Packing UV meshes results are invalid

[Korinin38]

Similar to #95
Tried packing Smiling boy from Real-World Textured Things dataset, ID#7. Repacking it results in a horrible manner:

As mentioned in #95, packing can create invalid geometry (though I doubt it should be happening with valid input). I tried fixing it by removing faces that include vertices with Vertex::atlasIndex = -1, but there are still stray overlapping faces (and untextured regions on object):

Relevant code:

std::vector<tinyobj::shape_t> shapes;
// ... import from tiny_obj_loader

xatlas::Atlas *atlas = xatlas::Create();

for (int i = 0; i < (int) shapes.size(); i++) {
    const tinyobj::mesh_t &objMesh = shapes[i].mesh;
    xatlas::UvMeshDecl uvMeshDecl;
    uvMeshDecl.faceMaterialData = (const uint32_t *)objMesh.material_ids.data();
    uvMeshDecl.vertexCount = (uint32_t) objMesh.texcoords.size() / 2;
    uvMeshDecl.vertexUvData = objMesh.texcoords.data();
    uvMeshDecl.vertexStride = sizeof(float) * 2;
    uvMeshDecl.indexCount = (uint32_t) objMesh.indices.size();
    uvMeshDecl.indexData = objMesh.indices.data();
    uvMeshDecl.indexFormat = xatlas::IndexFormat::UInt32;

    xatlas::AddMeshError error = xatlas::AddUvMesh(atlas, uvMeshDecl);
    // ... error-handling
}

xatlas::ComputeCharts(atlas);
xatlas::PackCharts(atlas, options);

// ... file creation
// export
uint32_t firstVertex = 0;
for (uint32_t i = 0; i < atlas->meshCount; i++) {
    const xatlas::Mesh &mesh = atlas->meshes[i];
    for (uint32_t v = 0; v < mesh.vertexCount; v++) {
        const xatlas::Vertex &vertex = mesh.vertexArray[v];
        const float *pos = &shapes[i].mesh.positions[vertex.xref * 3];
        fprintf(file, "v %g %g %g\n", vertex.uv[0] / atlas->width, vertex.uv[1] / atlas->height, 0.f);
    }
    fprintf(file, "o %s\n", shapes[i].name.c_str());
    fprintf(file, "s off\n");
    for (uint32_t f = 0; f < mesh.indexCount; f += 3) {
        bool valid_vertex = true;
        for (uint32_t j = 0; j < 3; j++) {
            if (mesh.vertexArray[mesh.indexArray[f + j]].atlasIndex == -1) 
                valid_vertex = false;
        }
        // removing faces with invalid vertices
        if (!valid_vertex) {
            continue;
        }
        fprintf(file, "f ");
        for (uint32_t j = 0; j < 3; j++) {
            const uint32_t index = firstVertex + mesh.indexArray[f + j] + 1; // 1-indexed
            fprintf(file, "%d/%d/%d%c", index, index, index, j == 2 ? '\n' : ' ');
        }
    }
    firstVertex += mesh.vertexCount;
}

PackCharts options

xatlas::PackOptions options;
options.maxChartSize = 0;
options.padding = 0;
options.texelsPerUnit = 0.0f;
options.resolution = 1024;
options.bilinear = true;
options.blockAlign = false;
options.bruteForce = true;
options.createImage = false;
options.rotateChartsToAxis = true;
options.rotateCharts = true;

[Korinin38]

I managed to isolate one component that is divided into two charts incorrectly:

this component becomes that after packing. (Sorry about scale inconsistencies)
The difference is apparent:
this

becomes that

Notice that a small part of the chart gets separated from the rest, while retaining the connection.

[Korinin38]

Found the reason for this behavior:
Face is ignored (mesh->faceIgnore.set(face)) if the area of the face is considered to be zero (area <= internal::kAreaEpsilon (relevant code)). Ignored faces are skipped when dividing UV into charts.
That calculation can be too imprecise for massive UVs with normalised coordinates.