Hexagonal tile factory

src/factory/HexagonalTileFactory.ts

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+import { ExtrudeGeometry, InstancedMesh, Material, MeshStandardMaterial, Object3D, Shape } from "three";
+
+export interface HexagonalTileOptions {
+  width: number;       // Total area width to fill (x-axis)
+  depth: number;       // Total area depth to fill (z-axis)
+  height: number;      // Height of each tile (y-axis)
+  radius: number;      // Radius of each hexagonal tile
+  gap: number;         // Gap spacing between tiles
+  material?: Material; // Optional custom material
+}
+
+/**
+ * Hexagonal tile pattern factory.
+ *
+ * Example usage:
+ * ```ts
+ *     const hexTile = createHexagonalTile({
+ *       width: 10,
+ *       depth: 10,
+ *       height: 0.01,
+ *       radius: 0.1,
+ *       gap: 0.01,
+ *       material: new THREE.MeshStandardMaterial({ color: ColorPalette.White }),
+ *     });
+ *
+ *     scene.add(hexTile);
+ * ```
+ */
+export function createHexagonalTile(options: HexagonalTileOptions): InstancedMesh {
+  const { width, depth, height, radius, gap, material } = options;
+
+  const tileMaterial = material || new MeshStandardMaterial({ color: 0x8b4513 }); // Default earthy color
+
+  // Effective spacing between hexagon centers, including the gap
+  const spacingX = (radius * 3) / 2 + gap; // Horizontal distance between hex centers
+  const spacingZ = Math.sqrt(3) * radius + gap; // Vertical distance between hex centers
+
+  // Calculate the number of tiles that fit within the area
+  const hexTileCountX = Math.floor(width / spacingX);
+  const hexTileCountZ = Math.floor(depth / spacingZ);
+
+  const hexTileCount = hexTileCountX * hexTileCountZ;
+
+  // Create a hexagonal prism geometry
+  const hexShape = new Shape();
+  for (let i = 0; i < 6; i++) {
+    const angle = (Math.PI / 3) * i; // 60-degree increments
+    const x = Math.cos(angle) * radius;
+    const y = Math.sin(angle) * radius;
+
+    if (i === 0) hexShape.moveTo(x, y);
+    else hexShape.lineTo(x, y);
+  }
+  hexShape.closePath();
+  const geometry = new ExtrudeGeometry(hexShape, { depth: height, bevelEnabled: false });
+
+  // Rotate geometry so tiles lay flat
+  geometry.rotateX(-Math.PI / 2);
+
+  // Create the instanced mesh
+  const instancedMesh = new InstancedMesh(geometry, tileMaterial, hexTileCount);
+
+  const dummy = new Object3D();
+  let index = 0;
+
+  for (let x = 0; x < hexTileCountX; x++) {
+    for (let z = 0; z < hexTileCountZ; z++) {
+      // Calculate the staggered row offset
+      const offsetX = x * spacingX;
+      const offsetZ = z * spacingZ + (x % 2) * (spacingZ / 2); // Stagger odd rows by half a tile
+
+      // Center the grid
+      const positionX = offsetX - (hexTileCountX * spacingX) / 2 + spacingX / 2;
+      const positionZ = offsetZ - (hexTileCountZ * spacingZ) / 2 + spacingZ / 2;
+
+      dummy.position.set(positionX, 0, positionZ);
+      dummy.updateMatrix();
+      instancedMesh.setMatrixAt(index++, dummy.matrix);
+    }
+  }
+
+  instancedMesh.instanceMatrix.needsUpdate = true;
+
+  return instancedMesh;
+}