Add Transform and client yaw helpers to Quaternion

Transform holds location, rotation and scale as the client's ArcObjectInfo
does, with parent x local composition (sb.exe 0x6516C0). Quaternion.fromYaw
matches the client's MakeRotateY and getYaw returns the angle it would need.
Nothing uses them yet.

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

src/engine/math/Quaternion.java

@@ -1142,6 +1142,17 @@ public class Quaternion {
         return opposite(this);
     }
 
+    // Client MakeRotateY (Math.dll 0x10002960): w = cos θ/2, y = sin θ/2, radians.
+    // Math rather than FastMath: FastMath.reduceSinAngle mis-reduces angles below -π.
+    public static Quaternion fromYaw(float yaw) {
+        return new Quaternion(0f, (float) Math.sin(yaw * 0.5), 0f, (float) Math.cos(yaw * 0.5));
+    }
+
+    // The angle MakeRotateY would need to produce this rotation; characters send it as one float.
+    public float getYaw() {
+        return 2 * FastMath.atan2(y, w);
+    }
+
     @Override
     public Quaternion clone() {
         try {

src/engine/math/Transform.java

@@ -0,0 +1,45 @@
+//  • ▌ ▄ ·.  ▄▄▄·  ▄▄ • ▪   ▄▄· ▄▄▄▄·  ▄▄▄·  ▐▄▄▄  ▄▄▄ .
+//  ·██ ▐███▪▐█ ▀█ ▐█ ▀ ▪██ ▐█ ▌▪▐█ ▀█▪▐█ ▀█ •█▌ ▐█▐▌·
+//  ▐█ ▌▐▌▐█·▄█▀▀█ ▄█ ▀█▄▐█·██ ▄▄▐█▀▀█▄▄█▀▀█ ▐█▐ ▐▌▐▀▀▀
+//  ██ ██▌▐█▌▐█ ▪▐▌▐█▄▪▐█▐█▌▐███▌██▄▪▐█▐█ ▪▐▌██▐ █▌▐█▄▄▌
+//  ▀▀  █▪▀▀▀ ▀  ▀ ·▀▀▀▀ ▀▀▀·▀▀▀ ·▀▀▀▀  ▀  ▀ ▀▀  █▪ ▀▀▀
+//      Magicbane Emulator Project © 2013 - 2026
+//                https://www.magicbane.com
+
+package engine.math;
+
+// The client's placement (ArcObjectInfo +0x28/+0x34/+0x44, math::Transformation); see MBDATA/specs/WorldPlacement.md §7.
+
+public class Transform {
+
+    public final Vector3fImmutable location;
+    public final Quaternion rotation;
+    public final Vector3f scale;
+
+    public Transform(Vector3fImmutable location, Quaternion rotation, Vector3f scale) {
+        this.location = location;
+        this.rotation = rotation;
+        this.scale = scale;
+    }
+
+    public static Transform fromYaw(Vector3fImmutable location, float yaw) {
+        return new Transform(location, Quaternion.fromYaw(yaw), new Vector3f(1.0f, 1.0f, 1.0f));
+    }
+
+    // world = parent × local, as the client composes zone and object transforms (sb.exe 0x6516C0).
+    public static Transform mult(Transform parent, Transform local) {
+
+        Vector3f scaledLocation;
+        Vector3f rotatedLocation;
+        Quaternion rotation;
+        Vector3f scale;
+
+        scaledLocation = new Vector3f(local.location).mult(parent.scale);
+        rotatedLocation = parent.rotation.mult(scaledLocation);
+        rotation = parent.rotation.mult(local.rotation);
+        scale = parent.scale.mult(local.scale);
+
+        return new Transform(parent.location.add(rotatedLocation), rotation, scale);
+    }
+
+}