Field-Aligned Surface-Filling Curve via Implicit Stitching

This repository contains the reference implementation of Field-Aligned Surface-Filling Curve via Implicit Stitching. It allows the generation of continuous, field-aligned curves on triangulated meshes. For more details, refer to the project page.

Building

The project is designed with minimal dependencies in mind, relying only on the C++17 standard library. This makes the build process straightforward.

Unix-like systems

Run the following commands:

mkdir build && cd build
cmake ..
make -j8

Windows

Create a folder named build and run CMake as on Unix-like systems. Then, open the generated solution with Visual Studio and compile it. Precompiled binaries are also available here.

Running the Code

Run the program from the build folder using the following command:

./curve input_mesh.(ply|obj) curve_spacing [-e|-i|-p|-n] [-r] [-q] [-c curve.ply] [DEBUG_OPTIONS]

where the basic parameters are:

input_mesh.(ply|obj): Input mesh to be processed. For PLY files, only the ASCII format is supported.  
curve_spacing: Target distance between parallel segments of the curve.

[-e]: Initialize the direction field using vertex colors as 3D directions. [Default]
[-i]: Initialize the direction field using vertex color luminosity as an angle (0° to 180°) from a smooth direction field.  
[-p]: Initialize the direction field using vertex color luminosity as an angle (0° to 180°) from a smooth direction field parallel to the mesh borders.
[-n]: Initialize the direction field using vertex color luminosity as an angle (0° to 180°) from the direction of the closest mesh borders.  
[-r]: Uniformly resample the curve. This does not guarantee that the curve remains on the surface.
[-R] Repulse the curve and greatly improve spacing [Experimental].
[-q]: Suppress console output.  
[-c curve.ply]: Export the curve as a polyline.

and the advanced debug options are:

[-x]: Disables the stitching step.
[-l]: Initialize the direction field using vertex color luminosity as an angle (0° to 180°) for 3D printing. This option works only on layers like geometries, not on general ones where multiple curves may be produced.
[-C thick_curve.ply]: Export the curve as a solid mesh.
[-s scalars.ply]: Export the scalar field as a vertex-colored mesh.
[-P stripes.ply]: Export the stripe pattern as a vertex-colored mesh.  
[-d directions.ply]: Export the direction field as a vertex-colored mesh.  
[-D thick_directions.ply]: Export the direction field as a solid mesh.  
[-g disk_cut.ply]: Export the edge cuts that convert the mesh into a topological disk.
[-o medial_axis.obj]: Export the OBJ for Surface-Filling Curve Flows via Implicit Medial Axes.

To reproduce the results shown in Figure 19, simply run the following commands:

./curve ../data/bunny.ply 4.0 -c ../data/curve_4.ply
./curve ../data/bunny.ply 2.0 -c ../data/curve_2.ply
./curve ../data/bunny.ply 1.0 -c ../data/curve_1.ply

The resulting curves are standard PLY files and can be opened with any 3D software, such as Blender.

Improving Spacing

The option -R applies a post-processing step using the implicit medial axis. While it is still experimental and was not used in the article, we strongly recommend using it to improve the spacing near singularity points.

Mesh Input Format

The input mesh must be both vertex and edge manifold. The direction field can be provided using the vertex color attributes of the PLY file format. Furthermore, no vertex seams should be present.

Note: Our PLY loader is naive and supports only a limited subset of the ASCII format. In particular, no attributes other than vertex position and color should be present. Please refer to the file data/bunny.ply for an example of the expected PLY header. To export a PLY file from Blender, use the following export options.

Blender 4.5 Add-on

We provide an add-on to use the code in Blender 4.5 LTS. To install the plugin, follow these steps:

1. In Blender, select Edit → Preferences, then go to the Add-ons tab. Click Install from Disk and select the file blender_addon.py.
2. Expand the newly installed add-on and, under Executable Path, select the executable produced when building the project.
3. The add-on is accessible from the side panel (press N to open it). Select a mesh and click Generate to produce the surface-filling curve.

Citation

If you use this code in your research, please cite:

@article{Cocco2026FieldAlignedSurface,
  author = {Cocco, Giovanni and Chermain, Xavier},
  title = {Field-Aligned Surface-Filling Curve via Implicit Stitching},
  year = {2026},
  doi = {10.1111/cgf.70361},
  journal = {Computer Graphics Forum (Proceedings of Eurographics)},
}

License

All files in this project are provided under the MIT License, with the exception of src/disk.cpp, which is provided under the MPL v2.0 as it is derived from libigl.