Sweeps

This is a research code investigating techniques to create coarse hex layouts for fitting multipatch B-splines to be used in isogeometric analysis. It uses foliations and harmonic functions to extend quad layouts to sweepable volumetric geometries. By restriction to linear B-splines, it can also generate hex meshes. The input to the algorithm is a tet mesh on the sweepable geometry, an indication of which portions of the boundary the sweep runs from and to (the source and target surfaces), and a quad layout on the source surface of the sweep which will be swept through the volume.

Papers

The following papers have been written based on the material in this codebase:

C. B. Goates and K. M. Shepherd, "Harmonic-based sweeps need not yield volumetric parameterizations," Computer-Aided Design (2025). DOI: 10.1016/j.cad.2025.104007

Presentations

The following presentations have been given based on the material in this codebase:

C. B. Goates and K. M. Shepherd, "Curvilinear hexahedral cell generation for swept trivariate splines using foliations," 12th International Conference on IsoGeometric Analysis (2024).

C. B. Goates and K. M. Shepherd, "Hexahedral mesh generation for swept splines using foliations," 2025 SIAM International Meshing Roundtable (2025).

C. B. Goates and K. M. Shepherd, "Curvilinear Hexahedral Cell Complexes for Swept Trivariate Splines via Foliations," 2025 SIAM Computational Science and Engineering (2025).

C. B. Goates and K. M. Shepherd, "Enabling high-order computational flow simulations using foliation-informed hexahedral spline discretizations," 18th U.S. National Congress on Computational Mechanics (2025).

Building

This project requires CMake 3.24 or newer. Once you have cloned the repo, build as follows:

In the build directory of choice (e.g. <git root>/build) run

cmake <path/to/git/root> -DCMAKE_BUILD_TYPE=Release
make -j10

Dependencies will be downloaded and built automatically. To run tests, run ctest -j10 in the build directory after building.

Recreating Results

To recreate the results published in the journal article "Harmonic-based sweeps need not yield volumetric parameterizations" (10.1016/j.cad.2025.104007), follow these steps: Once the code is built and the tests are passing, run the following command in the build directory to generate the results for the bordered surface counterexample that is a union of two cylinders:

src/sweep output-laplace counter2 output-critical-points

This will generate two files: test.vtu, containing the tetrahedral mesh with the discrete harmonic function defined on it as a field called "laplace" and critical_points.vtu, which contains the critical points of the discrete harmonic function.

To generate the results for the closed surface counterexample, run the command

src/sweep output-laplace part_torus_in_sphere output-critical-points

which will generate the same files, overwriting them if they exist. These .vtu files can be opened in ParaView to generate level sets using their Contour filter.

API

The sweeps codebase includes a work-in-progress Python API. To use the python API, after building the codebase, include the following in your python script:

import sys
sys.path.insert(0, '<path/to/build/directory>/src/api')
import sweeps

Documentation for the sweeps api can be found in python using help(sweeps). An example use of the api can be seen in scripts/test_sweep_param.py, particularly in the meshHookWithQuadMesh() function.