SLEEFE

A library to build Subdividable Linear Equi-spaced Efficient Function Enclosures (SLEEFE)

INTRODUCTION

This repository contains the source code and documentation files for the library SLEEFE. This library offers functionality to build tight lower and upper piecewise-linear envelopes for the graph of univariate polynomial functions in Bernstein-Bézier form. The picture below illustrates a sleefe for a univariate polynomial function of degree 3. The Bernstein-Bézier coefficients of the function are 3, -2, -1, and 0.5. The lower and upper envelopes of the sleefe have three line segments (i.e., four breakpoints) each.

The source code is organized as follows:

• bin - subdirectory where the executable sleefe-demo will be installed
• doc - subdirectory where Doxygen documentation files are
• ide - subdirectory where ready-to-use project files for Visual Studio, Visual Code, and Xcode are
• include - subdirectory where header files of the library will be installed
• lib - subdirectory where the lib file of the library will be installed
• plots - subdirectory containing plots of the anti-difference functions
• src - subdirectory containing the library, demo, and uni tests source files
• tst - subdirectory where the executable sleefe-tst will be installed
• CMakeLists.txt - input file for the CMake build system
• LICENSE.md - copyright and license file
• README.md - this file

USAGE

Detailed documentation on how to use the library can be found in the file refman.pdf inside the directory doc

INSTALLATION

You will need CMake 3.15 or higher and a C++ compiler that supports C++ 17 to build the library, the demo, and (optionally) the unit tests. If you enable the generation of unit tests, then CMake will try to download and install the GTest library from here. Both options have successfully been built with CMake version 3.22.1 on Linux (Ubuntu 22.04 LTS with GNU g++ 11.2.0), Windows 10 (MS Visual Studio 17), and macOS Monterrey version 12.6.2 (clang version 14.0.0).

If you wish `CMake' to create an Xcode project, then 2 above should be

• Run cmake -G Xcode -S . -B build

If you prefer not to use CMake to install the library, you can try the ready-to-use projects in directory ide. There are ready-to-use projects for Visual Studio (Windows), XCode (macOSX), and Linux (Visual Code). In all cases, the paths are relative. So, do not move these projects out of directory ide nor did move their files around. During the build, the projects will place the library file and the executable demo file in the directories lib and bin, respectively, using the relative paths.

To build and install the library, follow the steps below:

1. Download or clone the code, and then enter the directory SLEEFE
2. Run cmake -S . -B build
3. Run cmake --build build --config Release
4. Run cmake --install build --prefix <full path to your SLEEFE directory>

If all goes well, then you should see the executable sleefe-demo (or sleefe-demo.exe on Windows) in subdirectory bin and the library libslefe.a (or slefe.lib on Windows) in subdirectory lib.

If you wish to build the unit tests, then execute the steps above with the following change to step 2:

• Run cmake -S . -B build -D BUILD_UNIT_TESTS=ON

If all goes well, then you should see the application sleefe-tst (or sleefe-tst.exe on Windows) in subdirectory tst.

Likewise, if you wish to build Doxygen documentation files, then execute the same steps above with the following change to step 2:

• Run cmake -S . -B build -D BUILD_DOC=ON

or

• Run cmake -S . -B build -D BUILD_UNIT_TESTS=ON -D BUILD_DOC=ON

Documentation is generated only if CMake can find Doxygen in your system. If this is the case and the build succeeds, then the documentation files are placed in subdirectory doc.

If you wish `CMake' to create a Visual Studio project, then step 2 above should be

• Run cmake -G "Visual Studio 15 2017" -A x64 -S . -B build

The exact generator depends on the version of your Visual Studio. Please, refer to the CMake documentation to determine which one is right for you.

References

1. Lutterkort, D., Envelopes for Nonlinear Geometry, PhD thesis, Purdue University, May 2000.

2. Lutterkort, D. and Peters, J., Linear envelopes for uniform B-spline curves, Curves and Surface Fitting, Saint-Malo, France, July 1-7, 1999, p. 239-246.

3. Lutterkort, D. and Peters, J., Optimized refinable enclosures of multivariate polynomial pieces, CAGD, 18(9), 2001, p. 851-863.

4. Wu, X. and Peters, J., On the Optimality of Piecewise Linear Max-norm Enclosures based on Slefes, Curves and Surface Design, Saint-Malo, France, 2002, p. 335-344.

CONTACT

If you run into trouble compiling or using the library, please email me at:

mfsiqueira@gmail.com

Have fun!

Marcelo Siqueira