments;
+    }
+
+    /** Y positions where the limb is cut into pieces, not counting its ends. */
+    public float[] cuts() {
+        float[] cuts = new float[segments - 1];
+        for (int i = 1; i < segments; i++) {
+            cuts[i - 1] = start + length * i / segments;
+        }
+        return cuts;
+    }
+
+    private Bezier spine(float sharpness) {
+        float half = length / 2;
+        Vec3 top = new Vec3(0, start, 0);
+        Vec3 joint = new Vec3(0, start + half, 0);
+        Vec3 lower = new Vec3(dirX * (float) Math.sin(angle), (float) Math.cos(angle), dirZ * (float) Math.sin(angle));
+        Vec3 bottom = joint.add(lower.scale(half));
+        // At sharpness 0 this is the quadratic (top, joint, bottom) raised to a cubic.
+        float pull = 2f / 3 + sharpness / 3;
+        return Bezier.of(top, top.lerp(joint, pull), bottom.lerp(joint, pull), bottom);
+    }
+
+    private void buildRings(Bezier curve) {
+        // Arc length table, so rings can be spaced evenly along the curve.
+        float[] ts = new float[ARC_SAMPLES + 1];
+        float[] lengths = new float[ARC_SAMPLES + 1];
+        Vec3 previous = curve.point(0);
+        for (int i = 1; i <= ARC_SAMPLES; i++) {
+            ts[i] = (float) i / ARC_SAMPLES;
+            Vec3 point = curve.point(ts[i]);
+            lengths[i] = lengths[i - 1] + point.sub(previous).length();
+            previous = point;
+        }
+        // The curve cuts the corner, so it's shorter than the limb. Scale it about the top to fit.
+        float scale = length / lengths[ARC_SAMPLES];
+        Vec3 top = curve.point(0);
+        Vec3 dir = new Vec3(dirX, 0, dirZ);
+
+        int sample = 0;
+        for (int i = 0; i <= segments; i++) {
+            float target = lengths[ARC_SAMPLES] * i / segments;
+            while (sample < ARC_SAMPLES - 1 && lengths[sample + 1] < target) {
+                sample++;
+            }
+            float span = lengths[sample + 1] - lengths[sample];
+            float f = span > 0 ? (target - lengths[sample]) / span : 0;
+            float t = ts[sample] + (ts[sample + 1] - ts[sample]) * f;
+
+            Vec3 center = top.add(curve.point(t).sub(top).scale(scale));
+            Vec3 tangent = curve.derivative(t);
+            ringX[i] = center.x();
+            ringY[i] = center.y();
+            ringZ[i] = center.z();
+            ringAngle[i] = (float) Math.atan2(tangent.dot(dir), tangent.y());
+        }
+    }
+
+    /**
+     * Moves a point from the straight limb onto the bent one. Points above or below the limb follow
+     * the end rings' tangents, so overlay layers and armor that stick out past the limb stay attached.
+     *
+     * @param out receives the bent position as {x, y, z}
+     */
+    public void bendPoint(float x, float y, float z, float[] out) {
+        float along = (y - start) / length * segments;
+        int ring;
+        float f;
+        float extra = 0;
+        if (along <= 0) {
+            ring = 0;
+            f = 0;
+            extra = y - start;
+        } else if (along >= segments) {
+            ring = segments - 1;
+            f = 1;
+            extra = y - (start + length);
+        } else {
+            ring = Math.min((int) along, segments - 1);
+            f = along - ring;
+        }
+
+        float cx = lerp(ringX[ring], ringX[ring + 1], f);
+        float cy = lerp(ringY[ring], ringY[ring + 1], f);
+        float cz = lerp(ringZ[ring], ringZ[ring + 1], f);
+        float a = lerp(ringAngle[ring], ringAngle[ring + 1], f);
+
+        // The cross-section offset (x, extra, z) rotates with the ring. Past the ends, "extra"
+        // carries on along the end tangent.
+        rotate(x, extra, z, a, out);
+        out[0] += cx;
+        out[1] += cy;
+        out[2] += cz;
+    }
+
+    /** Rotates a direction (a face normal) the same way {@link #bendPoint} rotates points at {@code atY}. */
+    public void bendDirection(float atY, float nx, float ny, float nz, float[] out) {
+        float along = Math.max(0, Math.min(segments, (atY - start) / length * segments));
+        int ring = Math.min((int) along, segments - 1);
+        rotate(nx, ny, nz, lerp(ringAngle[ring], ringAngle[ring + 1], along - ring), out);
+    }
+
+    /** Rodrigues' rotation of v around the bend axis n by {@code a}. */
+    private void rotate(float x, float y, float z, float a, float[] out) {
+        float cos = (float) Math.cos(a);
+        float sin = (float) Math.sin(a);
+        // n = (axisX, 0, axisZ)
+        float crossX = -axisZ * y;
+        float crossY = axisZ * x - axisX * z;
+        float crossZ = axisX * y;
+        float dot = axisX * x + axisZ * z;
+        out[0] = x * cos + crossX * sin + axisX * dot * (1 - cos);
+        out[1] = y * cos + crossY * sin;
+        out[2] = z * cos + crossZ * sin + axisZ * dot * (1 - cos);
+    }
+
+    private static float lerp(float a, float b, float t) {
+        return a + (b - a) * t;
+    }
+}

core/src/main/java/org/saturnclient/emotes/core/bend/QuadSplitter.java

@@ -0,0 +1,71 @@
+package org.saturnclient.emotes.core.bend;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Cuts the faces of a box into horizontal strips so they can bend.
+ *
+ * <p>A quad is four vertices of {x, y, z, u, v}. Faces that run along Y (the sides of a limb) are cut
+ * at every Y in {@code cuts}, and each strip's UVs are interpolated along the face, so the strips
+ * together cover the same texture as the original face. Flat faces (the limb's ends) are kept as they
+ * are. Strips keep the original winding.
+ */
+public final class QuadSplitter {
+    private static final float EPSILON = 1e-4f;
+
+    private QuadSplitter() {
+    }
+
+    public static List<float[][]> split(float[][] quad, float[] cuts) {
+        float minY = Float.MAX_VALUE;
+        float maxY = -Float.MAX_VALUE;
+        for (float[] vertex : quad) {
+            minY = Math.min(minY, vertex[1]);
+            maxY = Math.max(maxY, vertex[1]);
+        }
+        if (maxY - minY < EPSILON) {
+            return List.<float[][]>of(quad);
+        }
+
+        // Each vertex's partner is its neighbour at the other end of the face's vertical edge.
+        int[] partner = new int[4];
+        for (int i = 0; i < 4; i++) {
+            int next = (i + 1) % 4;
+            int prev = (i + 3) % 4;
+            partner[i] = Math.abs(quad[next][1] - quad[i][1]) > EPSILON ? next : prev;
+        }
+
+        List<Float> bounds = new ArrayList<>();
+        bounds.add(minY);
+        for (float cut : cuts) {
+            if (cut > minY + EPSILON && cut < maxY - EPSILON) {
+                bounds.add(cut);
+            }
+        }
+        bounds.add(maxY);
+
+        List<float[][]> strips = new ArrayList<>(bounds.size() - 1);
+        for (int s = 0; s + 1 < bounds.size(); s++) {
+            float top = bounds.get(s);
+            float bottom = bounds.get(s + 1);
+            float[][] strip = new float[4][];
+            for (int i = 0; i < 4; i++) {
+                float[] from = quad[i];
+                float[] to = quad[partner[i]];
+                float target = from[1] < to[1] ? top : bottom;
+                strip[i] = lerp(from, to, (target - from[1]) / (to[1] - from[1]));
+            }
+            strips.add(strip);
+        }
+        return strips;
+    }
+
+    private static float[] lerp(float[] a, float[] b, float t) {
+        float[] out = new float[a.length];
+        for (int i = 0; i < a.length; i++) {
+            out[i] = a[i] + (b[i] - a[i]) * t;
+        }
+        return out;
+    }
+}

core/src/main/java/org/saturnclient/emotes/core/bend/Vec3.java

@@ -0,0 +1,39 @@
+package org.saturnclient.emotes.core.bend;
+
+/** A small immutable 3D vector, in model pixels. */
+public record Vec3(float x, float y, float z) {
+    public static final Vec3 ZERO = new Vec3(0, 0, 0);
+
+    public Vec3 add(Vec3 o) {
+        return new Vec3(x + o.x, y + o.y, z + o.z);
+    }
+
+    public Vec3 sub(Vec3 o) {
+        return new Vec3(x - o.x, y - o.y, z - o.z);
+    }
+
+    public Vec3 scale(float s) {
+        return new Vec3(x * s, y * s, z * s);
+    }
+
+    public Vec3 lerp(Vec3 o, float t) {
+        return new Vec3(x + (o.x - x) * t, y + (o.y - y) * t, z + (o.z - z) * t);
+    }
+
+    public float dot(Vec3 o) {
+        return x * o.x + y * o.y + z * o.z;
+    }
+
+    public Vec3 cross(Vec3 o) {
+        return new Vec3(y * o.z - z * o.y, z * o.x - x * o.z, x * o.y - y * o.x);
+    }
+
+    public float length() {
+        return (float) Math.sqrt(dot(this));
+    }
+
+    public Vec3 normalize() {
+        float length = length();
+        return length < 1e-7f ? ZERO : scale(1 / length);
+    }
+}

core/src/test/java/org/saturnclient/emotes/core/bend/BezierTest.java

@@ -0,0 +1,47 @@
+package org.saturnclient.emotes.core.bend;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
+import org.junit.jupiter.api.Test;
+
+class BezierTest {
+    private static void assertVec(Vec3 expected, Vec3 actual) {
+        assertEquals(expected.x(), actual.x(), 1e-5);
+        assertEquals(expected.y(), actual.y(), 1e-5);
+        assertEquals(expected.z(), actual.z(), 1e-5);
+    }
+
+    @Test
+    void passesThroughEndpoints() {
+        Bezier curve = Bezier.of(new Vec3(0, 0, 0), new Vec3(1, 2, 0), new Vec3(3, 2, 1), new Vec3(4, 0, 2));
+        assertVec(new Vec3(0, 0, 0), curve.point(0));
+        assertVec(new Vec3(4, 0, 2), curve.point(1));
+    }
+
+    @Test
+    void quadraticMidpoint() {
+        Bezier curve = Bezier.of(new Vec3(0, 0, 0), new Vec3(1, 2, 0), new Vec3(2, 0, 0));
+        // B(0.5) = 0.25 P0 + 0.5 P1 + 0.25 P2
+        assertVec(new Vec3(1, 1, 0), curve.point(0.5f));
+    }
+
+    @Test
+    void endTangentsFollowControlPolygon() {
+        Bezier curve = Bezier.of(new Vec3(0, 0, 0), new Vec3(0, 1, 0), new Vec3(1, 1, 0), new Vec3(2, 1, 0));
+        // B'(0) = n (P1 - P0), B'(1) = n (P3 - P2)
+        assertVec(new Vec3(0, 3, 0), curve.derivative(0));
+        assertVec(new Vec3(3, 0, 0), curve.derivative(1));
+    }
+
+    @Test
+    void derivativeMatchesFiniteDifference() {
+        Bezier curve = Bezier.of(new Vec3(0, 0, 0), new Vec3(1, 3, -1), new Vec3(2, -1, 4), new Vec3(5, 2, 0));
+        float t = 0.37f;
+        float h = 1e-3f;
+        Vec3 numeric = curve.point(t + h).sub(curve.point(t - h)).scale(1 / (2 * h));
+        Vec3 exact = curve.derivative(t);
+        assertEquals(exact.x(), numeric.x(), 1e-2);
+        assertEquals(exact.y(), numeric.y(), 1e-2);
+        assertEquals(exact.z(), numeric.z(), 1e-2);
+    }
+}

core/src/test/java/org/saturnclient/emotes/core/bend/LimbBendTest.java

@@ -0,0 +1,113 @@
+package org.saturnclient.emotes.core.bend;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+import org.junit.jupiter.api.Test;
+
+class LimbBendTest {
+    private static final float HALF_PI = (float) (Math.PI / 2);
+
+    /** An arm: pivot at the shoulder, box from y = -2 to 10. */
+    private static LimbBend arm(float angle, float axis) {
+        return new LimbBend(-2, 10, angle, axis, 0.5f, 12);
+    }
+
+    private static float[] bend(LimbBend bend, float x, float y, float z) {
+        float[] out = new float[3];
+        bend.bendPoint(x, y, z, out);
+        return out;
+    }
+
+    private static float distance(float[] a, float[] b) {
+        float dx = a[0] - b[0], dy = a[1] - b[1], dz = a[2] - b[2];
+        return (float) Math.sqrt(dx * dx + dy * dy + dz * dz);
+    }
+
+    @Test
+    void zeroBendLeavesPointsInPlace() {
+        LimbBend straight = arm(0, 0);
+        assertTrue(straight.isStraight());
+        assertArrayEquals(new float[] { 1.5f, 7, -2 }, bend(straight, 1.5f, 7, -2), 1e-5f);
+    }
+
+    @Test
+    void cutsDivideTheLimbEvenly() {
+        float[] cuts = arm(1, 0).cuts();
+        assertEquals(11, cuts.length);
+        assertEquals(-1, cuts[0], 1e-5);
+        assertEquals(9, cuts[10], 1e-5);
+    }
+
+    @Test
+    void topStaysAttachedToThePivot() {
+        LimbBend bend = arm(HALF_PI, 0);
+        assertArrayEquals(new float[] { 2, -2, 2 }, bend(bend, 2, -2, 2), 1e-4f);
+    }
+
+    @Test
+    void spineKeepsItsLength() {
+        LimbBend bend = arm(HALF_PI, 0);
+        float total = 0;
+        float[] previous = bend(bend, 0, -2, 0);
+        for (int i = 1; i <= 12; i++) {
+            float[] point = bend(bend, 0, -2 + i, 0);
+            total += distance(previous, point);
+            previous = point;
+        }
+        // Rings are chords of the curve, so they come out a hair shorter than its arc.
+        assertEquals(12, total, 0.05);
+    }
+
+    @Test
+    void forwardBendMovesTheHandForward() {
+        // Axis 0 folds towards -Z, the front of the model.
+        float[] hand = bend(arm(HALF_PI, 0), 0, 10, 0);
+        assertTrue(hand[2] < -4, "hand should be in front, z = " + hand[2]);
+        assertEquals(0, hand[0], 1e-4);
+    }
+
+    @Test
+    void axisTurnsTheBendDirection() {
+        float[] hand = bend(arm(HALF_PI, HALF_PI), 0, 10, 0);
+        assertTrue(hand[0] > 4, "hand should be towards +X, x = " + hand[0]);
+        assertEquals(0, hand[2], 1e-4);
+    }
+
+    @Test
+    void endPointsFollowTheLowerHalf() {
+        // Past the bottom of the limb, points carry on along the forearm, which points forward at 90°.
+        LimbBend bend = arm(HALF_PI, 0);
+        float[] bottom = bend(bend, 0, 10, 0);
+        float[] below = bend(bend, 0, 11, 0);
+        assertEquals(0, below[1] - bottom[1], 0.05);
+        assertEquals(-1, below[2] - bottom[2], 0.05);
+    }
+
+    @Test
+    void ringsMoveRigidly() {
+        // Every point on one ring keeps its distance from the ring's center.
+        LimbBend bend = arm(1.2f, 0.7f);
+        float[] center = bend(bend, 0, 4, 0);
+        float[] corner = bend(bend, 2, 4, -2);
+        assertEquals(Math.sqrt(8), distance(center, corner), 1e-4);
+    }
+
+    @Test
+    void neighbouringPiecesShareVertices() {
+        // A vertex on a cut is reached the same way from the piece above and the piece below.
+        LimbBend bend = arm(2, 0);
+        float[] fromAbove = bend(bend, 2, 3.99999f, 2);
+        float[] fromBelow = bend(bend, 2, 4.00001f, 2);
+        assertEquals(0, distance(fromAbove, fromBelow), 1e-3);
+    }
+
+    @Test
+    void normalsRotateWithTheLimb() {
+        // The front face's normal (-Z) points up (-Y) on the forearm after a 90° forward bend.
+        float[] normal = new float[3];
+        arm(HALF_PI, 0).bendDirection(10, 0, 0, -1, normal);
+        assertArrayEquals(new float[] { 0, -1, 0 }, normal, 1e-3f);
+    }
+}

core/src/test/java/org/saturnclient/emotes/core/bend/QuadSplitterTest.java

@@ -0,0 +1,67 @@
+package org.saturnclient.emotes.core.bend;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertSame;
+
+import java.util.List;
+
+import org.junit.jupiter.api.Test;
+
+class QuadSplitterTest {
+    // Front face of a 4 x 12 limb from y = 0 to 12, texture rows 20 to 32.
+    private static final float[][] FRONT = {
+            { 2, 0, -2, 8, 20 },
+            { -2, 0, -2, 4, 20 },
+            { -2, 12, -2, 4, 32 },
+            { 2, 12, -2, 8, 32 },
+    };
+
+    private static final float[] CUTS = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 };
+
+    @Test
+    void splitsSideFacesIntoOneStripPerSegment() {
+        List<float[][]> strips = QuadSplitter.split(FRONT, CUTS);
+        assertEquals(12, strips.size());
+        assertArrayEquals(new float[] { 2, 5, -2, 8, 25 }, strips.get(5)[0], 1e-5f);
+        assertArrayEquals(new float[] { -2, 6, -2, 4, 26 }, strips.get(5)[2], 1e-5f);
+    }
+
+    @Test
+    void stripsCoverTheFaceWithoutGaps() {
+        List<float[][]> strips = QuadSplitter.split(FRONT, CUTS);
+        for (int i = 0; i + 1 < strips.size(); i++) {
+            // The bottom edge of one strip is the top edge of the next.
+            assertArrayEquals(strips.get(i)[3], strips.get(i + 1)[0], 1e-5f);
+            assertArrayEquals(strips.get(i)[2], strips.get(i + 1)[1], 1e-5f);
+        }
+    }
+
+    @Test
+    void keepsFlatFaces() {
+        float[][] top = {
+                { 2, 0, -2, 4, 16 },
+                { -2, 0, -2, 8, 16 },
+                { -2, 0, 2, 8, 20 },
+                { 2, 0, 2, 4, 20 },
+        };
+        List<float[][]> strips = QuadSplitter.split(top, CUTS);
+        assertEquals(1, strips.size());
+        assertSame(top, strips.get(0));
+    }
+
+    @Test
+    void overlaysThatStickOutGetShorterEndStrips() {
+        // A sleeve inflated by 0.25 runs from -0.25 to 12.25.
+        float[][] sleeve = {
+                { 2.25f, -0.25f, -2.25f, 48, 36 },
+                { -2.25f, -0.25f, -2.25f, 44, 36 },
+                { -2.25f, 12.25f, -2.25f, 44, 48 },
+                { 2.25f, 12.25f, -2.25f, 48, 48 },
+        };
+        List<float[][]> strips = QuadSplitter.split(sleeve, CUTS);
+        assertEquals(12, strips.size());
+        assertEquals(-0.25f, strips.get(0)[0][1], 1e-5);
+        assertEquals(1, strips.get(0)[3][1], 1e-5);
+    }
+}

src/main/java/org/saturnclient/emotes/fabric/BentCubeRenderer.java

@@ -0,0 +1,66 @@
+package org.saturnclient.emotes.fabric;
+
+import java.util.List;
+
+import org.joml.Matrix4f;
+import org.joml.Vector3f;
+import org.saturnclient.emotes.core.bend.LimbBend;
+import org.saturnclient.emotes.core.bend.QuadSplitter;
+
+import com.mojang.blaze3d.vertex.PoseStack;
+import com.mojang.blaze3d.vertex.VertexConsumer;
+
+import net.minecraft.client.model.geom.ModelPart;
+
+/**
+ * Draws a part's cubes bent. Each vanilla face is cut into strips at the bend's rings (UVs split with
+ * it), and every vertex is moved onto the bent limb. Vertices that were shared stay shared, so the
+ * mesh has no gaps, and the texture is the same as vanilla apart from the cuts.
+ */
+public final class BentCubeRenderer {
+    private BentCubeRenderer() {
+    }
+
+    public static void render(List<ModelPart.Cube> cubes, LimbBend bend, PoseStack.Pose pose,
+            VertexConsumer consumer, int light, int overlay, int color) {
+        Matrix4f matrix = pose.pose();
+        float[] cuts = bend.cuts();
+        float[] bent = new float[3];
+        Vector3f position = new Vector3f();
+        Vector3f normal = new Vector3f();
+
+        for (ModelPart.Cube cube : cubes) {
+            for (ModelPart.Polygon polygon : cube.polygons) {
+                ModelPart.Vertex[] vertices = polygon.vertices();
+                float[][] quad = new float[vertices.length][];
+                for (int i = 0; i < vertices.length; i++) {
+                    quad[i] = vertex(vertices[i]);
+                }
+
+                for (float[][] strip : QuadSplitter.split(quad, cuts)) {
+                    // The strip's normal turns with the ring at its middle. End caps are flat, so theirs
+                    // turns with the end they're at.
+                    float stripY = (strip[0][1] + strip[2][1]) / 2;
+                    bend.bendDirection(stripY, polygon.normal().x(), polygon.normal().y(), polygon.normal().z(),
+                            bent);
+                    pose.transformNormal(normal.set(bent[0], bent[1], bent[2]), normal);
+
+                    for (float[] vertex : strip) {
+                        bend.bendPoint(vertex[0], vertex[1], vertex[2], bent);
+                        matrix.transformPosition(bent[0] / 16, bent[1] / 16, bent[2] / 16, position);
+                        consumer.addVertex(position.x(), position.y(), position.z(), color, vertex[3], vertex[4],
+                                overlay, light, normal.x(), normal.y(), normal.z());
+                    }
+                }
+            }
+        }
+    }
+
+    /** {x, y, z, u, v} in model pixels. */
+    private static float[] vertex(ModelPart.Vertex vertex) {
+        //? if >=1.21.9 {
+        return new float[] { vertex.x(), vertex.y(), vertex.z(), vertex.u(), vertex.v() };
+        //?} else
+        /*return new float[] { vertex.pos().x(), vertex.pos().y(), vertex.pos().z(), vertex.u(), vertex.v() };*/
+    }
+}

src/main/java/org/saturnclient/emotes/fabric/PoseApplier.java

@@ -3,6 +3,8 @@ package org.saturnclient.emotes.fabric;
 import org.saturnclient.emotes.core.Bone;
 import org.saturnclient.emotes.core.BoneTransform;
 import org.saturnclient.emotes.core.Pose;
+import org.saturnclient.emotes.core.bend.LimbBend;
+import org.saturnclient.emotes.fabric.access.BendablePart;
 
 import net.minecraft.client.model.HumanoidModel;
 import net.minecraft.client.model.geom.ModelPart;
@@ -12,12 +14,21 @@ import net.minecraft.client.model.geom.ModelPart;
  * jacket, pants) are children of the base parts, so they follow automatically.
  */
 public final class PoseApplier {
+    /** How tightly joints curve, from 0 (round) to 1 (tight). See {@link LimbBend}. */
+    private static final float SHARPNESS = 0.5f;
+
     private PoseApplier() {
     }
 
     public static void apply(HumanoidModel<?> model, Pose pose) {
-        for (var entry : pose.bones().entrySet()) {
-            apply(part(model, entry.getKey()), entry.getValue());
+        for (Bone bone : Bone.values()) {
+            ModelPart part = part(model, bone);
+            BoneTransform transform = pose.get(bone).orElse(null);
+            if (transform != null) {
+                apply(part, transform);
+            }
+            // Models are shared between entities, so bends from the last one drawn must be cleared.
+            ((BendablePart) (Object) part).saturnEmotes$setBend(bend(bone, transform));
         }
     }
 
@@ -40,6 +51,23 @@ public final class PoseApplier {
         part.xRot = transform.pitch();
         part.yRot = transform.yaw();
         part.zRot = transform.roll();
-        // TODO: bend (transform.bend(), transform.bendAxis()) needs a custom mesh.
+    }
+
+    private static LimbBend bend(Bone bone, BoneTransform transform) {
+        if (transform == null || transform.bend() == 0) {
+            return null;
+        }
+        // Vanilla player limbs, in each part's own space. Armor uses the same ranges so it bends with
+        // the limb instead of along its own (inflated) box.
+        return switch (bone) {
+            case HEAD -> null;
+            case RIGHT_ARM, LEFT_ARM -> limb(-2, 10, transform);
+            case BODY, RIGHT_LEG, LEFT_LEG -> limb(0, 12, transform);
+        };
+    }
+
+    /** One segment per texture row, so each piece keeps a whole row of pixels. */
+    private static LimbBend limb(float start, float end, BoneTransform transform) {
+        return new LimbBend(start, end, transform.bend(), transform.bendAxis(), SHARPNESS, Math.round(end - start));
     }
 }

src/main/java/org/saturnclient/emotes/fabric/access/BendablePart.java

@@ -0,0 +1,13 @@
+package org.saturnclient.emotes.fabric.access;
+
+import org.jetbrains.annotations.Nullable;
+import org.saturnclient.emotes.core.bend.LimbBend;
+
+/** Mixed into ModelPart. A part with a bend draws its cubes bent instead of rigid. */
+public interface BendablePart {
+    @Nullable
+    LimbBend saturnEmotes$getBend();
+
+    /** Sets the bend on this part and all its children (overlay layers like sleeves). */
+    void saturnEmotes$setBend(@Nullable LimbBend bend);
+}

src/main/java/org/saturnclient/emotes/fabric/mixin/HumanoidModelMixin.java

@@ -1,6 +1,5 @@
 package org.saturnclient.emotes.fabric.mixin;
 
-import org.saturnclient.emotes.core.Pose;
 import org.saturnclient.emotes.fabric.PoseApplier;
 import org.saturnclient.emotes.fabric.access.EmotePoseHolder;
 import org.spongepowered.asm.mixin.Mixin;
@@ -21,9 +20,7 @@ public class HumanoidModelMixin {
             method = "setupAnim(Lnet/minecraft/client/renderer/entity/state/HumanoidRenderState;)V",
             at = @At("TAIL"))
     private void saturnEmotes$applyPose(HumanoidRenderState state, CallbackInfo ci) {
-        Pose pose = ((EmotePoseHolder) state).saturnEmotes$getPose();
-        if (!pose.isEmpty()) {
-            PoseApplier.apply((HumanoidModel<?>) (Object) this, pose);
-        }
+        // Always applied, even for an empty pose, so bends left over from another entity get cleared.
+        PoseApplier.apply((HumanoidModel<?>) (Object) this, ((EmotePoseHolder) state).saturnEmotes$getPose());
     }
 }

src/main/java/org/saturnclient/emotes/fabric/mixin/ModelPartMixin.java

@@ -0,0 +1,60 @@
+package org.saturnclient.emotes.fabric.mixin;
+
+import java.util.List;
+import java.util.Map;
+
+import org.jetbrains.annotations.Nullable;
+import org.saturnclient.emotes.core.bend.LimbBend;
+import org.saturnclient.emotes.fabric.BentCubeRenderer;
+import org.saturnclient.emotes.fabric.access.BendablePart;
+import org.spongepowered.asm.mixin.Final;
+import org.spongepowered.asm.mixin.Mixin;
+import org.spongepowered.asm.mixin.Shadow;
+import org.spongepowered.asm.mixin.Unique;
+import org.spongepowered.asm.mixin.injection.At;
+import org.spongepowered.asm.mixin.injection.Inject;
+import org.spongepowered.asm.mixin.injection.callback.CallbackInfo;
+
+import com.mojang.blaze3d.vertex.PoseStack;
+import com.mojang.blaze3d.vertex.VertexConsumer;
+
+import net.minecraft.client.model.geom.ModelPart;
+
+@Mixin(ModelPart.class)
+public class ModelPartMixin implements BendablePart {
+    @Shadow
+    @Final
+    private List<ModelPart.Cube> cubes;
+
+    @Shadow
+    @Final
+    private Map<String, ModelPart> children;
+
+    @Unique
+    private @Nullable LimbBend saturnEmotes$bend;
+
+    @Override
+    public @Nullable LimbBend saturnEmotes$getBend() {
+        return saturnEmotes$bend;
+    }
+
+    @Override
+    public void saturnEmotes$setBend(@Nullable LimbBend bend) {
+        if (bend == null && saturnEmotes$bend == null) {
+            return;
+        }
+        saturnEmotes$bend = bend;
+        for (ModelPart child : children.values()) {
+            ((BendablePart) (Object) child).saturnEmotes$setBend(bend);
+        }
+    }
+
+    @Inject(method = "compile", at = @At("HEAD"), cancellable = true)
+    private void saturnEmotes$compileBent(PoseStack.Pose pose, VertexConsumer consumer, int light, int overlay,
+            int color, CallbackInfo ci) {
+        if (saturnEmotes$bend != null && !saturnEmotes$bend.isStraight()) {
+            BentCubeRenderer.render(cubes, saturnEmotes$bend, pose, consumer, light, overlay, color);
+            ci.cancel();
+        }
+    }
+}

src/main/resources/saturn_emotes.mixins.json

@@ -5,7 +5,8 @@
   "client": [
     "HumanoidModelMixin",
     "LivingEntityRenderStateMixin",
-    "LivingEntityRendererMixin"
+    "LivingEntityRendererMixin",
+    "ModelPartMixin"
   ],
   "injectors": {
     "defaultRequire": 1

src/testmod/java/org/saturnclient/emotes/testmod/EmotesGameTest.java

@@ -0,0 +1,56 @@
+package org.saturnclient.emotes.testmod;
+
+import org.saturnclient.emotes.fabric.Emotes;
+
+import net.fabricmc.fabric.api.client.gametest.v1.FabricClientGameTest;
+import net.fabricmc.fabric.api.client.gametest.v1.context.ClientGameTestContext;
+import net.fabricmc.fabric.api.client.gametest.v1.context.TestSingleplayerContext;
+import net.minecraft.client.CameraType;
+
+/**
+ * Screenshots each test animation at its peak, from the front and from the side.
+ * Run with {@code ./gradlew :<mc>:runClientGameTest}. Screenshots land in
+ * {@code versions/<mc>/build/run/clientGameTest/screenshots/}.
+ */
+public final class EmotesGameTest implements FabricClientGameTest {
+    private static final String MINECRAFT = /*$ minecraft*/ "1.21.11";
+
+    /** Animation name and the tick where it's at its most bent. */
+    private static final Object[][] SHOTS = {
+            { "tpose", 10 },
+            { "bend", 20 },
+            { "flap", 15 },
+            { "squat", 20 },
+    };
+
+    @Override
+    public void runTest(ClientGameTestContext context) {
+        try (TestSingleplayerContext singleplayer = context.worldBuilder().create()) {
+            singleplayer.getClientWorld().waitForChunksRender();
+            context.runOnClient(client -> {
+                client.options.hideGui = true;
+                client.options.setCameraType(CameraType.THIRD_PERSON_FRONT);
+            });
+            context.waitTicks(20);
+
+            for (Object[] shot : SHOTS) {
+                String name = (String) shot[0];
+                context.runOnClient(client -> Emotes.play(client.player.getUUID(), TestAnimations.ALL.get(name)));
+                context.waitTicks((Integer) shot[1]);
+                screenshot(context, name + "-front", 0);
+                screenshot(context, name + "-side", 90);
+                context.runOnClient(client -> Emotes.stop(client.player.getUUID()));
+            }
+        }
+    }
+
+    /** Turns the body (not the camera) by {@code turn} degrees, then takes a screenshot. */
+    private static void screenshot(ClientGameTestContext context, String name, float turn) {
+        context.runOnClient(client -> {
+            float body = client.player.getYRot() + turn;
+            client.player.setYBodyRot(body);
+            client.player.yBodyRotO = body;
+        });
+        context.takeScreenshot(MINECRAFT + "-" + name);
+    }
+}

src/testmod/java/org/saturnclient/emotes/testmod/TestAnimations.java

@@ -33,13 +33,31 @@ final class TestAnimations {
                         .set(Bone.LEFT_ARM, new BoneTransform(0, drop, 0, 0, 0, 0, 0, 0))
                         .build();
             }),
-            // Arms forward with elbows folding in and out. Bend isn't rendered yet.
+            // Arms forward with elbows folding in and out. Tests bending towards the front.
             "bend", of(40, true, t -> {
                 float bend = HALF_PI * 0.5f * (1 - (float) Math.cos(t / 40f * 2 * Math.PI));
                 return Pose.builder()
                         .set(Bone.RIGHT_ARM, BoneTransform.rotation(-HALF_PI, 0, 0).withBend(bend, 0))
                         .set(Bone.LEFT_ARM, BoneTransform.rotation(-HALF_PI, 0, 0).withBend(bend, 0))
                         .build();
+            }),
+            // Arms out to the sides with elbows folding down. Tests the bend axis.
+            "flap", of(30, true, t -> {
+                float bend = HALF_PI * 0.5f * (1 - (float) Math.cos(t / 30f * 2 * Math.PI));
+                return Pose.builder()
+                        .set(Bone.RIGHT_ARM, BoneTransform.rotation(0, 0, HALF_PI).withBend(bend, HALF_PI))
+                        .set(Bone.LEFT_ARM, BoneTransform.rotation(0, 0, -HALF_PI).withBend(bend, -HALF_PI))
+                        .build();
+            }),
+            // Thighs forward and knees folding back, past 90°. Tests legs, pants and sharp bends.
+            "squat", of(40, true, t -> {
+                float depth = 0.5f * (1 - (float) Math.cos(t / 40f * 2 * Math.PI));
+                BoneTransform leg = BoneTransform.rotation(-1.2f * depth, 0, 0)
+                        .withBend(2.2f * depth, (float) Math.PI);
+                return Pose.builder()
+                        .set(Bone.RIGHT_LEG, leg)
+                        .set(Bone.LEFT_LEG, leg)
+                        .build();
             }));
 
     private TestAnimations() {

src/testmod/resources/fabric.mod.json

@@ -7,7 +7,8 @@
   "license": "Apache-2.0",
   "environment": "client",
   "entrypoints": {
-    "client": ["org.saturnclient.emotes.testmod.EmotesTestmod"]
+    "client": ["org.saturnclient.emotes.testmod.EmotesTestmod"],
+    "fabric-client-gametest": ["org.saturnclient.emotes.testmod.EmotesGameTest"]
   },
   "depends": {
     "saturn_emotes": "*",