Adaptive Multigrid Solvers (Version 10.05)

links executables usage changes

This code-base was born from the Poisson Surface Reconstruction code. It has evolved to support more general adaptive finite-elements systems:



  1. The implementation of the --samplesPerNode parameter has been modified so that a value of "1" more closely corresponds to a distribution with one sample per leaf node.
  2. The code has been modified to support compilation under MSVC 2010 and the associated solution and project files are now provided. (Due to a bug in the Visual Studios compiler, this required modifying the implementation of some of the bit-shifting operators.)
Version 4:
  1. The code supports screened reconstruction, with interpolation weight specified through the --pointWeight parameter.
  2. The code has been implemented to support parallel processing, with the number of threads used for parallelization specified by the --threads parameter.
  3. The input point set can now also be in PLY format, and the file-type is determined by the extension, so that the --binary flag is now obsolete.
  4. At depths coarser than the one specified by the value --minDepth the octree is no longer adaptive but rather complete, simplifying the prolongation operator.
Version 4.5:
  1. The algorithmic complexity of the solver was reduced from log-linear to linear.
Version 4.51:
  1. Smart pointers were added to ensure that memory accesses were in bounds.
Version 5:
  1. The --density flag was added to the reconstructor to output the estimated depth of the iso-vertices.
  2. The SurfaceTrimmer executable was added to support trimming off the subset of the reconstructed surface that are far away from the input samples, thereby allowing for the generation of non-water-tight surface.
Version 5.1:
  1. Minor bug-fix to address incorrect neighborhood estimation in the octree finalization.
Version 5.5a:
  1. Modified to support depths greater than 14. (Should work up to 18 or 19 now.)
  2. Improved speed and memory performance by removing the construction of integral and value tables.
  3. Fixed a bug in Version 5.5 that used memory and took more time without doing anything useful.
Version 5.6:
  1. Added the --normalWeight flag to support setting a point's interpolation weight in proportion to the magnitude of its normal.
Version 5.7:
  1. Modified the setting of the constraints, replacing the map/reduce implementation with OpenMP atomics to reduce memory usage.
  2. Fixed bugs that caused numerical overflow when processing large point clouds on multi-core machines.
  3. Improved efficiency of the iso-surface extraction phse.
Version 5.71:
  1. Added the function GetSolutionValue to support the evaluation of the implicit function at a specific point.
Version 6:
  1. Modified the solver to use Gauss-Seidel relaxation instead of conjugate-gradients at finer resolution.
  2. Re-ordered the implementation of the solver so that only a windowed subset of the matrix is in memory at any time, thereby reducing the memory usage during the solver phase.
  3. Separated the storage of the data associated with the octree nodes from the topology.
Version 6.1:
  1. Re-ordered the implementation of the iso-surface extraction so that only a windowed subset of the octree is in memory at any time, thereby reducing the memory usage during the extracted phase.
Version 6.11:
  1. Fixed a bug that created a crash in the evaluation phase when --pointWeight is set zero.
Version 6.12:
  1. Removed the OpenMP firstprivate directive as it seemed to cause trouble under Linux compilations.
Version 6.13:
  1. Added a MemoryPointStream class in PointStream.inl to support in-memory point clouds.
  2. Modified the signature of Octree::SetTree in MultiGridOctreeData.h to take in a pointer to an object of type PointStream rather than a file-name.
Version 6.13a:
  1. Modified the signature of Octree::SetIsoSurface to rerun a void. [cloudcompare]
  2. Added a definition of SetIsoVertexValue supporting double precision vertices. [cloudcompare]
  3. Removed Time.[h/cpp] from the repository. [cloudcompare/asmaloney]
  4. Fixed assignment bug in Octree::SetSliceIsoVertices. [asmaloney]
  5. Fixed initialization bug in SortedTreeNodes::SliceTableData and SortedTreeNodes::XSliceTableData. [asmaloney]
  6. Included stdlib.h in Geometry.h. [asmaloney]
  7. Fixed default value bug in declaration of Octree::SetTree. [asmaloney]
Version 7.0:
  1. Added functionality to support color extrapolation if present in the input.
  2. Modified a bug with the way in which sample contributions were scaled.
Version 8.0:
  1. Added support for different degree B-splines. (Note that as the B-spline degree is a template parameter, only degree 1 through 4 are supported. If higher order degrees are desired, additional template parameters can be easily added in the body of the Execute function inside of PoissonRecon.cpp. Similarly, to reduce compilation times, support for specific degrees can be removed.)
  2. Added the --primalVoxel flag to support to extraction of a voxel grid using primal sampling.
  3. Changed the implementation of the voxel sampling so that computation is now linear, rather than log-linear, in the number of samples.
Version 9.0:
  1. Added support for free boundary conditions.
  2. Extended the solver to support more general linear systems. This makes it possible to use the same framework to implement the Smoothed Signed Distance Reconstruction of Calakli and Taubin (2011).
  3. Modified the implementation of density estimation and input representation. This tends to define a slightly larger system. On its own, this results in slightly increased running-time/footprint for full-res reconstructions, but provides a substantially faster implementation when the output complexity is smaller than the input.
Version 9.01:
  1. Reverted the density estimation to behave as in Version 8.0.
Version 9.011:
  1. Added a parameter for specifying the temporary directory.
Version 10.00:
  1. The code has been reworked to support arbitrary dimensions, finite elements of arbitrary degree, generally SPD systems in the evaluated/integrated values and derivatives of the functions, etc.
  2. For the reconstruction code, added the --width flag which allows the system to compute the depth of the octree given a target depth for the finest resolution nodes.
  3. For the reconstruction code, fixed a bug in the handling of the confidence encoded in the lengths of the normals. In addition, added the flags --confidence and --confidenceBias which allow the user more control of how confidence is used to affect the contribution of a sample.
Version 10.01:
  1. Modified the reconstruction code to facilitate interpolation of other input-sample quantities, in addition to color.
Version 10.02:
  1. Set the default value for --degree in PoissonRecon to 1 and change the definitiion of DATA_DEGREE to 0 for sharper color interpolation.
Version 10.03:
  1. Cleaned up memory leaks and fixed a bug causing ImageStitching and EDTInHeat to SEGFAULT on Linux.
Version 10.04:
  1. Replaced the ply I/O code with an object-oriented implementation.
  2. Updated the code to support compilation under gcc version 4.8.
Version 10.05:
  1. Added cleaner support for warning and error handling.
  2. Minor bug fixes.
  3. Added a --inCore flag that enables keeping the pointset in memory instead of streaming it in from disk.

This work genersouly supported by NSF grants #0746039 and #1422325.