The Concentric Interpolation method efficiently interpolates multi-dimensional data on multi-dimensional spaces. It is based on a concentric placement of the function samples, i.e. centered around the origin and placed along equidistributed directions at certain radii. This structure is exploited by means of a two-staged interpolation: first, a radial interpolation is performed, i.e. a one-dimensional interpolation along each direction by means of piecewise defined polynomial. Second, a tangential interpolation is performed using classical spherical basis functions. For more information, see the associated research article:
| Authors | Oliver Kunc and Felix Fritzen |
| Title | Generation of energy-minimizing point sets on spheres and their application in mesh-free interpolation and differentiation |
| Journal | Advances in Computational Mathematics |
| Year | 2019 |
| Volume | 45 |
| Issue | 5-6 |
| Pages | 3021-3056 |
| DOI | 10.1007/s10444-019-09726-5 |
A C++ compiler (e.g. g++), the CMake utility and an implementation of LAPACKE are required. In Debian or Ubuntu systems, the command
sudo apt install g++ cmake liblapacke-devshould suffice.
Build command for the documentation:
doxygen ConcentricInterpolation.doxyThis requires doxygen software which can be installed by running
sudo apt install doxygenon Debian or Ubuntu systems. Then, see doxygen output in ./doxygen/html/index.html or in ./doxygen/latex/*.pdf. See inline comments for further details.
For the library, in the project root run (1. configure cmake and generate build files, 2. perform actual build)
mkdir build
cd build
cmake ..
cmake --build .Optional: To make the library available systemwide you can install it by running (add --prefix <install_dir> for a test install):
sudo cmake --install .Alternatively you can use the CMake feature FetchContent and refer to this git repository to pull the code and compile it as part of your project (See CMake documentation for details). Independent of the way you chose to incorporate the library into your project you can use target_link_libraries(tgt ConInter::ConInter) to link to the library.
The following CMake configuration options exist (set them by -DOPTION=ON/OFF):
-
CMAKE_BUILD_TYPE: Sets the build type. Common values are Debug, Release, RelWithDebInfo, and MinSizeRel. Have a look at the CMake Documentation for details. -
CMAKE_INTERPROCEDURAL_OPTIMIZATION: Enable inter-procedural optimization (IPO) for all targets.- Default: ON (if supported)
- Note: When you run the configure step for the first time, IPO support is automatically checked and enabled if available. A status message will indicate whether IPO is activated or not supported.
-
CONINTER_BUILD_SHARED: Build a shared library instead.- Default: OFF
-
CONINTER_BUILD_EXAMPLES: Build the examples.- Default: ON if top level project
-
CONINTER_MKL: Use Intel MKL library for CBLAS and LAPACKE.- Default: OFF
-
CONINTER_DEPS_FALLBACK: Skip automatic dependency detection and use hardcoded dependency paths.- Default: OFF
-
CONINTER_DEPS_LINK_STATIC: Link statically against dependencies LAPACK, LAPACKE and BLAS.- Default: ON
When referring to this software, please cite the article mentioned above in Section 1 What's this.
- Indentation by 4 spaces, no tabs.
- Camel case function names, variable names less strict.
- No trailing whitespaces.
- Function arguments begin with "a_" in order to strictly separate from local identifiers. Local identifiers do not begin with "a_".
- Error handling not rigorous yet. Unclear where to go from here, depends on yet unknown user requirements.
- Working on low-level pointer objects: the user is required to assure that memory bounds are respected. Setup functions and destructors take care of the basic management, but access to components is unrestricted. Read or write access is controlled via the respective Get... or Set... functions.
- Const correctness: top-level pointers are not const, all lower levels should be const. This is mostly but not 100% consistent atm.
- For essential conditional checks in functions, use UTILITY::assert_msg()
- If a scope (e.g. body of a loop) consists of only one line, don't use braces "{}" but only indentation.
Please report bugs and suggestions to the administrators of the corresponding github repository: https://github.com/EMMA-Group/ConcentricInterpolation or directly e-mail [email protected] or [email protected]
See file LICENSE