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An Efficient Implementation of Analytic Mesh Algorithm for 3D Iso-surface Extraction from Neural Networks


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Analytic Marching is an exact meshing solution from neural networks. Compared to standard methods, it completely avoids geometric and topological errors that result from insufficient sampling, by means of mathematically guaranteed analysis.

This repository gives an implementation of Analytic Marching algorithm. This algorithm is initially proposed in our conference paper Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks, then finally improved in our journal paper: Learning and Meshing from Deep Implicit Surface Networks Using an Efficient Implementation of Analytic Marching.

This figure shows different meshing patterns obtained from different meshing methods. AM: Analytic Marching (ours); GM: Greedy Mesh; MC: Marching Cubes; MT: Marching Tetrahedra; DC: Dual Contouring. Interestingly, AM's pattern is seemingly irregular, where each line indicates a crease formed by the space-folding mechanism. Also, our mesh is exact, which means for every point sampled from the mesh surface, its level value is exactly zero.

Our codes provide web pages for manipulating your models via graphic interface, and a backend for giving full control of the algorithm by writing python codes.


First please download our codes:

git clone --depth=1
cd AnalyticMesh
export AMROOT=`pwd`


Backend gives a python binding of analytic marching. You can write simple python codes in your own project after compiling the backend.

Our implementation supports pytorch, and possibly also other deep learning frameworks (e.g. tensorflow), because we use an Open Neural Network Exchange (ONNX) format to store model as file, but we haven't tested any other frameworks yet. If you are interested in other frameworks, welcome to make contribution.



cd $AMROOT/backend
mkdir build && cd build
cmake ..
make -j8
cd ..

If your pytorch version < 1.5.1, you may need to fix cpp extension compile failure on some envs.

Make sure compiled library can pass the tests. Run:

CUDA_VISIBLE_DEVICES=0 PYTHONDONTWRITEBYTECODE=1 pytest -s -p no:warnings -p no:cacheprovider

It will generate some files under folder $AMROOT/backend/tmp. Generally, those generated meshes (.ply) are watertight, you can check with meshlab.

If it passes all the tests, you can finally link to somewhere so that python can find it:

ln -s $AMROOT `python -c 'import site; print(site.getsitepackages()[0])'`


We also provide an easy-to-use interactive interface to apply analytic marching to your input network model by just clicking your mouse. To use the web interface, you may follow steps below to install.


Before compiling, you may need to modify the server information given in file frontend/pages/src/assets/index.js. Then you can compile those files by running:

cd $AMROOT/frontend/pages
npm install
npm run build

The $AMROOT/frontend/pages/dist directory is ready to be deployed. If you want to deploy web pages to a server, please additionally follow these instructions.

To start the server, simply run:

cd $AMROOT/frontend && python

You can open the interface via either opening file $AMROOT/frontend/pages/dist/index.html on your local machine or opening the url to which the page is deployed.


We provide some samples in $AMROOT/examples, you can try them.

Here we show a simple example (which is from $AMROOT/examples/

import os
import torch
from AnalyticMesh import save_model, load_model, AnalyticMarching

class MLPPolytope(torch.nn.Module):
    def __init__(self):
        super(MLPPolytope, self).__init__()
        self.linear0 = torch.nn.Linear(3, 14)
        self.linear1 = torch.nn.Linear(14, 1)
        with torch.no_grad(): # here we give the weights explicitly since training takes time
            weight0 = torch.tensor([[ 1,  1,  1],
                                    [-1, -1, -1],
                                    [ 0,  1,  1],
                                    [ 0, -1, -1],
                                    [ 1,  0,  1],
                                    [-1,  0, -1],
                                    [ 1,  1,  0],
                                    [-1, -1,  0],
                                    [ 1,  0,  0],
                                    [-1,  0,  0],
                                    [ 0,  1,  0],
                                    [ 0, -1,  0],
                                    [ 0,  0,  1],
                                    [ 0,  0, -1]], dtype=torch.float32)
            bias0 = torch.zeros(14)
            weight1 = torch.ones([14], dtype=torch.float32).unsqueeze(0)
            bias1 = torch.tensor([-2], dtype=torch.float32)

            add_noise = lambda x: x + torch.randn_like(x) * (1e-7)

    def forward(self, x):
        return self.linear1(torch.relu(self.linear0(x)))

if __name__ == "__main__":
    #### save onnx
    DIR = os.path.dirname(os.path.abspath(__file__)) # the directory to save files
    onnx_path = os.path.join(DIR, "polytope.onnx")
    save_model(MLPPolytope(), onnx_path) # we save the model as onnx format
    print(f"we save onnx to: {onnx_path}")

    #### save ply
    ply_path = os.path.join(DIR, "polytope.ply")
    model = load_model(onnx_path) # load as a specific model
    AnalyticMarching(model, ply_path) # do analytic marching
    print(f"we save ply to: {ply_path}")


We mainly provide the following two ways to use analytic marching:

  • Web interface (provides an easy-to-use graphic interface)
  • Python API (gives more detailed control)
  1. Web interface

    You should compile both the backend and frontend to use this web interface. Its usage is detailed in the user guide on the web page.

  2. Python API

    It's very simple to use, just three lines of code.

    from AnalyticMesh import load_model, AnalyticMarching 
    model = load_model(load_onnx_path) 
    AnalyticMarching(model, save_ply_path)

    If results are not satisfactory, you may need to change default values of the AnalyticMarching function.

    To obtain an onnx model file, you can just use the save_model function we provide.

    from AnalyticMesh import save_model
    save_model(your_custom_nn_module, save_onnx_path)

Some tips:

  • It is highly recommended that you try dichotomy first as the initialization method.
  • If CUDA runs out of memory, try setting voxel_configs. It will partition the space and solve them serially.
  • More details are commented in our source codes.

Use Analytic Marching in your own project

There are generally three ways to use Analytic Marching.

  1. Directly representing a single shape by a multi-layer perceptron. For a single object, you can simply represent the shape as a single network. For example, you can directly fit a point cloud by a multi-layer perceptron. In this way, the weights of the network uniquely determine the shape.
  2. Generating the weights of multi-layer perceptron from a hyper-network. To learn from multiple shapes, one can use hyper-network to generate the weights of multi-layer perceptron in a learnable manner.
  3. Re-parameterizing the latent code into the bias of the first layer. To learn from multiple shapes, we can condition the network with a latent code input at the first layer (e.g. 3+256 -> 512 -> 512 -> 1). Note that the concatenated latent code can be re-parameterized and combined into the bias of the first layer. More specifically, the computation of the first layer can be re-parameterized as , where the newly computed bias is .


This repository is mainly maintained by Jiabao Lei (backend) and Yongyi Su (frontend). If you find our works useful, please consider citing our papers.

    title = {Analytic Marching: An Analytic Meshing Solution from Deep Implicit Surface Networks},
    author = {Jiabao Lei and Kui Jia},
    booktitle = {International Conference on Machine Learning 2020 {ICML-20}},
    year = {2020},
    month = {7}

    author={Lei, Jiabao and Jia, Kui and Ma, Yi},
    journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
    title={Learning and Meshing from Deep Implicit Surface Networks Using an Efficient Implementation of Analytic Marching}, 

If you have any questions, feel free to create an issue on github, or you can also email me via:



An Efficient Implementation of Analytic Mesh Algorithm for 3D Iso-surface Extraction from Neural Networks








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