Bend limbs along a single axis with a Bézier spine

- core: Bezier (any degree, De Casteljau), LimbBend (cubic spine through
  the rigid upper/joint/lower shape, one ring per texture row spaced by
  arc length, rigid rings so pieces share vertices) and QuadSplitter
  (cuts faces at the rings, interpolating UVs).
- fabric: ModelPartMixin draws parts that have a bend with
  BentCubeRenderer, which deforms vanilla's own cubes. Overlays and armor
  use the limb's spine so they stay attached. Bends are reset every
  setupAnim because models are shared between entities.
- testmod: flap and squat animations, and a client gametest that
  screenshots each animation from the front and side
  (runClientGameTest). The tester runs with the full Fabric API because
  single modules don't bring their version-specific dependencies.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

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