ForCAD: A parallel Fortran library for geometric modeling using NURBS (Non-Uniform Rational B-Splines).

ForCAD supports B-Spline, NURBS, Bezier and Rational Bezier curves, surfaces and volumes.

Table of Contents

• Table of Contents
• Main Features
• Examples
• Installation
  • Requirements
  • Clone the repository
  • Install PyVista (Optional)
  • Using fpm
    • Running Examples with fpm
    • Using ForCAD as a fpm Dependency
  • Using CMake
    • Install
    • Uninstall
    • Using ForCAD with CMake
• Configuration
  • Do Concurrent Support
  • Precision Configuration
• CI Status
• API documentation
• Roadmap
• Contributing
• Citation
• References

Main Features

• Parallelized using do concurrent.
• Create NURBS objects by specifying control points, weights and knots.
• Refine NURBS objects by inserting or removing knots and elevating degree.
• Compute analytical basis functions and their first and second derivatives for NURBS and B-Spline objects.
• Generation of IGA-compatible element connectivity and shape functions.
• Obtain visualized elements connectivity and coordinates for geometry and control geometry.
• Mesh insertion into a NURBS object.
• Export NURBS objects to VTK files for visualization.
• Export of NURBS curves and surfaces to IGES format (volumes currently not supported).
• Includes predefined NURBS shapes: Circle, Half Circle, Tetragon, Hexahedron, 2D Ring, Half 2D Ring, 3D Ring, Half 3D Ring, C-shapes.
• Rotate and translate NURBS objects.
• Visualization using provided python PyVista scripts.
• Least squares fitting for B-Spline curves, surfaces and volumes.
• Numerical integration of: NURBS curve length, NURBS surface area and NURBS volume.

Examples

Below are some sample outputs from the examples directory:

Installation

Requirements

• Fortran compiler:

  • GNU Fortran (gfortran)
  • Intel Fortran Compiler (ifx)
  • NVIDIA HPC SDK Fortran Compiler (nvfortran)
  • LLVM Flang (flang)

  Note: Latest compiler versions are required to ensure compatibility.

• Build system:

  • Fortran Package Manager (fpm)
  • CMake

• Optional visualization tools:

  • PyVista (recommended)
  • ParaView

Clone the repository

Clone the ForCAD repository from GitHub:

git clone https://github.com/gha3mi/forcad.git
cd forcad

Install PyVista (Optional)

To install PyVista, run the following command:

pip install pyvista

Using fpm

Running Examples with fpm

fpm run --example <file name excluding the .f90 extension> --compiler gfortran --profile release --flag "-ftree-parallelize-loops=8 -march=native"

After executing the examples, .vtk files will be generated in the vtk directory. To visualize these files, a show() method is provided which utilizes PyVista. Alternatively, other visualization tools like ParaView can also be used.

Using ForCAD as a fpm Dependency

If you want to use ForCAD as a dependency in your own fpm project, you can easily include it by adding the following line to your fpm.toml file:

[dependencies]
forcad = {git="https://github.com/gha3mi/forcad.git"}

Using CMake

Install

cmake -S . -B build/cmake -DCMAKE_BUILD_TYPE=Release -DBUILD_SHARED_LIBS=ON -DCMAKE_INSTALL_PREFIX=. -G Ninja
cmake --build build/cmake --config Release
cmake --install build/cmake --config Release --verbose

Uninstall

cmake --build build/cmake --target uninstall

Using ForCAD with CMake

find_package(forcad REQUIRED)
add_executable(app main.f90)
target_link_libraries(app PRIVATE forcad::forcad)

Configuration

Do Concurrent Support

Compiler flags for enabling do concurrent parallelism:

Compiler	Flag(s)
gfortran	-fopenmp -ftree-parallelize-loops=n
ifx	-qopenmp -fopenmp-target-do-concurrent
nvfortran	-stdpar=multicore,gpu -Minfo=stdpar,accel
flang-new	?
lfortran	?

Compiler flags can be passed to fpm using the --flag option, for example:

fpm build --flag "-stdpar=multicore,gpu -Minfo=stdpar,accel"

Alternatively, flags can be added to a fpm.rsp file in the root directory of the project.

Precision Configuration

The library uses double precision (real64) by default for all real-valued computations. To change the precision, you can define one of the following preprocessor flags during compilation:

Preprocessor Flag	Fortran Kind	Description
REAL32	selected_real_kind(6)	Single precision
REAL64 (default)	selected_real_kind(15)	Double precision
REALXDP	selected_real_kind(18)	Extended double precision
REAL128	selected_real_kind(33)	Quadruple precision

Note: The examples example_ppm1.f90, example_ppm2.f90 and example_ppm3.f90 use the ForColormap library, which only supports REAL64 precision.

Example: Building with double precision

fpm build --profile release --flag "-DREAL64"

CI Status

Compiler	macos	ubuntu	windows
flang-new	-	fpm ✅ cmake ✅	fpm ✅ cmake ❌
gfortran	fpm ✅ cmake ✅	fpm ✅ cmake ✅	fpm ✅ cmake ✅
ifx	-	fpm ✅ cmake ✅	fpm ✅ cmake ❌
lfortran	fpm ❌ cmake ❌	fpm ❌ cmake ❌	fpm ❌ cmake ❌
nvfortran	-	fpm ✅ cmake ✅	-

This table is automatically generated by the CI workflow using setup-fortran-conda.

API documentation

The most up-to-date API documentation for the master branch is available here. To generate the API documentation for ForCAD using ford run the following command:

ford README.md

Contributing

To contribute to ForCAD, please review the CONTRIBUTING.md.

Citation

If you use ForCAD in your research, please cite it as follows:

@software{seyed_ali_ghasemi_2025_10904447,
  author       = {Ghasemi, S. A.},
  title        = {gha3mi/ForCAD},
  year         = {2025},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.10904447},
  url          = {https://doi.org/10.5281/zenodo.10904447}
}

References

• Piegl, L., & Tiller, W. (1995). The NURBS Book. In Monographs in Visual Communications. Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-97385-7

• An Introduction to NURBS. (2001). Elsevier. https://doi.org/10.1016/b978-1-55860-669-2.x5000-3

• Sullivan et al., (2019). PyVista: 3D plotting and mesh analysis through a streamlined interface for the Visualization Toolkit (VTK). Journal of Open Source Software, 4(37), 1450, https://doi.org/10.21105/joss.01450

• Ahrens, James, Geveci, Berk, Law, Charles, ParaView: An End-User Tool for Large Data Visualization, Visualization Handbook, Elsevier, 2005, ISBN-13: 9780123875822