diff --git a/src/geometry/box-brush-mesh.ts b/src/geometry/box-brush-mesh.ts
new file mode 100644
index 00000000..62e92ba7
--- /dev/null
+++ b/src/geometry/box-brush-mesh.ts
@@ -0,0 +1,459 @@
+import { BufferAttribute, BufferGeometry } from "three";
+
+import type { Vec2, Vec3 } from "../core/vector";
+import {
+  BOX_EDGE_IDS,
+  BOX_FACE_IDS,
+  type BoxBrush,
+  type BoxEdgeId,
+  type BoxFaceId,
+  type BoxVertexId,
+  type FaceUvState
+} from "../document/brushes";
+import { transformProjectedFaceUv } from "./box-face-uvs";
+
+const FACE_VERTEX_IDS: Record<BoxFaceId, readonly [BoxVertexId, BoxVertexId, BoxVertexId, BoxVertexId]> = {
+  posX: ["posX_negY_posZ", "posX_negY_negZ", "posX_posY_negZ", "posX_posY_posZ"],
+  negX: ["negX_negY_negZ", "negX_negY_posZ", "negX_posY_posZ", "negX_posY_negZ"],
+  posY: ["negX_posY_posZ", "posX_posY_posZ", "posX_posY_negZ", "negX_posY_negZ"],
+  negY: ["negX_negY_negZ", "posX_negY_negZ", "posX_negY_posZ", "negX_negY_posZ"],
+  posZ: ["negX_negY_posZ", "posX_negY_posZ", "posX_posY_posZ", "negX_posY_posZ"],
+  negZ: ["posX_negY_negZ", "negX_negY_negZ", "negX_posY_negZ", "posX_posY_negZ"]
+};
+
+const EDGE_VERTEX_IDS: Record<BoxEdgeId, readonly [BoxVertexId, BoxVertexId]> = {
+  edgeX_negY_negZ: ["negX_negY_negZ", "posX_negY_negZ"],
+  edgeX_posY_negZ: ["negX_posY_negZ", "posX_posY_negZ"],
+  edgeX_negY_posZ: ["negX_negY_posZ", "posX_negY_posZ"],
+  edgeX_posY_posZ: ["negX_posY_posZ", "posX_posY_posZ"],
+  edgeY_negX_negZ: ["negX_negY_negZ", "negX_posY_negZ"],
+  edgeY_posX_negZ: ["posX_negY_negZ", "posX_posY_negZ"],
+  edgeY_negX_posZ: ["negX_negY_posZ", "negX_posY_posZ"],
+  edgeY_posX_posZ: ["posX_negY_posZ", "posX_posY_posZ"],
+  edgeZ_negX_negY: ["negX_negY_negZ", "negX_negY_posZ"],
+  edgeZ_posX_negY: ["posX_negY_negZ", "posX_negY_posZ"],
+  edgeZ_negX_posY: ["negX_posY_negZ", "negX_posY_posZ"],
+  edgeZ_posX_posY: ["posX_posY_negZ", "posX_posY_posZ"]
+};
+
+export interface BoxBrushGeometryDiagnostic {
+  code: string;
+  message: string;
+  faceId?: BoxFaceId;
+}
+
+export interface DerivedBoxBrushFaceSurface {
+  faceId: BoxFaceId;
+  vertexIds: readonly [BoxVertexId, BoxVertexId, BoxVertexId, BoxVertexId];
+  triangles: Array<readonly [number, number, number]>;
+  normal: Vec3;
+}
+
+export interface DerivedBoxBrushMeshData {
+  geometry: BufferGeometry;
+  faceSurfaces: DerivedBoxBrushFaceSurface[];
+  edgeSegments: Array<{ edgeId: BoxEdgeId; start: Vec3; end: Vec3 }>;
+  colliderVertices: Float32Array;
+  colliderIndices: Uint32Array;
+  localBounds: { min: Vec3; max: Vec3 };
+}
+
+function cloneVec3(vector: Vec3): Vec3 {
+  return { x: vector.x, y: vector.y, z: vector.z };
+}
+
+function subtractVec3(left: Vec3, right: Vec3): Vec3 {
+  return {
+    x: left.x - right.x,
+    y: left.y - right.y,
+    z: left.z - right.z
+  };
+}
+
+function crossVec3(left: Vec3, right: Vec3): Vec3 {
+  return {
+    x: left.y * right.z - left.z * right.y,
+    y: left.z * right.x - left.x * right.z,
+    z: left.x * right.y - left.y * right.x
+  };
+}
+
+function dotVec3(left: Vec3, right: Vec3): number {
+  return left.x * right.x + left.y * right.y + left.z * right.z;
+}
+
+function getVectorLength(vector: Vec3): number {
+  return Math.sqrt(dotVec3(vector, vector));
+}
+
+function normalizeVec3(vector: Vec3): Vec3 {
+  const length = getVectorLength(vector);
+
+  if (length <= 1e-8) {
+    return { x: 0, y: 0, z: 0 };
+  }
+
+  return {
+    x: vector.x / length,
+    y: vector.y / length,
+    z: vector.z / length
+  };
+}
+
+function computeNewellNormal(vertices: Vec3[]): Vec3 {
+  let normal = { x: 0, y: 0, z: 0 };
+
+  for (let index = 0; index < vertices.length; index += 1) {
+    const current = vertices[index];
+    const next = vertices[(index + 1) % vertices.length];
+    normal.x += (current.y - next.y) * (current.z + next.z);
+    normal.y += (current.z - next.z) * (current.x + next.x);
+    normal.z += (current.x - next.x) * (current.y + next.y);
+  }
+
+  return normalizeVec3(normal);
+}
+
+function chooseProjectionAxes(normal: Vec3): [keyof Vec3, keyof Vec3] {
+  const absoluteNormal = {
+    x: Math.abs(normal.x),
+    y: Math.abs(normal.y),
+    z: Math.abs(normal.z)
+  };
+
+  if (absoluteNormal.x >= absoluteNormal.y && absoluteNormal.x >= absoluteNormal.z) {
+    return ["y", "z"];
+  }
+
+  if (absoluteNormal.y >= absoluteNormal.z) {
+    return ["x", "z"];
+  }
+
+  return ["x", "y"];
+}
+
+function projectVerticesTo2d(vertices: Vec3[], normal: Vec3): Vec2[] {
+  const [uAxis, vAxis] = chooseProjectionAxes(normal);
+  return vertices.map((vertex) => ({
+    x: vertex[uAxis],
+    y: vertex[vAxis]
+  }));
+}
+
+function computeSignedArea(points: Vec2[]): number {
+  let area = 0;
+
+  for (let index = 0; index < points.length; index += 1) {
+    const current = points[index];
+    const next = points[(index + 1) % points.length];
+    area += current.x * next.y - next.x * current.y;
+  }
+
+  return area * 0.5;
+}
+
+function isPointInTriangle(point: Vec2, triangle: [Vec2, Vec2, Vec2], orientation: number): boolean {
+  const [a, b, c] = triangle;
+  const edges = [
+    (b.x - a.x) * (point.y - a.y) - (b.y - a.y) * (point.x - a.x),
+    (c.x - b.x) * (point.y - b.y) - (c.y - b.y) * (point.x - b.x),
+    (a.x - c.x) * (point.y - c.y) - (a.y - c.y) * (point.x - c.x)
+  ];
+
+  return orientation > 0 ? edges.every((value) => value >= -1e-8) : edges.every((value) => value <= 1e-8);
+}
+
+function triangulateQuad(vertices: Vec3[]): Array<readonly [number, number, number]> {
+  const normal = computeNewellNormal(vertices);
+  const projected = projectVerticesTo2d(vertices, normal);
+  const orientation = computeSignedArea(projected);
+
+  if (Math.abs(orientation) <= 1e-8) {
+    throw new Error("Face projection is degenerate.");
+  }
+
+  const remaining = [0, 1, 2, 3];
+  const triangles: Array<readonly [number, number, number]> = [];
+
+  while (remaining.length > 3) {
+    let earFound = false;
+
+    for (let offset = 0; offset < remaining.length; offset += 1) {
+      const previousIndex = remaining[(offset + remaining.length - 1) % remaining.length];
+      const currentIndex = remaining[offset];
+      const nextIndex = remaining[(offset + 1) % remaining.length];
+      const previousPoint = projected[previousIndex];
+      const currentPoint = projected[currentIndex];
+      const nextPoint = projected[nextIndex];
+      const cross =
+        (currentPoint.x - previousPoint.x) * (nextPoint.y - previousPoint.y) -
+        (currentPoint.y - previousPoint.y) * (nextPoint.x - previousPoint.x);
+
+      if ((orientation > 0 && cross <= 1e-8) || (orientation < 0 && cross >= -1e-8)) {
+        continue;
+      }
+
+      const candidateTriangle: [Vec2, Vec2, Vec2] = [previousPoint, currentPoint, nextPoint];
+      const containsOtherPoint = remaining.some((candidateIndex) => {
+        if (candidateIndex === previousIndex || candidateIndex === currentIndex || candidateIndex === nextIndex) {
+          return false;
+        }
+
+        return isPointInTriangle(projected[candidateIndex], candidateTriangle, orientation);
+      });
+
+      if (containsOtherPoint) {
+        continue;
+      }
+
+      triangles.push([previousIndex, currentIndex, nextIndex]);
+      remaining.splice(offset, 1);
+      earFound = true;
+      break;
+    }
+
+    if (!earFound) {
+      throw new Error("Face triangulation could not find a stable ear.");
+    }
+  }
+
+  triangles.push([remaining[0], remaining[1], remaining[2]]);
+  return triangles;
+}
+
+function projectLocalVertexToFaceUv(vertexPosition: Vec3, faceId: BoxFaceId, faceBounds: { min: Vec3; max: Vec3 }): Vec2 {
+  switch (faceId) {
+    case "posX":
+      return {
+        x: faceBounds.max.z - vertexPosition.z,
+        y: vertexPosition.y - faceBounds.min.y
+      };
+    case "negX":
+      return {
+        x: vertexPosition.z - faceBounds.min.z,
+        y: vertexPosition.y - faceBounds.min.y
+      };
+    case "posY":
+      return {
+        x: vertexPosition.x - faceBounds.min.x,
+        y: faceBounds.max.z - vertexPosition.z
+      };
+    case "negY":
+      return {
+        x: vertexPosition.x - faceBounds.min.x,
+        y: vertexPosition.z - faceBounds.min.z
+      };
+    case "posZ":
+      return {
+        x: vertexPosition.x - faceBounds.min.x,
+        y: vertexPosition.y - faceBounds.min.y
+      };
+    case "negZ":
+      return {
+        x: faceBounds.max.x - vertexPosition.x,
+        y: vertexPosition.y - faceBounds.min.y
+      };
+  }
+}
+
+function getFaceUvSize(faceId: BoxFaceId, faceBounds: { min: Vec3; max: Vec3 }): Vec2 {
+  switch (faceId) {
+    case "posX":
+    case "negX":
+      return {
+        x: faceBounds.max.z - faceBounds.min.z,
+        y: faceBounds.max.y - faceBounds.min.y
+      };
+    case "posY":
+    case "negY":
+      return {
+        x: faceBounds.max.x - faceBounds.min.x,
+        y: faceBounds.max.z - faceBounds.min.z
+      };
+    case "posZ":
+    case "negZ":
+      return {
+        x: faceBounds.max.x - faceBounds.min.x,
+        y: faceBounds.max.y - faceBounds.min.y
+      };
+  }
+}
+
+function computeFaceBounds(vertices: Vec3[]): { min: Vec3; max: Vec3 } {
+  const firstVertex = vertices[0];
+  const min = { ...firstVertex };
+  const max = { ...firstVertex };
+
+  for (const vertex of vertices.slice(1)) {
+    min.x = Math.min(min.x, vertex.x);
+    min.y = Math.min(min.y, vertex.y);
+    min.z = Math.min(min.z, vertex.z);
+    max.x = Math.max(max.x, vertex.x);
+    max.y = Math.max(max.y, vertex.y);
+    max.z = Math.max(max.z, vertex.z);
+  }
+
+  return { min, max };
+}
+
+export function getBoxBrushFaceVertexIds(faceId: BoxFaceId): readonly [BoxVertexId, BoxVertexId, BoxVertexId, BoxVertexId] {
+  return FACE_VERTEX_IDS[faceId];
+}
+
+export function getBoxBrushEdgeVertexIds(edgeId: BoxEdgeId): readonly [BoxVertexId, BoxVertexId] {
+  return EDGE_VERTEX_IDS[edgeId];
+}
+
+export function getBoxBrushLocalVertexPosition(brush: BoxBrush, vertexId: BoxVertexId): Vec3 {
+  return cloneVec3(brush.geometry.vertices[vertexId]);
+}
+
+export function buildBoxBrushDerivedMeshData(brush: BoxBrush): DerivedBoxBrushMeshData {
+  const diagnostics = validateBoxBrushGeometry(brush);
+
+  if (diagnostics.length > 0) {
+    throw new Error(diagnostics[0].message);
+  }
+
+  const positions: number[] = [];
+  const normals: number[] = [];
+  const uvs: number[] = [];
+  const indices: number[] = [];
+  const colliderVertices: number[] = [];
+  const colliderIndices: number[] = [];
+  const faceSurfaces: DerivedBoxBrushFaceSurface[] = [];
+  const groups: Array<{ start: number; count: number; materialIndex: number }> = [];
+  const vertexIndexMap = new Map<BoxVertexId, number>();
+
+  for (const vertexId of Object.keys(brush.geometry.vertices) as BoxVertexId[]) {
+    const vertex = brush.geometry.vertices[vertexId];
+    vertexIndexMap.set(vertexId, colliderVertices.length / 3);
+    colliderVertices.push(vertex.x, vertex.y, vertex.z);
+  }
+
+  for (const [materialIndex, faceId] of BOX_FACE_IDS.entries()) {
+    const faceVertexIds = FACE_VERTEX_IDS[faceId];
+    const faceVertices = faceVertexIds.map((vertexId) => getBoxBrushLocalVertexPosition(brush, vertexId));
+    const triangles = triangulateQuad(faceVertices);
+    const normal = computeNewellNormal(faceVertices);
+    const faceBounds = computeFaceBounds(faceVertices);
+    const uvSize = getFaceUvSize(faceId, faceBounds);
+    const indexStart = indices.length;
+
+    faceSurfaces.push({
+      faceId,
+      vertexIds: faceVertexIds,
+      triangles,
+      normal
+    });
+
+    for (const triangle of triangles) {
+      for (const vertexOffset of triangle) {
+        const vertex = faceVertices[vertexOffset];
+        const projectedUv = projectLocalVertexToFaceUv(vertex, faceId, faceBounds);
+        const transformedUv = transformProjectedFaceUv(projectedUv, uvSize, brush.faces[faceId].uv as FaceUvState);
+        positions.push(vertex.x, vertex.y, vertex.z);
+        normals.push(normal.x, normal.y, normal.z);
+        uvs.push(transformedUv.x, transformedUv.y);
+        indices.push(indices.length);
+      }
+    }
+
+    groups.push({
+      start: indexStart,
+      count: indices.length - indexStart,
+      materialIndex
+    });
+
+    for (const triangle of triangles) {
+      colliderIndices.push(
+        vertexIndexMap.get(faceVertexIds[triangle[0]]) ?? 0,
+        vertexIndexMap.get(faceVertexIds[triangle[1]]) ?? 0,
+        vertexIndexMap.get(faceVertexIds[triangle[2]]) ?? 0
+      );
+    }
+  }
+
+  const geometry = new BufferGeometry();
+  geometry.setAttribute("position", new BufferAttribute(new Float32Array(positions), 3));
+  geometry.setAttribute("normal", new BufferAttribute(new Float32Array(normals), 3));
+  geometry.setAttribute("uv", new BufferAttribute(new Float32Array(uvs), 2));
+  geometry.setIndex(indices);
+
+  for (const group of groups) {
+    geometry.addGroup(group.start, group.count, group.materialIndex);
+  }
+
+  geometry.computeBoundingBox();
+  geometry.computeBoundingSphere();
+
+  const firstVertex = brush.geometry.vertices.negX_negY_negZ;
+  const localBounds = {
+    min: cloneVec3(firstVertex),
+    max: cloneVec3(firstVertex)
+  };
+
+  for (const vertex of Object.values(brush.geometry.vertices)) {
+    localBounds.min.x = Math.min(localBounds.min.x, vertex.x);
+    localBounds.min.y = Math.min(localBounds.min.y, vertex.y);
+    localBounds.min.z = Math.min(localBounds.min.z, vertex.z);
+    localBounds.max.x = Math.max(localBounds.max.x, vertex.x);
+    localBounds.max.y = Math.max(localBounds.max.y, vertex.y);
+    localBounds.max.z = Math.max(localBounds.max.z, vertex.z);
+  }
+
+  return {
+    geometry,
+    faceSurfaces,
+    edgeSegments: BOX_EDGE_IDS.map((edgeId) => {
+      const [startId, endId] = EDGE_VERTEX_IDS[edgeId];
+      return {
+        edgeId,
+        start: getBoxBrushLocalVertexPosition(brush, startId),
+        end: getBoxBrushLocalVertexPosition(brush, endId)
+      };
+    }),
+    colliderVertices: new Float32Array(colliderVertices),
+    colliderIndices: new Uint32Array(colliderIndices),
+    localBounds
+  };
+}
+
+export function validateBoxBrushGeometry(brush: BoxBrush): BoxBrushGeometryDiagnostic[] {
+  const diagnostics: BoxBrushGeometryDiagnostic[] = [];
+
+  for (const [vertexId, vertex] of Object.entries(brush.geometry.vertices) as Array<[BoxVertexId, Vec3]>) {
+    if (!Number.isFinite(vertex.x) || !Number.isFinite(vertex.y) || !Number.isFinite(vertex.z)) {
+      diagnostics.push({
+        code: "invalid-box-geometry-vertex",
+        message: `Whitebox vertex ${vertexId} must remain finite.`
+      });
+    }
+  }
+
+  for (const faceId of BOX_FACE_IDS) {
+    const faceVertices = FACE_VERTEX_IDS[faceId].map((vertexId) => brush.geometry.vertices[vertexId]);
+    const normal = computeNewellNormal(faceVertices);
+
+    if (getVectorLength(normal) <= 1e-8) {
+      diagnostics.push({
+        code: "degenerate-box-face",
+        message: `Whitebox face ${faceId} is degenerate and cannot be triangulated.`,
+        faceId
+      });
+      continue;
+    }
+
+    try {
+      triangulateQuad(faceVertices);
+    } catch (error) {
+      diagnostics.push({
+        code: "invalid-box-face-triangulation",
+        message: error instanceof Error ? `Whitebox face ${faceId} could not be triangulated: ${error.message}` : `Whitebox face ${faceId} could not be triangulated.`,
+        faceId
+      });
+    }
+  }
+
+  return diagnostics;
+}
\ No newline at end of file