Signed Heat Method

signed-heat-3d is a C++ library implementing the Signed Heat Method for computing robust signed distance fields (SDFs) to triangle meshes, polygon meshes, and point clouds in 3D.

teaser image

Python bindings to this C++ code also exist via the signedheat3d package on PyPI: toggle the “C++/Python” switch at the top of this page to see documentation for the Python version.

Sample:

The library uses geometry-central to manage mesh and point cloud structures.

#include "signedheat3d/signed_heat_grid_solver.h"
#include "signedheat3d/signed_heat_tet_solver.h"

#include "geometrycentral/surface/vertex_position_geometry.h"
#include "geometrycentral/pointcloud/point_position_normal_geometry.h"

using namespace geometrycentral;
using namespace geometrycentral::surface;
using namespace geometrycentral::pointcloud;

// Assume we have some input geometry -- these are geometry-central objects.
SurfaceMesh mesh;
VertexPositionGeometry geometry;
PointPositionNormalGeometry pointGeom;

// Initalize tet mesh solver
SignedHeatTetSolver tetSolver = SignedHeatTetSolver();

// Configure some options
SignedHeat3DOptions solveOptions; // all the default options should be pretty good

// Solve!
Vector<double> sdf = tetSolver.computeDistance(geometry, solveOptions); // get distance to the mesh!
Vector<double> sdf = tetSolver.computeDistance(pointGeom, solveOptions); // get distance to the point cloud!

// Solve on a grid instead.
SignedHeatGridSolver gridSolver = SignedHeatGridSolver();
solveOptions.resolution = {64, 64, 64}; // change the resolution of the grid
Vector<double> sdf = gridSolver.computeDistance(geometry, solveOptions); // get distance to the mesh!
Vector<double> sdf = gridSolver.computeDistance(pointGeom, solveOptions); // get distance to the point cloud!

See the sample project to get started with a GUI and build system.

More info about the method, including a blog-style summary, an introductory 10-minute talk, and the corresponding academic paper are all located at the project page here.

Related libraries

The Signed Heat Method has been implemented in both C++ and Python, in 2D and in 3D.

If you’re interested in using the Signed Heat Method on 2D surface domains, rather than in 3D space, the method has been implemented in geometry-central for triangle mesh domains, polygon mesh domains, and point cloud domains. A demo project exists at signed-heat-demo.
Likewise, Python bindings to the geometry-central C++ code has been implemented in the Python package potpourri3d.

Credits

If this code contributes to an academic publication, cite it as:

@article{Feng:2024:SHM,
    author = {Feng, Nicole and Crane, Keenan},
    title = {A Heat Method for Generalized Signed Distance},
    year = {2024},
    issue_date = {August 2024},
    publisher = {Association for Computing Machinery},
    address = {New York, NY, USA},
    volume = {43},
    number = {4},
    issn = {0730-0301},
    url = {https://doi.org/10.1145/3658220},
    doi = {10.1145/3658220},
    journal = {ACM Trans. Graph.},
    month = {jul},
    articleno = {92},
    numpages = {16}
}