Fix #139753: Discontinuity in mesh tangent without UV map

when there is no uv, we call the function `map_to_sphere()` to create
temporary uv for computing the tangent. It could happen that a triangle
has vertices with the u coordinates going across the line where u wraps
from 1 to 0. In this case, just computing the difference of the u
coordinates results in the wrong triangle area.

To fix this problem, we compute distance in toroidal (wrap around)
space.

This is safe for coordinates generated by `map_to_sphere()` function,
because it is not supposed to map the positions of a triangle to u
coordinates that span larger than 0.5.

Pull Request: https://projects.blender.org/blender/blender/pulls/139880

intern/cycles/scene/mesh.cpp

@@ -67,7 +67,7 @@ struct MikkMeshWrapper {
   {
     /* TODO: Check whether introducing a template boolean in order to
      * turn this into a constexpr is worth it. */
-    if (uv != nullptr) {
+    if (has_uv()) {
       const int corner_index = CornerIndex(face_num, vert_num);
       const float2 tfuv = uv[corner_index];
       return mikk::float3(tfuv.x, tfuv.y, 1.0f);
@@ -101,6 +101,11 @@ struct MikkMeshWrapper {
     }
   }
 
+  bool has_uv() const
+  {
+    return uv != nullptr;
+  }
+
   const Mesh *mesh;
 
   const float3 *normal;

intern/mikktspace/mikktspace.hh

@@ -253,6 +253,11 @@ template<typename Mesh> class Mikktspace {
     return mesh.GetTexCoord(f, v);
   }
 
+  bool has_uv() const
+  {
+    return mesh.has_uv();
+  }
+
   ///////////////////////////////////////////////////////////////////////////////////////////////////
   ///////////////////////////////////////////////////////////////////////////////////////////////////
 
@@ -522,9 +527,16 @@ template<typename Mesh> class Mikktspace {
       const float3 t2 = getTexCoord(triangle.vertices[1]);
       const float3 t3 = getTexCoord(triangle.vertices[2]);
 
-      const float t21x = t2.x - t1.x;
+      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 t31x = t3.x - t1.x;
       const float t31y = t3.y - t1.y;
       const float3 d1 = v2 - v1, d2 = v3 - v1;
 

source/blender/blenkernel/intern/editmesh_tangent.cc

@@ -95,7 +95,7 @@ struct SGLSLEditMeshToTangent {
   mikk::float3 GetTexCoord(const uint face_num, const uint vert_index)
   {
     const BMLoop *l = GetLoop(face_num, vert_index);
-    if (cd_loop_uv_offset != -1) {
+    if (has_uv()) {
       const float *uv = (const float *)BM_ELEM_CD_GET_VOID_P(l, cd_loop_uv_offset);
       return mikk::float3(uv[0], uv[1], 1.0f);
     }
@@ -130,6 +130,11 @@ struct SGLSLEditMeshToTangent {
     copy_v4_fl4(p_res, T.x, T.y, T.z, orientation ? 1.0f : -1.0f);
   }
 
+  bool has_uv()
+  {
+    return cd_loop_uv_offset != -1;
+  }
+
   Span<float3> face_normals;
   Span<float3> corner_normals;
   Span<std::array<BMLoop *, 3>> looptris;

source/blender/blenkernel/intern/mesh_tangent.cc

@@ -70,6 +70,11 @@ struct BKEMeshToTangent {
     copy_v4_fl4(p_res, T.x, T.y, T.z, orientation ? 1.0f : -1.0f);
   }
 
+  bool has_uv() const
+  {
+    return true;
+  }
+
   OffsetIndices<int> faces;         /* faces */
   const int *corner_verts;          /* faces vertices */
   const float (*positions)[3];      /* vertices */
@@ -227,7 +232,7 @@ struct SGLSLMeshToTangent {
     int3 tri;
     int face_index;
     uint loop_index = GetLoop(face_num, vert_num, tri, face_index);
-    if (mloopuv != nullptr) {
+    if (has_uv()) {
       const float2 &uv = mloopuv[loop_index];
       return mikk::float3(uv[0], uv[1], 1.0f);
     }
@@ -281,6 +286,11 @@ struct SGLSLMeshToTangent {
     copy_v4_fl4(tangent[loop_index], T.x, T.y, T.z, orientation ? 1.0f : -1.0f);
   }
 
+  bool has_uv() const
+  {
+    return mloopuv != nullptr;
+  }
+
   Span<float3> face_normals;
   Span<float3> corner_normals;
   const int3 *corner_tris;

tests/files/render/mesh/cycles_renders/tangent_no_uv.png

@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:cd07487f8bb71a4199fb15cf994599317670ca806757fdae24c00c85a26d3be2
+oid sha256:7fa3ab720f94fa70de22f70f9e87bd74b8cc06bff20a82352b53ee24d02e14d8
-size 28659
+size 28195

tests/files/render/mesh/eevee_next_renders/tangent_no_uv.png

@@ -1,3 +1,3 @@
 version https://git-lfs.github.com/spec/v1
-oid sha256:4a3a786cd629cbd7074a40c5ece486d6dccd031e8cafdf41ad5bd62f9c1afb1a
+oid sha256:e69131fc75964401791a7a13a29d50a44e04699f29f8ff23d827ddbd75899d3a
-size 20981
+size 20489

tests/python/eevee_render_tests.py

@@ -43,8 +43,6 @@ BLOCKLIST = [
 ]
 
 BLOCKLIST_METAL = [
-    # Blocked due to difference in tangent space calculation (to be fixed).
-    "tangent_no_uv.blend",
     # Blocked due to difference in volume lightprobe bakes (to be fixed).
     "clamp_.*.blend",
     "shadow_all_max_bounces.blend",