I have a problem with the FBX SDK. I read in the data for the vertex position and the uv coordinates. It works fine, but now I want to read for each polygon to which texture it belongs, so that I can have models with multiple textures. Can anyone tell me how I can get the texture name (file name) for my polygon. My code to read in vertex position and uv coordinates is the following:

int i, j, lPolygonCount = pMesh->GetPolygonCount();
FbxVector4* lControlPoints = pMesh->GetControlPoints(); 


int vertexId = 0;
for (i = 0; i < lPolygonCount; i++)
{

    int lPolygonSize = pMesh->GetPolygonSize(i);

    for (j = 0; j < lPolygonSize; j++)
    {


        int lControlPointIndex = pMesh->GetPolygonVertex(i, j);
        FbxVector4 pos = lControlPoints[lControlPointIndex];
        current_model[vertex_index].x = pos.mData[0] - pivot_offset[0];
        current_model[vertex_index].y = pos.mData[1] - pivot_offset[1];
        current_model[vertex_index].z = pos.mData[2]- pivot_offset[2];

        FbxVector4 vertex_normal;
        pMesh->GetPolygonVertexNormal(i,j, vertex_normal); 


        current_model[vertex_index].nx = vertex_normal.mData[0];
        current_model[vertex_index].ny = vertex_normal.mData[1];
        current_model[vertex_index].nz = vertex_normal.mData[2];



        //read in UV data
        FbxStringList lUVSetNameList;
        pMesh->GetUVSetNames(lUVSetNameList);


        //get lUVSetIndex-th uv set
        const char* lUVSetName = lUVSetNameList.GetStringAt(0);
        const FbxGeometryElementUV* lUVElement = pMesh->GetElementUV(lUVSetName);

        if(!lUVElement)
            continue;

            // only support mapping mode eByPolygonVertex and eByControlPoint
        if( lUVElement->GetMappingMode() != FbxGeometryElement::eByPolygonVertex &&
            lUVElement->GetMappingMode() != FbxGeometryElement::eByControlPoint )
            return;

        //index array, where holds the index referenced to the uv data
        const bool lUseIndex = lUVElement->GetReferenceMode() != FbxGeometryElement::eDirect;
        const int lIndexCount= (lUseIndex) ? lUVElement->GetIndexArray().GetCount() : 0;

        FbxVector2 lUVValue;

        //get the index of the current vertex in control points array
        int lPolyVertIndex = pMesh->GetPolygonVertex(i,j);

        //the UV index depends on the reference mode
        //int lUVIndex = lUseIndex ? lUVElement->GetIndexArray().GetAt(lPolyVertIndex) : lPolyVertIndex;
        int lUVIndex = pMesh->GetTextureUVIndex(i, j);
        lUVValue = lUVElement->GetDirectArray().GetAt(lUVIndex);
        current_model[vertex_index].tu = (float)lUVValue.mData[0];
        current_model[vertex_index].tv = (float)lUVValue.mData[1];


        vertex_index ++;
        }

    }

    float v1[3], v2[3], v3[3];
    v1[0] = current_model[vertex_index - 3].x;
    v1[1] = current_model[vertex_index - 3].y;
    v1[2] = current_model[vertex_index - 3].z;

    v2[0] = current_model[vertex_index - 2].x;
    v2[1] = current_model[vertex_index - 2].y;
    v2[2] = current_model[vertex_index - 2].z;

    v3[0] = current_model[vertex_index - 1].x;
    v3[1] = current_model[vertex_index - 1].y;
    v3[2] = current_model[vertex_index - 1].z;

    collision_model->addTriangle(v1,v2,v3);