一些关于UE的ProceduralMeshComponent的知识
Engine\Plugins\Runtime\ProceduralMeshComponent\Source\ProceduralMeshComponent\Private\KismetProceduralMeshLibrary.cpp
CreateGridMeshTriangles是简单的一种构建vertex index的方法，这和x，y的循环嵌套顺序有关
void UKismetProceduralMeshLibrary::CreateGridMeshTriangles(int32 NumX, int32 NumY, bool bWinding, TArray<int32>& Triangles)
{
Triangles.Reset();
if (NumX >= 2 && NumY >= 2)
{
// 两个for循环嵌套分出一个个四边形
for (int XIdx = 0; XIdx < NumX - 1; XIdx++)
{
for (int YIdx = 0; YIdx < NumY - 1; YIdx++)
{
const int32 I0 = (XIdx + 0)*NumY + (YIdx + 0);
const int32 I1 = (XIdx + 1)*NumY + (YIdx + 0);
const int32 I2 = (XIdx + 1)*NumY + (YIdx + 1);
const int32 I3 = (XIdx + 0)*NumY + (YIdx + 1);
//再把每个四边形分成三角形给到Triangles，Winding是false则逆时针
if (bWinding)
{
ConvertQuadToTriangles(Triangles, I0, I1, I2, I3);
}
else
{
ConvertQuadToTriangles(Triangles, I0, I3, I2, I1);
}
}
}
}
}
void UKismetProceduralMeshLibrary::ConvertQuadToTriangles(TArray<int32>& Triangles, int32 Vert0, int32 Vert1, int32 Vert2, int32 Vert3)
{
Triangles.Add(Vert0);
Triangles.Add(Vert1);
Triangles.Add(Vert3);
Triangles.Add(Vert1);
Triangles.Add(Vert2);
Triangles.Add(Vert3);
}
CalculateTangentsforMesh函数, 此函数执行消耗可以被命令行stat ProceduralMesh捕获
首先声明一些变量做准备
void UKismetProceduralMeshLibrary::CalculateTangentsForMesh(const TArray<FVector>& Vertices, const TArray<int32>& Triangles, const TArray<FVector2D>& UVs, TArray<FVector>& Normals, TArray<FProcMeshTangent>& Tangents)
{
// 三角形面数
const int32 NumTris = Triangles.Num() / 3;
// 顶点数
const int32 NumVerts = Vertices.Num();
// key是Vertices数组的index即VertexIndex，value是三角形面的index
TMultiMap<int32, int32> VertToTriMap;
// 和上面类似，不过会对重叠的点做一些处理来使后面计算的normal更平滑
TMultiMap<int32, int32> VertToTriSmoothMap;
// 每个三角面的TBN
TArray<FVector3f> FaceTangentX, FaceTangentY, FaceTangentZ;
FaceTangentX.AddUninitialized(NumTris);
FaceTangentY.AddUninitialized(NumTris);
FaceTangentZ.AddUninitialized(NumTris);
之后遍历每个三角面来填充这些变量
for (int TriIdx = 0; TriIdx < NumTris; TriIdx++)
{
int32 CornerIndex[3];//UV的index
FVector3f P[3];//顶点数据
//遍历三角形的三个点
for (int32 CornerIdx = 0; CornerIdx < 3; CornerIdx++)
{
// 计算三角形顶点的index
int32 VertIndex = FMath::Min(Triangles[(TriIdx * 3) + CornerIdx], NumVerts - 1);
CornerIndex[CornerIdx] = VertIndex;
P[CornerIdx] = (FVector3f)Vertices[VertIndex];
// 这里就是重叠的点，之后对VertToTriSmoothMap做处理
TArray<int32> VertOverlaps;
FindVertOverlaps(VertIndex, Vertices, VertOverlaps);
// Remember which triangles map to this vert
VertToTriMap.AddUnique(VertIndex, TriIdx);
VertToTriSmoothMap.AddUnique(VertIndex, TriIdx);
// 处理重叠的点
for (int32 OverlapIdx = 0; OverlapIdx < VertOverlaps.Num(); OverlapIdx++)
{
// For each vert we overlap..
int32 OverlapVertIdx = VertOverlaps[OverlapIdx];
// 将同位置的点都添加当前三角形index
VertToTriSmoothMap.AddUnique(OverlapVertIdx, TriIdx);
// 将当前顶点index添加同位置点所在的三角形index
TArray<int32> OverlapTris;
VertToTriMap.MultiFind(OverlapVertIdx, OverlapTris);
for (int32 OverlapTriIdx = 0; OverlapTriIdx < OverlapTris.Num(); OverlapTriIdx++)
{
VertToTriSmoothMap.AddUnique(VertIndex, OverlapTris[OverlapTriIdx]);
}
}
}
// 三角形两边叉乘作为此三角形的法线
const FVector3f Edge21 = P[1] - P[2];
const FVector3f Edge20 = P[0] - P[2];
const FVector3f TriNormal = (Edge21 ^ Edge20).GetSafeNormal();
// If we have UVs, use those to calc
if (UVs.Num() == Vertices.Num())
{
const FVector2D T1 = UVs[CornerIndex[0]];
const FVector2D T2 = UVs[CornerIndex[1]];
const FVector2D T3 = UVs[CornerIndex[2]];
FMatrix ParameterToLocal(
FPlane(P[1].X - P[0].X, P[1].Y - P[0].Y, P[1].Z - P[0].Z, 0),
FPlane(P[2].X - P[0].X, P[2].Y - P[0].Y, P[2].Z - P[0].Z, 0),
FPlane(P[0].X, P[0].Y, P[0].Z, 0),
FPlane(0, 0, 0, 1)
);
FMatrix ParameterToTexture(
FPlane(T2.X - T1.X, T2.Y - T1.Y, 0, 0),
FPlane(T3.X - T1.X, T3.Y - T1.Y, 0, 0),
FPlane(T1.X, T1.Y, 1, 0),
FPlane(0, 0, 0, 1)
);
// 纹理坐标矩阵的逆矩阵乘以三角形两边组成的矩阵得到矩阵(T,B)参考：https://learnopengl-cn.github.io/05%20Advanced%20Lighting/04%20Normal%20Mapping/
const FMatrix TextureToLocal = ParameterToTexture.Inverse() * ParameterToLocal;
// 即乘以(1,0,0)得到T
FaceTangentX[TriIdx] = FVector4f(TextureToLocal.TransformVector(FVector(1, 0, 0)).GetSafeNormal());
// 即乘以(0,1,0)得到B
FaceTangentY[TriIdx] = FVector4f(TextureToLocal.TransformVector(FVector(0, 1, 0)).GetSafeNormal());
}
else
{
FaceTangentX[TriIdx] = Edge20.GetSafeNormal();
FaceTangentY[TriIdx] = (FaceTangentX[TriIdx] ^ TriNormal).GetSafeNormal();
}
FaceTangentZ[TriIdx] = TriNormal;
}
计算完所有三角形面后，再根据之前记录的VertToTriMap和VertToTriSmoothMap将同一个顶点上的TBN数据进行简单相加(无权，不是有权相加，比如可使用面积或夹角等方法进行加权，确保越大的三角形对顶点的影响越大)
// Arrays to accumulate tangents into
TArray<FVector3f> VertexTangentXSum, VertexTangentYSum, VertexTangentZSum;
VertexTangentXSum.AddZeroed(NumVerts);
VertexTangentYSum.AddZeroed(NumVerts);
VertexTangentZSum.AddZeroed(NumVerts);
// For each vertex..
for (int VertxIdx = 0; VertxIdx < Vertices.Num(); VertxIdx++)
{
// Find relevant triangles for normal
TArray<int32> SmoothTris;
VertToTriSmoothMap.MultiFind(VertxIdx, SmoothTris);
for (int i = 0; i < SmoothTris.Num(); i++)
{
int32 TriIdx = SmoothTris[i];
VertexTangentZSum[VertxIdx] += FaceTangentZ[TriIdx];
}
// Find relevant triangles for tangents
TArray<int32> TangentTris;
VertToTriMap.MultiFind(VertxIdx, TangentTris);
for (int i = 0; i < TangentTris.Num(); i++)
{
int32 TriIdx = TangentTris[i];
VertexTangentXSum[VertxIdx] += FaceTangentX[TriIdx];
VertexTangentYSum[VertxIdx] += FaceTangentY[TriIdx];
}
}
最后归一化并使用施密特正交化确保T与N正交
// Finally, normalize tangents and build output arrays
Normals.Reset();
Normals.AddUninitialized(NumVerts);
Tangents.Reset();
Tangents.AddUninitialized(NumVerts);
for (int VertxIdx = 0; VertxIdx < NumVerts; VertxIdx++)
{
FVector3f& TangentX = VertexTangentXSum[VertxIdx];
FVector3f& TangentY = VertexTangentYSum[VertxIdx];
FVector3f& TangentZ = VertexTangentZSum[VertxIdx];
TangentX.Normalize();
TangentZ.Normalize();
Normals[VertxIdx] = (FVector)TangentZ;
// T' = normalize(T - dot(T, N) * N),由于N已经归一化于是除以N^2则省略了
TangentX -= TangentZ * (TangentZ | TangentX);
TangentX.Normalize();
// See if we need to flip TangentY when generating from cross product
const bool bFlipBitangent = ((TangentZ ^ TangentX) | TangentY) < 0.f;
Tangents[VertxIdx] = FProcMeshTangent((FVector)TangentX, bFlipBitangent);
}
}