Add Chromium-only Blender WebEngine parity work

blender-5.2.0/intern/mikktspace/mikktspace.hh

@@ -0,0 +1,849 @@
+/* SPDX-FileCopyrightText: 2011 Morten S. Mikkelsen
+ * SPDX-FileCopyrightText: 2022 Blender Authors
+ *
+ * SPDX-License-Identifier: Apache-2.0 */
+
+/** \file
+ * \ingroup mikktspace
+ */
+
+#include <algorithm>
+#include <cassert>
+#include <unordered_map>
+
+#ifdef WITH_TBB
+#  include <tbb/parallel_for.h>
+#endif
+
+#include "mikk_atomic_hash_set.hh"
+#include "mikk_float3.hh"
+#include "mikk_util.hh"
+
+namespace mikk {
+
+static constexpr uint UNSET_ENTRY = 0xffffffffu;
+
+template<typename Mesh> class Mikktspace {
+  struct Triangle {
+    /* Stores neighboring triangle for group assignment. */
+    std::array<uint, 3> neighbor;
+    /* Stores assigned group of each vertex. */
+    std::array<uint, 3> group;
+    /* Stores vertex indices that make up the triangle. */
+    std::array<uint, 3> vertices;
+
+    /* Computed face tangent, will be accumulated into group. */
+    float3 tangent;
+
+    /* Index of the face that this triangle belongs to. */
+    uint faceIdx;
+    /* Index of the first of this triangle's vertices' TSpaces. */
+    uint tSpaceIdx;
+
+    /* Stores mapping from this triangle's vertices to the original
+     * face's vertices (relevant for quads). */
+    std::array<uint8_t, 3> faceVertex;
+
+    // flags
+    bool markDegenerate : 1;
+    bool quadOneDegenTri : 1;
+    bool groupWithAny : 1;
+    bool orientPreserving : 1;
+
+    Triangle(uint faceIdx_, uint tSpaceIdx_)
+        : tangent{0.0f},
+          faceIdx{faceIdx_},
+          tSpaceIdx{tSpaceIdx_},
+          markDegenerate{false},
+          quadOneDegenTri{false},
+          groupWithAny{true},
+          orientPreserving{false}
+    {
+      neighbor.fill(UNSET_ENTRY);
+      group.fill(UNSET_ENTRY);
+    }
+
+    void setVertices(uint8_t i0, uint8_t i1, uint8_t i2)
+    {
+      faceVertex[0] = i0;
+      faceVertex[1] = i1;
+      faceVertex[2] = i2;
+      vertices[0] = pack_index(faceIdx, i0);
+      vertices[1] = pack_index(faceIdx, i1);
+      vertices[2] = pack_index(faceIdx, i2);
+    }
+  };
+
+  struct Group {
+    float3 tangent;
+    uint vertexRepresentative;
+    bool orientPreserving;
+
+    Group(uint vertexRepresentative_, bool orientPreserving_)
+        : tangent{0.0f},
+          vertexRepresentative{vertexRepresentative_},
+          orientPreserving{orientPreserving_}
+    {
+    }
+
+    void normalizeTSpace()
+    {
+      tangent = tangent.normalize();
+    }
+
+    void accumulateTSpaceAtomic(float3 v_tangent)
+    {
+      float_add_atomic(&tangent.x, v_tangent.x);
+      float_add_atomic(&tangent.y, v_tangent.y);
+      float_add_atomic(&tangent.z, v_tangent.z);
+    }
+
+    void accumulateTSpace(float3 v_tangent)
+    {
+      tangent += v_tangent;
+    }
+  };
+
+  struct TSpace {
+    float3 tangent = float3(1.0f, 0.0f, 0.0f);
+    uint counter = 0;
+    bool orientPreserving = false;
+
+    void accumulateGroup(const Group &group)
+    {
+      assert(counter < 2);
+
+      if (counter == 0) {
+        tangent = group.tangent;
+      }
+      else if (tangent == group.tangent) {
+        // this if is important. Due to floating point precision
+        // averaging when ts0==ts1 will cause a slight difference
+        // which results in tangent space splits later on, so do nothing
+      }
+      else {
+        tangent = (tangent + group.tangent).normalize();
+      }
+
+      counter++;
+      orientPreserving = group.orientPreserving;
+    }
+  };
+
+  Mesh &mesh;
+
+  std::vector<Triangle> triangles;
+  std::vector<TSpace> tSpaces;
+  std::vector<Group> groups;
+
+  uint nrTSpaces, nrFaces, nrTriangles, totalTriangles;
+
+  int nrThreads;
+  bool isParallel;
+
+ public:
+  Mikktspace(Mesh &mesh_) : mesh(mesh_) {}
+
+  void genTangSpace()
+  {
+    nrFaces = uint(mesh.GetNumFaces());
+
+#ifdef WITH_TBB
+    nrThreads = tbb::this_task_arena::max_concurrency();
+    isParallel = (nrThreads > 1) && (nrFaces > 10000);
+#else
+    nrThreads = 1;
+    isParallel = false;
+#endif
+
+    // make an initial triangle --> face index list
+    generateInitialVerticesIndexList();
+
+    if (nrTriangles == 0) {
+      return;
+    }
+
+    // make a welded index list of identical positions and attributes (pos, norm, texc)
+    generateSharedVerticesIndexList();
+
+    // mark all triangle pairs that belong to a quad with only one
+    // good triangle. These need special treatment in degenEpilogue().
+    // Additionally, move all good triangles to the start of
+    // triangles[] without changing order and
+    // put the degenerate triangles last.
+    degenPrologue();
+
+    if (nrTriangles == 0) {
+      // No point in building tangents if there are no non-degenerate triangles, so just zero them
+      tSpaces.resize(nrTSpaces);
+    }
+    else {
+      // evaluate triangle level attributes and neighbor list
+      initTriangle();
+
+      // match up edge pairs
+      buildNeighbors();
+
+      // based on the 4 rules, identify groups based on connectivity
+      build4RuleGroups();
+
+      // make tspaces, each group is split up into subgroups.
+      // Finally a tangent space is made for every resulting subgroup
+      generateTSpaces();
+
+      // degenerate quads with one good triangle will be fixed by copying a space from
+      // the good triangle to the coinciding vertex.
+      // all other degenerate triangles will just copy a space from any good triangle
+      // with the same welded index in vertices[].
+      degenEpilogue();
+    }
+
+    uint index = 0;
+    for (uint f = 0; f < nrFaces; f++) {
+      const uint verts = mesh.GetNumVerticesOfFace(f);
+      if (verts != 3 && verts != 4) {
+        continue;
+      }
+
+      // set data
+      for (uint i = 0; i < verts; i++) {
+        const TSpace &tSpace = tSpaces[index++];
+        mesh.SetTangentSpace(f, i, tSpace.tangent, tSpace.orientPreserving);
+      }
+    }
+  }
+
+ protected:
+  template<typename F> void runParallel(uint start, uint end, F func)
+  {
+#ifdef WITH_TBB
+    if (isParallel) {
+      tbb::parallel_for(start, end, func);
+    }
+    else
+#endif
+    {
+      for (uint i = start; i < end; i++) {
+        func(i);
+      }
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  float3 getPosition(uint vertexID)
+  {
+    uint f, v;
+    unpack_index(f, v, vertexID);
+    return mesh.GetPosition(f, v);
+  }
+
+  float3 getNormal(uint vertexID)
+  {
+    uint f, v;
+    unpack_index(f, v, vertexID);
+    return mesh.GetNormal(f, v);
+  }
+
+  float3 getTexCoord(uint vertexID)
+  {
+    uint f, v;
+    unpack_index(f, v, vertexID);
+    return mesh.GetTexCoord(f, v);
+  }
+
+  bool has_uv() const
+  {
+    return mesh.has_uv();
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  void generateInitialVerticesIndexList()
+  {
+    nrTriangles = 0;
+    for (uint f = 0; f < nrFaces; f++) {
+      const uint verts = mesh.GetNumVerticesOfFace(f);
+      if (verts == 3) {
+        nrTriangles += 1;
+      }
+      else if (verts == 4) {
+        nrTriangles += 2;
+      }
+    }
+
+    triangles.reserve(nrTriangles);
+
+    nrTSpaces = 0;
+    for (uint f = 0; f < nrFaces; f++) {
+      const uint verts = mesh.GetNumVerticesOfFace(f);
+      if (verts != 3 && verts != 4) {
+        continue;
+      }
+
+      uint tA = uint(triangles.size());
+      triangles.emplace_back(f, nrTSpaces);
+      Triangle &triA = triangles[tA];
+
+      if (verts == 3) {
+        triA.setVertices(0, 1, 2);
+      }
+      else {
+        uint tB = uint(triangles.size());
+        triangles.emplace_back(f, nrTSpaces);
+        Triangle &triB = triangles[tB];
+
+        // need an order independent way to evaluate
+        // tspace on quads. This is done by splitting
+        // along the shortest diagonal.
+        float distSQ_02 = (mesh.GetTexCoord(f, 2) - mesh.GetTexCoord(f, 0)).length_squared();
+        float distSQ_13 = (mesh.GetTexCoord(f, 3) - mesh.GetTexCoord(f, 1)).length_squared();
+        bool quadDiagIs_02;
+        if (distSQ_02 != distSQ_13) {
+          quadDiagIs_02 = (distSQ_02 < distSQ_13);
+        }
+        else {
+          distSQ_02 = (mesh.GetPosition(f, 2) - mesh.GetPosition(f, 0)).length_squared();
+          distSQ_13 = (mesh.GetPosition(f, 3) - mesh.GetPosition(f, 1)).length_squared();
+          quadDiagIs_02 = !(distSQ_13 < distSQ_02);
+        }
+
+        if (quadDiagIs_02) {
+          triA.setVertices(0, 1, 2);
+          triB.setVertices(0, 2, 3);
+        }
+        else {
+          triA.setVertices(0, 1, 3);
+          triB.setVertices(1, 2, 3);
+        }
+      }
+
+      nrTSpaces += verts;
+    }
+  }
+
+  struct VertexHash {
+    Mikktspace<Mesh> *mikk;
+    uint operator()(const uint &k) const
+    {
+      return hash_float3x3(mikk->getPosition(k), mikk->getNormal(k), mikk->getTexCoord(k));
+    }
+  };
+
+  struct VertexEqual {
+    Mikktspace<Mesh> *mikk;
+    bool operator()(const uint &kA, const uint &kB) const
+    {
+      return mikk->getTexCoord(kA) == mikk->getTexCoord(kB) &&
+             mikk->getNormal(kA) == mikk->getNormal(kB) &&
+             mikk->getPosition(kA) == mikk->getPosition(kB);
+    }
+  };
+
+  /* Merge identical vertices.
+   * To find vertices with identical position, normal and texcoord, we calculate a hash of the 9
+   * values. Then, by sorting based on that hash, identical elements (having identical hashes) will
+   * be moved next to each other. Since there might be hash collisions, the elements of each block
+   * are then compared with each other and duplicates are merged.
+   */
+  template<bool isAtomic> void generateSharedVerticesIndexList_impl()
+  {
+    uint numVertices = nrTriangles * 3;
+    AtomicHashSet<uint, isAtomic, VertexHash, VertexEqual> set(numVertices, {this}, {this});
+    runParallel(0u, nrTriangles, [&](uint t) {
+      for (uint i = 0; i < 3; i++) {
+        auto res = set.emplace(triangles[t].vertices[i]);
+        if (!res.second) {
+          triangles[t].vertices[i] = res.first;
+        }
+      }
+    });
+  }
+  void generateSharedVerticesIndexList()
+  {
+    if (isParallel) {
+      generateSharedVerticesIndexList_impl<true>();
+    }
+    else {
+      generateSharedVerticesIndexList_impl<false>();
+    }
+  }
+
+  /////////////////////////////////////////////////////////////////////////////////////////////
+  /////////////////////////////////// Degenerate triangles ////////////////////////////////////
+
+  void degenPrologue()
+  {
+    // Mark all degenerate triangles
+    totalTriangles = nrTriangles;
+    std::atomic<uint> degenTriangles(0);
+    runParallel(0u, totalTriangles, [&](uint t) {
+      const float3 p0 = getPosition(triangles[t].vertices[0]);
+      const float3 p1 = getPosition(triangles[t].vertices[1]);
+      const float3 p2 = getPosition(triangles[t].vertices[2]);
+      if (p0 == p1 || p0 == p2 || p1 == p2)  // degenerate
+      {
+        triangles[t].markDegenerate = true;
+        degenTriangles.fetch_add(1);
+      }
+    });
+    nrTriangles -= degenTriangles.load();
+
+    if (totalTriangles == nrTriangles) {
+      return;
+    }
+
+    // locate quads with only one good triangle
+    runParallel(0u, totalTriangles - 1, [&](uint t) {
+      Triangle &triangleA = triangles[t], &triangleB = triangles[t + 1];
+      if (triangleA.faceIdx != triangleB.faceIdx) {
+        /* Individual triangle, skip. */
+        return;
+      }
+      if (triangleA.markDegenerate != triangleB.markDegenerate) {
+        triangleA.quadOneDegenTri = true;
+        triangleB.quadOneDegenTri = true;
+      }
+    });
+
+    std::stable_partition(triangles.begin(), triangles.end(), [](const Triangle &tri) {
+      return !tri.markDegenerate;
+    });
+  }
+
+  void degenEpilogue()
+  {
+    if (nrTriangles == totalTriangles) {
+      return;
+    }
+
+    std::unordered_map<uint, uint> goodTriangleMap;
+    for (uint t = 0; t < nrTriangles; t++) {
+      for (uint i = 0; i < 3; i++) {
+        goodTriangleMap.emplace(triangles[t].vertices[i], pack_index(t, i));
+      }
+    }
+
+    // deal with degenerate triangles
+    // punishment for degenerate triangles is O(nrTriangles) extra memory.
+    for (uint t = nrTriangles; t < totalTriangles; t++) {
+      // degenerate triangles on a quad with one good triangle are skipped
+      // here but processed in the next loop
+      if (triangles[t].quadOneDegenTri) {
+        continue;
+      }
+
+      for (uint i = 0; i < 3; i++) {
+        const auto entry = goodTriangleMap.find(triangles[t].vertices[i]);
+        if (entry == goodTriangleMap.end()) {
+          // Matching vertex from good triangle is not found.
+          continue;
+        }
+
+        uint tSrc, iSrc;
+        unpack_index(tSrc, iSrc, entry->second);
+        const uint iSrcVert = triangles[tSrc].faceVertex[iSrc];
+        const uint iSrcOffs = triangles[tSrc].tSpaceIdx;
+        const uint iDstVert = triangles[t].faceVertex[i];
+        const uint iDstOffs = triangles[t].tSpaceIdx;
+        // copy tspace
+        tSpaces[iDstOffs + iDstVert] = tSpaces[iSrcOffs + iSrcVert];
+      }
+    }
+
+    // deal with degenerate quads with one good triangle
+    for (uint t = 0; t < nrTriangles; t++) {
+      // this triangle belongs to a quad where the
+      // other triangle is degenerate
+      if (!triangles[t].quadOneDegenTri) {
+        continue;
+      }
+      uint vertFlag = (1u << triangles[t].faceVertex[0]) | (1u << triangles[t].faceVertex[1]) |
+                      (1u << triangles[t].faceVertex[2]);
+      uint missingFaceVertex = 0;
+      if ((vertFlag & 2) == 0) {
+        missingFaceVertex = 1;
+      }
+      else if ((vertFlag & 4) == 0) {
+        missingFaceVertex = 2;
+      }
+      else if ((vertFlag & 8) == 0) {
+        missingFaceVertex = 3;
+      }
+
+      uint faceIdx = triangles[t].faceIdx;
+      float3 dstP = mesh.GetPosition(faceIdx, missingFaceVertex);
+      bool found = false;
+      for (uint i = 0; i < 3; i++) {
+        const uint faceVertex = triangles[t].faceVertex[i];
+        const float3 srcP = mesh.GetPosition(faceIdx, faceVertex);
+        if (srcP == dstP) {
+          const uint offset = triangles[t].tSpaceIdx;
+          tSpaces[offset + missingFaceVertex] = tSpaces[offset + faceVertex];
+          found = true;
+          break;
+        }
+      }
+      assert(found);
+      (void)found;
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  // returns the texture area times 2
+  float calcTexArea(uint tri)
+  {
+    const float3 t1 = getTexCoord(triangles[tri].vertices[0]);
+    const float3 t2 = getTexCoord(triangles[tri].vertices[1]);
+    const float3 t3 = getTexCoord(triangles[tri].vertices[2]);
+
+    const float t21x = t2.x - t1.x;
+    const float t21y = t2.y - t1.y;
+    const float t31x = t3.x - t1.x;
+    const float t31y = t3.y - t1.y;
+
+    const float signedAreaSTx2 = t21x * t31y - t21y * t31x;
+    return fabsf(signedAreaSTx2);
+  }
+
+  void initTriangle()
+  {
+    // triangles[f].iFlag is cleared in generateInitialVerticesIndexList()
+    // which is called before this function.
+
+    // evaluate first order derivatives
+    runParallel(0u, nrTriangles, [&](uint t) {
+      Triangle &triangle = triangles[t];
+
+      // initial values
+      const float3 v1 = getPosition(triangle.vertices[0]);
+      const float3 v2 = getPosition(triangle.vertices[1]);
+      const float3 v3 = getPosition(triangle.vertices[2]);
+      const float3 t1 = getTexCoord(triangle.vertices[0]);
+      const float3 t2 = getTexCoord(triangle.vertices[1]);
+      const float3 t3 = getTexCoord(triangle.vertices[2]);
+
+      float t21x = t2.x - t1.x;
+      float t31x = t3.x - t1.x;
+      if (!has_uv()) {
+        /* Compute edge length in toroidal space, since the u generated by `map_to_sphere()` might
+         * go cross the seam. */
+        t21x -= floorf(t21x + 0.5f);
+        t31x -= floorf(t31x + 0.5f);
+      }
+
+      const float t21y = t2.y - t1.y;
+      const float t31y = t3.y - t1.y;
+      const float3 d1 = v2 - v1, d2 = v3 - v1;
+
+      const float signedAreaSTx2 = t21x * t31y - t21y * t31x;
+      const float3 vOs = (t31y * d1) - (t21y * d2);   // eq 18
+      const float3 vOt = (-t31x * d1) + (t21x * d2);  // eq 19
+
+      triangle.orientPreserving = (signedAreaSTx2 > 0);
+
+      if (not_zero(signedAreaSTx2)) {
+        const float lenOs2 = vOs.length_squared();
+        const float lenOt2 = vOt.length_squared();
+        const float fS = triangle.orientPreserving ? 1.0f : (-1.0f);
+        if (not_zero(lenOs2)) {
+          triangle.tangent = vOs * (fS / sqrtf(lenOs2));
+        }
+
+        // if this is a good triangle
+        if (not_zero(lenOs2) && not_zero(lenOt2)) {
+          triangle.groupWithAny = false;
+        }
+      }
+    });
+
+    // force otherwise healthy quads to a fixed orientation
+    runParallel(0u, nrTriangles - 1, [&](uint t) {
+      Triangle &triangleA = triangles[t], &triangleB = triangles[t + 1];
+      if (triangleA.faceIdx != triangleB.faceIdx) {
+        // this is not a quad
+        return;
+      }
+
+      // bad triangles should already have been removed by
+      // degenPrologue(), but just in case check that neither are degenerate
+      if (!(triangleA.markDegenerate || triangleB.markDegenerate)) {
+        // if this happens the quad has extremely bad mapping!!
+        if (triangleA.orientPreserving != triangleB.orientPreserving) {
+          bool chooseOrientFirstTri = false;
+          if (triangleB.groupWithAny) {
+            chooseOrientFirstTri = true;
+          }
+          else if (calcTexArea(t) >= calcTexArea(t + 1)) {
+            chooseOrientFirstTri = true;
+          }
+
+          // force match
+          const uint t0 = chooseOrientFirstTri ? t : (t + 1);
+          const uint t1 = chooseOrientFirstTri ? (t + 1) : t;
+          triangles[t1].orientPreserving = triangles[t0].orientPreserving;
+        }
+      }
+    });
+  }
+
+  /////////////////////////////////////////////////////////////////////////////////////////////
+  /////////////////////////////////////////// Edges ///////////////////////////////////////////
+
+  struct NeighborShard {
+    struct Entry {
+      Entry(uint32_t key_, uint data_) : key(key_), data(data_) {}
+      uint key, data;
+    };
+    std::vector<Entry> entries;
+
+    NeighborShard(size_t capacity)
+    {
+      entries.reserve(capacity);
+    }
+
+    void buildNeighbors(Mikktspace<Mesh> *mikk)
+    {
+      /* Entries are added by iterating over t, so by using a stable sort,
+       * we don't have to compare based on t as well. */
+      {
+        std::vector<Entry> tempEntries(entries.size(), {0, 0});
+        radixsort(entries, tempEntries, [](const Entry &e) { return e.key; });
+      }
+
+      for (uint i = 0; i < entries.size(); i++) {
+        const Entry &a = entries[i];
+        uint tA, iA;
+        unpack_index(tA, iA, a.data);
+        Mikktspace<Mesh>::Triangle &triA = mikk->triangles[tA];
+
+        if (triA.neighbor[iA] != UNSET_ENTRY) {
+          continue;
+        }
+
+        uint i0A = triA.vertices[iA], i1A = triA.vertices[(iA != 2) ? (iA + 1) : 0];
+        for (uint j = i + 1; j < entries.size(); j++) {
+          const Entry &b = entries[j];
+          uint tB, iB;
+          unpack_index(tB, iB, b.data);
+          Mikktspace<Mesh>::Triangle &triB = mikk->triangles[tB];
+
+          if (b.key != a.key) {
+            break;
+          }
+
+          if (triB.neighbor[iB] != UNSET_ENTRY) {
+            continue;
+          }
+
+          uint i1B = triB.vertices[iB], i0B = triB.vertices[(iB != 2) ? (iB + 1) : 0];
+          if (i0A == i0B && i1A == i1B) {
+            triA.neighbor[iA] = tB;
+            triB.neighbor[iB] = tA;
+            break;
+          }
+        }
+      }
+    }
+  };
+
+  void buildNeighbors()
+  {
+    /* In order to parallelize the processing, we divide the vertices into shards.
+     * Since only vertex pairs with the same key will be checked, we can process
+     * shards independently as long as we ensure that all vertices with the same
+     * key go into the same shard.
+     * This is done by hashing the key to get the shard index of each vertex.
+     */
+    // TODO: Two-step filling that first counts and then fills? Could be parallel then.
+    uint targetNrShards = isParallel ? uint(4 * nrThreads) : 1;
+    uint nrShards = 1, hashShift = 32;
+    while (nrShards < targetNrShards) {
+      nrShards *= 2;
+      hashShift -= 1;
+    }
+
+    /* Reserve 25% extra to account for variation due to hashing. */
+    size_t reserveSize = size_t(double(3 * nrTriangles) * 1.25 / nrShards);
+    std::vector<NeighborShard> shards(nrShards, {reserveSize});
+
+    for (uint t = 0; t < nrTriangles; t++) {
+      Triangle &triangle = triangles[t];
+      for (uint i = 0; i < 3; i++) {
+        const uint i0 = triangle.vertices[i];
+        const uint i1 = triangle.vertices[(i != 2) ? (i + 1) : 0];
+        const uint high = std::max(i0, i1), low = std::min(i0, i1);
+        const uint hash = hash_uint3(high, low, 0);
+        /* TODO: Reusing the hash here means less hash space inside each shard.
+         * Computing a second hash with a different seed it probably not worth it? */
+        const uint shard = isParallel ? (hash >> hashShift) : 0;
+        shards[shard].entries.emplace_back(hash, pack_index(t, i));
+      }
+    }
+
+    runParallel(0u, nrShards, [&](uint s) { shards[s].buildNeighbors(this); });
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  void assignRecur(const uint t, uint groupId)
+  {
+    if (t == UNSET_ENTRY) {
+      return;
+    }
+
+    Triangle &triangle = triangles[t];
+    Group &group = groups[groupId];
+
+    // track down vertex
+    const uint vertRep = group.vertexRepresentative;
+    uint i = 3;
+    if (triangle.vertices[0] == vertRep) {
+      i = 0;
+    }
+    else if (triangle.vertices[1] == vertRep) {
+      i = 1;
+    }
+    else if (triangle.vertices[2] == vertRep) {
+      i = 2;
+    }
+    assert(i < 3);
+
+    // early out
+    if (triangle.group[i] != UNSET_ENTRY) {
+      return;
+    }
+
+    if (triangle.groupWithAny) {
+      // first to group with a group-with-anything triangle
+      // determines its orientation.
+      // This is the only existing order dependency in the code!!
+      if (triangle.group[0] == UNSET_ENTRY && triangle.group[1] == UNSET_ENTRY &&
+          triangle.group[2] == UNSET_ENTRY)
+      {
+        triangle.orientPreserving = group.orientPreserving;
+      }
+    }
+
+    if (triangle.orientPreserving != group.orientPreserving) {
+      return;
+    }
+
+    triangle.group[i] = groupId;
+
+    const uint t_L = triangle.neighbor[i];
+    const uint t_R = triangle.neighbor[i > 0 ? (i - 1) : 2];
+    assignRecur(t_L, groupId);
+    assignRecur(t_R, groupId);
+  }
+
+  void build4RuleGroups()
+  {
+    /* NOTE: This could be parallelized by grouping all [t, i] pairs into
+     * shards by hash(triangles[t].vertices[i]). This way, each shard can be processed
+     * independently and in parallel.
+     * However, the `groupWithAny` logic needs special handling (e.g. lock a mutex when
+     * encountering a `groupWithAny` triangle, then sort it out, then unlock and proceed). */
+    for (uint t = 0; t < nrTriangles; t++) {
+      Triangle &triangle = triangles[t];
+      for (uint i = 0; i < 3; i++) {
+        // if not assigned to a group
+        if (triangle.groupWithAny || triangle.group[i] != UNSET_ENTRY) {
+          continue;
+        }
+
+        const uint newGroupId = uint(groups.size());
+        triangle.group[i] = newGroupId;
+
+        groups.emplace_back(triangle.vertices[i], bool(triangle.orientPreserving));
+
+        const uint t_L = triangle.neighbor[i];
+        const uint t_R = triangle.neighbor[i > 0 ? (i - 1) : 2];
+        assignRecur(t_L, newGroupId);
+        assignRecur(t_R, newGroupId);
+      }
+    }
+  }
+
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+  ///////////////////////////////////////////////////////////////////////////////////////////////////
+
+  template<bool atomic> void accumulateTSpaces(uint t)
+  {
+    const Triangle &triangle = triangles[t];
+    // only valid triangles get to add their contribution
+    if (triangle.groupWithAny) {
+      return;
+    }
+
+    /* TODO: Vectorize?
+     * Also: Could add special case for flat shading, when all normals are equal half of the fCos
+     * projections and two of the three tangent projections are unnecessary. */
+    std::array<float3, 3> n, p;
+    for (uint i = 0; i < 3; i++) {
+      n[i] = getNormal(triangle.vertices[i]);
+      p[i] = getPosition(triangle.vertices[i]);
+    }
+
+    std::array<float, 3> fCos = {dot(project(n[0], p[1] - p[0]), project(n[0], p[2] - p[0])),
+                                 dot(project(n[1], p[2] - p[1]), project(n[1], p[0] - p[1])),
+                                 dot(project(n[2], p[0] - p[2]), project(n[2], p[1] - p[2]))};
+
+    for (uint i = 0; i < 3; i++) {
+      uint groupId = triangle.group[i];
+      if (groupId != UNSET_ENTRY) {
+        float3 tangent = project(n[i], triangle.tangent) *
+                         fast_acosf(std::clamp(fCos[i], -1.0f, 1.0f));
+        if constexpr (atomic) {
+          groups[groupId].accumulateTSpaceAtomic(tangent);
+        }
+        else {
+          groups[groupId].accumulateTSpace(tangent);
+        }
+      }
+    }
+  }
+
+  void generateTSpaces()
+  {
+    if (isParallel) {
+      runParallel(0u, nrTriangles, [&](uint t) { accumulateTSpaces<true>(t); });
+    }
+    else {
+      for (uint t = 0; t < nrTriangles; t++) {
+        accumulateTSpaces<false>(t);
+      }
+    }
+
+    /* TODO: Worth parallelizing? Probably not. */
+    for (Group &group : groups) {
+      group.normalizeTSpace();
+    }
+
+    tSpaces.resize(nrTSpaces);
+
+    for (uint t = 0; t < nrTriangles; t++) {
+      Triangle &triangle = triangles[t];
+      for (uint i = 0; i < 3; i++) {
+        uint groupId = triangle.group[i];
+        if (groupId == UNSET_ENTRY) {
+          continue;
+        }
+        const Group group = groups[groupId];
+        assert(triangle.orientPreserving == group.orientPreserving);
+
+        // output tspace
+        const uint offset = triangle.tSpaceIdx;
+        const uint faceVertex = triangle.faceVertex[i];
+        tSpaces[offset + faceVertex].accumulateGroup(group);
+      }
+    }
+  }
+};
+
+}  // namespace mikk