feat(04-01): add Vec3.lerp and ParticleTrail sampler with JUnit suite

- Vec3.lerp(other, t) for linear interpolation between two points
- ParticleTrail.sample(from, to, density) emits density-based interpolated
  points strictly between endpoints (endpoints excluded by construction)
- TRAIL_DENSITY = 4.0 particles per block
- 6 ParticleTrail tests + 3 Vec3.lerp tests, all green
- Zero Hytale imports — chain/ frontier preserved

src/main/java/com/mythlane/chainlightning/chain/ParticleTrail.java

@@ -0,0 +1,56 @@
+package com.mythlane.chainlightning.chain;
+
+import java.util.ArrayList;
+import java.util.List;
+
+/**
+ * Pure-Java sampler for the electric trail between two endpoints.
+ * <p>
+ * Produces evenly-spaced interpolated points strictly between {@code from} and
+ * {@code to}; both endpoints are excluded by construction (the parametric
+ * interpolation parameter {@code t} never reaches 0 or 1).
+ * <p>
+ * Density is expressed in particles per block. The sample count for a given
+ * segment is {@code ceil(distance * density)}.
+ * <p>
+ * This class has ZERO Hytale imports — it lives behind the Phase 2 sealed
+ * frontier so it can be unit-tested without runtime dependencies.
+ */
+public final class ParticleTrail {
+
+    /** Default trail density in particles per block. */
+    public static final double TRAIL_DENSITY = 4.0;
+
+    private ParticleTrail() {
+        // utility class — no instances
+    }
+
+    /**
+     * Sample interpolated points strictly between {@code from} and {@code to}.
+     * Endpoints are NOT included in the returned list. The list is freshly
+     * allocated on each call.
+     *
+     * @param from    start endpoint (excluded from output)
+     * @param to      end endpoint (excluded from output)
+     * @param density particles per block
+     * @return newly-allocated list of interpolated points; empty if the
+     *         endpoints coincide or {@code density} produces a non-positive
+     *         count.
+     */
+    public static List<Vec3> sample(Vec3 from, Vec3 to, double density) {
+        double dist = from.distance(to);
+        if (dist <= 0) {
+            return List.of();
+        }
+        int count = (int) Math.ceil(dist * density);
+        if (count <= 0) {
+            return List.of();
+        }
+        List<Vec3> out = new ArrayList<>(count);
+        for (int i = 1; i <= count; i++) {
+            double t = (double) i / (count + 1);
+            out.add(from.lerp(to, t));
+        }
+        return out;
+    }
+}

src/main/java/com/mythlane/chainlightning/chain/Vec3.java

@@ -22,4 +22,13 @@ public record Vec3(double x, double y, double z) {
     public double distance(Vec3 other) {
         return Math.sqrt(distanceSquared(other));
     }
+
+    /** Linear interpolation: t=0 returns this, t=1 returns other. */
+    public Vec3 lerp(Vec3 other, double t) {
+        return new Vec3(
+            this.x + (other.x - this.x) * t,
+            this.y + (other.y - this.y) * t,
+            this.z + (other.z - this.z) * t
+        );
+    }
 }

src/test/java/com/mythlane/chainlightning/chain/ParticleTrailTest.java

@@ -0,0 +1,82 @@
+package com.mythlane.chainlightning.chain;
+
+import java.util.List;
+
+import org.junit.jupiter.api.Test;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertTrue;
+
+final class ParticleTrailTest {
+
+    private static final double EPS = 1e-9;
+
+    @Test
+    void zeroDistance() {
+        Vec3 p = new Vec3(2, 3, 4);
+        List<Vec3> out = ParticleTrail.sample(p, p, 4.0);
+        assertTrue(out.isEmpty());
+    }
+
+    @Test
+    void subBlockDistance() {
+        // distance 0.5 along X with density 4 → ceil(2.0) = 2
+        Vec3 from = new Vec3(0, 0, 0);
+        Vec3 to = new Vec3(0.5, 0, 0);
+        List<Vec3> out = ParticleTrail.sample(from, to, 4.0);
+        assertEquals(2, out.size());
+        // Both points strictly between endpoints
+        for (Vec3 v : out) {
+            assertTrue(from.distanceSquared(v) > EPS, "sample equals from");
+            assertTrue(to.distanceSquared(v) > EPS, "sample equals to");
+        }
+    }
+
+    @Test
+    void integerDistanceCount() {
+        Vec3 from = new Vec3(0, 0, 0);
+        Vec3 to = new Vec3(5, 0, 0);
+        List<Vec3> out = ParticleTrail.sample(from, to, 4.0);
+        assertEquals(20, out.size());
+    }
+
+    @Test
+    void fractionalDistanceCount() {
+        Vec3 from = new Vec3(0, 0, 0);
+        Vec3 to = new Vec3(3.7, 0, 0);
+        List<Vec3> out = ParticleTrail.sample(from, to, 4.0);
+        // ceil(3.7 * 4) = ceil(14.8) = 15
+        assertEquals(15, out.size());
+    }
+
+    @Test
+    void endpointsExcluded() {
+        Vec3 from = new Vec3(1, 2, 3);
+        Vec3 to = new Vec3(7, 8, 9);
+        List<Vec3> out = ParticleTrail.sample(from, to, 4.0);
+        assertTrue(out.size() > 0);
+        for (Vec3 v : out) {
+            assertTrue(from.distanceSquared(v) > EPS, "sample equals from endpoint");
+            assertTrue(to.distanceSquared(v) > EPS, "sample equals to endpoint");
+        }
+    }
+
+    @Test
+    void uniformSpacing() {
+        Vec3 from = new Vec3(0, 0, 0);
+        Vec3 to = new Vec3(5, 0, 0);
+        List<Vec3> out = ParticleTrail.sample(from, to, 4.0);
+        assertEquals(20, out.size());
+        double total = from.distance(to);
+        double expectedSpacing = total / (out.size() + 1);
+
+        // from -> first
+        assertEquals(expectedSpacing, from.distance(out.get(0)), EPS);
+        // last -> to
+        assertEquals(expectedSpacing, out.get(out.size() - 1).distance(to), EPS);
+        // consecutive
+        for (int i = 1; i < out.size(); i++) {
+            assertEquals(expectedSpacing, out.get(i - 1).distance(out.get(i)), EPS);
+        }
+    }
+}

src/test/java/com/mythlane/chainlightning/chain/Vec3Test.java

@@ -41,4 +41,34 @@ final class Vec3Test {
         assertEquals(12.0, a.distanceSquared(b), 1e-9);
         assertTrue(a.distance(b) > 3.4 && a.distance(b) < 3.5);
     }
+
+    @Test
+    void lerpAtZeroReturnsFrom() {
+        Vec3 from = Vec3.ZERO;
+        Vec3 to = new Vec3(10, 10, 10);
+        Vec3 result = from.lerp(to, 0.0);
+        assertEquals(from.x(), result.x(), 1e-9);
+        assertEquals(from.y(), result.y(), 1e-9);
+        assertEquals(from.z(), result.z(), 1e-9);
+    }
+
+    @Test
+    void lerpAtOneReturnsTo() {
+        Vec3 from = Vec3.ZERO;
+        Vec3 to = new Vec3(10, 10, 10);
+        Vec3 result = from.lerp(to, 1.0);
+        assertEquals(to.x(), result.x(), 1e-9);
+        assertEquals(to.y(), result.y(), 1e-9);
+        assertEquals(to.z(), result.z(), 1e-9);
+    }
+
+    @Test
+    void lerpAtHalfReturnsMidpoint() {
+        Vec3 from = new Vec3(0, 0, 0);
+        Vec3 to = new Vec3(10, 0, 0);
+        Vec3 result = from.lerp(to, 0.5);
+        assertEquals(5.0, result.x(), 1e-9);
+        assertEquals(0.0, result.y(), 1e-9);
+        assertEquals(0.0, result.z(), 1e-9);
+    }
 }