Feature/Geometry type for tetrahedral meshes

[benjaminum]

This PR implements a new geometry type TetraMesh.

• Creation from PointClouds with Delaunay triangulation

• Isosurface extraction as TriangleMesh

• Visualization as lines

• Unit tests

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This change is 

[griegler]

Nice! I just have a few minor comments below.

Reviewed 24 of 25 files at r1.
Reviewable status: 24 of 25 files reviewed, 12 unresolved discussions (waiting on @benjaminum)

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src/Open3D/Geometry/Qhull.h, line 44 at r1 (raw file):

            const std::vector<Eigen::Vector3d>& points);

    static std::shared_ptr<TetraMesh> ComputeDelaunayTriangulation3D(

Suffix 3D needed? Why not simply ComputeDelaunayTriangulation? Or should it not be ComputeDelaunayTetrahedralization?

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src/Open3D/Geometry/Qhull.cpp, line 119 at r1 (raw file):

        delaunay_triangulation->tetras_.push_back(Vector4i(0, 1, 2, 3));
        return delaunay_triangulation;
    } else if (points.size() < 3) {

Is this case not already handled above?

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src/Open3D/Geometry/TetraMesh.h, line 89 at r1 (raw file):

    /// Function to extract a triangle mesh of the specified iso-surface at
    /// \param level. \param values are values per-vertex.

Can you add some references to the specific method that is used?

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src/Open3D/Geometry/TetraMesh.h, line 94 at r1 (raw file):

    /// Function that creates a tetrahedral mesh (TetraMeshFactory.cpp).
    /// from a point cloud.

Can you add some references to the specific method that is used, i.e., Delaunay from qhull?

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src/Open3D/Geometry/TetraMesh.cpp, line 190 at r1 (raw file):

dubplicates

typo

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src/Open3D/Geometry/TetraMesh.cpp, line 281 at r1 (raw file):

    }

    auto surface_intersection_test = [](double v0, double v1, double level) {

Functions/Lambdas should be CamelCase => SurfaceIntersectionTest

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src/Open3D/Geometry/TetraMesh.cpp, line 285 at r1 (raw file):

    };

    auto compute_edge_vertex = [&values, level, this](Index idx1, Index idx2) {

style

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src/Open3D/Geometry/TetraMesh.cpp, line 299 at r1 (raw file):

    };

    auto compute_triangle_normal = [](const Eigen::Vector3d &a,

style

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src/Open3D/Geometry/TetraMesh.cpp, line 302 at r1 (raw file):

                                      const Eigen::Vector3d &b,
                                      const Eigen::Vector3d &c) {
        Eigen::Vector3d ab(b - a);

Why using a constructor and not simply Eigen::Vector3d ab = b - a?

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src/Open3D/Geometry/TetraMesh.cpp, line 307 at r1 (raw file):

    };

    auto make_sorted_tuple2 = [](Index a, Index b) {

style

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src/Open3D/Geometry/TetraMesh.cpp, line 314 at r1 (raw file):

    };

    auto has_common_vertex_index = [](Index2 a, Index2 b) {

style

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src/Open3D/Geometry/TetraMesh.cpp, line 315 at r1 (raw file):

    auto has_common_vertex_index = [](Index2 a, Index2 b) {
        if (std::get<0>(b) == std::get<0>(a) ||

direct return instead of if/else

[benjaminum]

Reviewable status: 24 of 25 files reviewed, 12 unresolved discussions (waiting on @griegler)

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src/Open3D/Geometry/Qhull.h, line 44 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Suffix 3D needed? Why not simply ComputeDelaunayTriangulation? Or should it not be ComputeDelaunayTetrahedralization?

Fn name was inspired by the name in CGAL. I am fine with 3D suffix or Tetrahedralization.

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src/Open3D/Geometry/Qhull.cpp, line 119 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Is this case not already handled above?

Yes. Done.

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src/Open3D/Geometry/TetraMesh.h, line 89 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Can you add some references to the specific method that is used?

Done.

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src/Open3D/Geometry/TetraMesh.h, line 94 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Can you add some references to the specific method that is used, i.e., Delaunay from qhull?

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 190 at r1 (raw file):

Previously, griegler (Gernot) wrote…

dubplicates

typo

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 281 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Functions/Lambdas should be CamelCase => SurfaceIntersectionTest

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 285 at r1 (raw file):

Previously, griegler (Gernot) wrote…

style

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 299 at r1 (raw file):

Previously, griegler (Gernot) wrote…

style

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 302 at r1 (raw file):

Previously, griegler (Gernot) wrote…

Why using a constructor and not simply Eigen::Vector3d ab = b - a?

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 307 at r1 (raw file):

Previously, griegler (Gernot) wrote…

style

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 314 at r1 (raw file):

Previously, griegler (Gernot) wrote…

style

Done.

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src/Open3D/Geometry/TetraMesh.cpp, line 315 at r1 (raw file):

Previously, griegler (Gernot) wrote…

direct return instead of if/else

Done.

[yxlao]

Looks great! Thanks Benjamin.

Reviewed 11 of 25 files at r1, 5 of 5 files at r2.
Reviewable status: all files reviewed, 13 unresolved discussions (waiting on @benjaminum and @griegler)

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src/Open3D/Geometry/TetraMesh.cpp, line 181 at r2 (raw file):

    typedef decltype(tetras_)::value_type::Scalar Index;
    typedef std::tuple<Index, Index, Index, Index> Index4;
    std::unordered_map<Index4, size_t, utility::hash_tuple::hash<Index4>>

It is okay since we did the same for triangle mesh. We could also use eigen::Vector4i and utility::hash_eigen to avoid defying a new type.

[griegler]

LGTM

@griegler already approved

[AI-ML-Enthusiast]

@griegler
Would you give some idea to calculate Delaunay Triangulation using open3d in python? Thanks in advanced

[griegler]

https://github.com/intel-isl/Open3D/blob/master/src/Open3D/Geometry/TetraMesh.h#L109

[AI-ML-Enthusiast]

@griegler Thanks for your comment. but it gives precision error.H How can I use Qhull option for scaling?