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# Calculating Tangents (Vector4)

Hello!

I'm writing an importer and I would like to know if there's a way to generate tangents from my vertex,uvs and normals. Because mesh.RecalculateNormals isn't giving me the result I want.

thx!

sanryoga

**Answer** by Aras
·
Nov 16, 2009 at 05:28 PM

I assume you know what tangent space is then (in short: it's a surface-relative coordinate system, and consists of tangent, bitangent and normal; mostly used for normal mapped shaders).

Tangents in Unity are Vector4. Three components (xyz) of it store the tangent vector itself, and w component is used to determine "handedness" of the bitangent. Bitangent (sometimes called binormal) is always computed from tangent and normal. In Cg shader code:

```
float3 binormal = cross (normal, tangent.xyz) * tangent.w;
```

Now, computing tangents needs a texture coordinate set (UVs). There's actually tons of resources for that, e.g. Lengyel's approach is a good starting point. NVIDIA also has a NVMeshMender library that does it. Calculating tangents *can* get quite nasty when you want to make it fully robust.

**Answer** by noontz
·
Mar 30, 2010 at 06:00 PM

Here is the javascript derived from the link above & developed with help from t$$anonymous$$s thread http://forum.unity3d.com/viewtopic.php?t=41476

`/* Derived from Lengyel, Eric. Computing Tangent Space Basis Vectors for an Arbitrary Mesh. Terathon Software 3D Grap$$anonymous$$cs Library, 2001. http://www.terathon.com/code/tangent.html */`

` `

class TangentSolver { function TangentSolver(theMesh : Mesh) { vertexCount = theMesh.vertexCount; vertices = theMesh.vertices; normals = theMesh.normals; texcoords = theMesh.uv; triangles = theMesh.triangles; triangleCount = triangles.length/3; tangents = new Vector4[vertexCount]; tan1 = new Vector3[vertexCount]; tan2 = new Vector3[vertexCount]; tri = 0; for ( i = 0; i < (triangleCount); i++) { i1 = triangles[tri]; i2 = triangles[tri+1]; i3 = triangles[tri+2];

```
v1 = vertices[i1];
v2 = vertices[i2];
v3 = vertices[i3];
w1 = texcoords[i1];
w2 = texcoords[i2];
w3 = texcoords[i3];
x1 = v2.x - v1.x;
x2 = v3.x - v1.x;
y1 = v2.y - v1.y;
y2 = v3.y - v1.y;
z1 = v2.z - v1.z;
z2 = v3.z - v1.z;
s1 = w2.x - w1.x;
s2 = w3.x - w1.x;
t1 = w2.y - w1.y;
t2 = w3.y - w1.y;
r = 1.0 / (s1 * t2 - s2 * t1);
sdir = new Vector3((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
tdir = new Vector3((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);
tan1[i1] += sdir;
tan1[i2] += sdir;
tan1[i3] += sdir;
tan2[i1] += tdir;
tan2[i2] += tdir;
tan2[i3] += tdir;
tri += 3;
}
for (i = 0; i < (vertexCount); i++)
{
n = normals[i];
t = tan1[i];
// Gram-Schmidt orthogonalize
Vector3.OrthoNormalize( n, t );
tangents[i].x = t.x;
tangents[i].y = t.y;
tangents[i].z = t.z;
// Calculate handedness
tangents[i].w = ( Vector3.Dot(Vector3.Cross(n, t), tan2[i]) < 0.0 ) ? -1.0 : 1.0;
}
theMesh.tangents = tangents;
}
```

`} `

**Answer** by N1nja
·
May 29, 2010 at 03:47 PM

and the same script in C#..

```
class TangentSolver
{
public static void Solve(Mesh mesh)
{
int triangleCount = mesh.triangles.Length / 3;
int vertexCount = mesh.vertices.Length;
```

```
```

```
Vector3[] tan1 = new Vector3[vertexCount];
Vector3[] tan2 = new Vector3[vertexCount];
Vector4[] tangents = new Vector4[vertexCount];
for(long a = 0; a < triangleCount; a+=3)
{
long i1 = mesh.triangles[a+0];
long i2 = mesh.triangles[a+1];
long i3 = mesh.triangles[a+2];
Vector3 v1 = mesh.vertices[i1];
Vector3 v2 = mesh.vertices[i2];
Vector3 v3 = mesh.vertices[i3];
Vector2 w1 = mesh.uv[i1];
Vector2 w2 = mesh.uv[i2];
Vector2 w3 = mesh.uv[i3];
float x1 = v2.x - v1.x;
float x2 = v3.x - v1.x;
float y1 = v2.y - v1.y;
float y2 = v3.y - v1.y;
float z1 = v2.z - v1.z;
float z2 = v3.z - v1.z;
float s1 = w2.x - w1.x;
float s2 = w3.x - w1.x;
float t1 = w2.y - w1.y;
float t2 = w3.y - w1.y;
float r = 1.0f / (s1 * t2 - s2 * t1);
Vector3 sdir = new Vector3((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
Vector3 tdir = new Vector3((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);
tan1[i1] += sdir;
tan1[i2] += sdir;
tan1[i3] += sdir;
tan2[i1] += tdir;
tan2[i2] += tdir;
tan2[i3] += tdir;
}
for (long a = 0; a < vertexCount; ++a)
{
Vector3 n = mesh.normals[a];
Vector3 t = tan1[a];
Vector3 tmp = (t - n * Vector3.Dot(n, t)).normalized;
tangents[a] = new Vector4(tmp.x, tmp.y, tmp.z);
tangents[a].w = (Vector3.Dot(Vector3.Cross(n, t), tan2[a]) < 0.0f) ? -1.0f : 1.0f;
}
mesh.tangents = tangents;
}
```

}

**Answer** by cyble
·
Jul 07, 2012 at 01:50 PM

In the C# version: to prevent corrupt tangents, make sure you catch the division by zero as it will result in a NaN. You can do t$$anonymous$$s by replacing the calculation of r with somet$$anonymous$$ng like t$$anonymous$$s:

```
float div = s1 * t2 - s2 * t1;
float r = div == 0.0f ? 0.0f : 1.0f / div;
```

**Answer** by dvorm
·
Jul 09, 2019 at 06:45 AM

Thank you for t$$anonymous$$s one. It works fine even today.

Both triangleCount vertexCount and are int w$$anonymous$$le a is long. That seems inconsistent. Can anyone explain?

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