point_cloud_perception_experimental: canon_calibrate | data_acquisition_ptu | eigen_tests | heat_equation_solver | mapping_tools | object_mapping | octomap2 | octovis2 | pcl_detectors | pcl_detectors_clients | pcl_opencv_bridge | pcl_point_cloud2_image_color | pcl_registration_experimental | point_cloud_python | range_image_tests | surface_reconstruction | virtual_scanner
Package Summary
A special purpose linear system solver to solve the heat equation on an nD grid, given inputs of temperature 0 or 1 and given a uniform conductivity between neighboring cells. It is designed primarily for use by model_assembler.
- Author: Romain Thibaux
- License: BSD
- Repository: wg-ros-pkg
- Source: svn https://code.ros.org/svn/wg-ros-pkg/branches/trunk_cturtle/stacks/point_cloud_perception_experimental/heat_equation_solver
Contents
Algorithm
In a n-dimensional grid, each cell is connected to its 2n neighbors by a thermal conductivity k (called "smoothness" in the code), and to an external temperature source, with temperature and thermal conductivity given as input.
This class computes the equilibrium solution according to the heat equation. It can give an approximate solution using a multigrid method, i.e. solving first on a very coarse grid and extending the solution to finer and finer grids, and it can solve iteratively the original system (finest grid). All vector operations rely on Eigen.
Here is an example solution in 2D (rendered with matlab).
Input sources of heat and cold |
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Equilibrium solution of the heat equation |
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