From 17b427ef3b72f2cd0477c38ce5f44f64d4b66e1d Mon Sep 17 00:00:00 2001
From: Pietro Incardona <incardon@mpi-cbg.de>
Date: Thu, 15 Oct 2020 18:03:04 +0200
Subject: [PATCH] Adding example files
---
.../example_sussman_circle/Makefile | 24 +
.../example_sussman_circle/config.cfg | 2 +
.../example_sussman_circle/main.cpp | 454 ++++++++++++++++++
.../example_sussman_images_2D/Makefile | 24 +
.../example_sussman_images_2D/config.cfg | 2 +
.../input/circle.bin | 1 +
.../input/dolphin.bin | 1 +
.../example_sussman_images_2D/input/face.bin | 1 +
.../input/triangle.bin | 1 +
.../example_sussman_images_2D/main.cpp | 278 +++++++++++
.../example_sussman_images_3D/Makefile | 24 +
.../example_sussman_images_3D/config.cfg | 2 +
.../input/sphere.bin | 1 +
.../example_sussman_images_3D/main.cpp | 279 +++++++++++
.../example_sussman_sphere/Makefile | 24 +
.../example_sussman_sphere/config.cfg | 2 +
.../example_sussman_sphere/main.cpp | 446 +++++++++++++++++
.../image_binary_conversion/config.cfg | 2 +
.../image2binary_circle.ipynb | 153 ++++++
.../image2binary_create_sphere.ipynb | 170 +++++++
.../image2binary_dolphin.ipynb | 181 +++++++
.../image2binary_face.ipynb | 198 ++++++++
.../image2binary_triangle.ipynb | 241 ++++++++++
.../lib/image_process_and_save.py | 26 +
.../lib/morphological_operations.py | 40 ++
install | 8 +-
26 files changed, 2581 insertions(+), 4 deletions(-)
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_circle/Makefile
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_circle/config.cfg
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_circle/main.cpp
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/Makefile
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/config.cfg
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/circle.bin
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/dolphin.bin
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/face.bin
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/triangle.bin
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_2D/main.cpp
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_3D/Makefile
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_3D/config.cfg
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_3D/input/sphere.bin
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_images_3D/main.cpp
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_sphere/Makefile
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_sphere/config.cfg
create mode 100644 example/Numerics/Sussman_redistancing/example_sussman_sphere/main.cpp
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/config.cfg
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_circle.ipynb
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_create_sphere.ipynb
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_dolphin.ipynb
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_face.ipynb
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_triangle.ipynb
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/lib/image_process_and_save.py
create mode 100644 example/Numerics/Sussman_redistancing/image_binary_conversion/lib/morphological_operations.py
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_circle/Makefile b/example/Numerics/Sussman_redistancing/example_sussman_circle/Makefile
new file mode 100644
index 000000000..495aa0d89
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_circle/Makefile
@@ -0,0 +1,24 @@
+include ../../../example.mk
+
+CC=mpic++
+
+LDIR =
+
+OBJ = main.o
+
+%.o: %.cpp
+ $(CC) -O3 -c --std=c++11 -o $@ $< $(INCLUDE_PATH)
+
+example_sussman_circle: $(OBJ)
+ $(CC) -o $@ $^ $(CFLAGS) $(LIBS_PATH) $(LIBS)
+
+all: example_sussman_circle
+
+run: all
+ mpirun -np 2 ./example_sussman_circle
+
+.PHONY: clean all run
+
+clean:
+ rm -f *.o *~ core example_sussman_circle
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_circle/config.cfg b/example/Numerics/Sussman_redistancing/example_sussman_circle/config.cfg
new file mode 100644
index 000000000..1eecbac35
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_circle/config.cfg
@@ -0,0 +1,2 @@
+[pack]
+files = main.cpp Makefile
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_circle/main.cpp b/example/Numerics/Sussman_redistancing/example_sussman_circle/main.cpp
new file mode 100644
index 000000000..8e88054fe
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_circle/main.cpp
@@ -0,0 +1,454 @@
+//
+// Created by jstark on 2020-05-18.
+//
+/**
+ * @file example_sussman_circle/main.cpp
+ * @page Examples_SussmanRedistancing Examples Sussman Redistancing
+ *
+ * @subpage example_sussman_circle
+ * @subpage example_sussman_sphere
+ * @subpage example_sussman_images_2D
+ * @subpage example_sussman_images_3D
+ *
+ * In each of these examples, we either create a geometrical object on a grid or load a binary image / volume onto
+ * the grid. The geometrical objects are initially defined by the following indicator function
+ *
+ * @f[ \phi_{\text{indicator}} = \begin{cases}
+ * +1 & \text{point lies inside the object} \\
+ * -1 & \text{point lies outside the object} \\
+ * \end{cases} @f]
+
+ * This indicator function is already some form of a level-set-function.
+ * In order to convert Phi_indicator into a signed-distance function (SDF), where @f[|\nabla\phi| = 1@f] we
+ * will perform Sussman redistancing (see: <a href="https://www.researchgate
+ * .net/publication/2642502_An_Efficient_Interface_Preserving_Level_Set_Re
+ * -Distancing_Algorithm_And_Its_Application_To_Interfacial_Incompressible_Fluid_Flow.html">M. Sussman and E. Fatemi,
+ * “Efficient, interface-preserving level set redistancing algorithm and its application to interfacial
+ * incompressible fluid flow†(1999)</a>, Appendix A).
+ *
+ * In the Sussman-redistancing, a level-set-function, which can be as simple as a step-function but requires a switch
+ * of sign accross the surface of the object, is reinitialized to a SDF by finding the steady-state solution of the
+ * following PDE:
+ * @f[ \phi_{t} + sgn(\phi_{0})(|\nabla\phi| - 1) = 0 @f]
+ *
+ * For improved numerical stability and faster convergence, the sign function is replaced by:
+ * @f[ sgn_{\epsilon}(\phi) = \frac{\phi}{ \sqrt{\phi^2 + |\nabla\phi|^2 \Delta x^2} }@f]
+ *
+ * where the \a φ is the approximation of the SDF from the last iteration (see: <a href="https://www.math.uci
+ * .edu/~zhao/publication/mypapers/ps/local_levelset.ps">Peng \a et \a al. "A PDE-Based Fast Local
+ * Level Set Method"</a>, equation (36)).
+ */
+
+
+
+
+
+/**
+ * @page example_sussman_circle Circle 2D
+ *
+ * # Get the signed distance function for a 2D circle via Sussman Redistancing #
+ *
+ * In this example, we perform Sussman redistancing on a filled 2D circle. Here, the circle is constructed via
+ * equation. For image based reconstruction and redistancing see @ref example_sussman_images_2D.
+ *
+ * A filled circle with center a, b can be constructed by the following equation:
+ *
+ *
+ * @f[ (x-a)^2 + (y-b)^2 <= r^2 @f]
+ *
+ * We will create a filled circle on a 2D grid, where the circle is represented by a -1/+1 step function
+ * (indicator function) as:
+ *
+ * @f[ \phi_{\text{indicator}} = \begin{cases}
+ * +1 & \text{point lies inside the object} \\
+ * 0 & \text{object surface} \\
+ * -1 & \text{point lies outside the object} \\
+ * \end{cases} @f]
+ *
+ * By Sussman redistancing, this indicator function is transformed into a signed distance function:
+ *
+ * @f[ \phi_{\text{SDF}} = \begin{cases}
+ * +d & \text{orthogonal distance to the closest surface of a point lying inside the object} \\
+ * 0 & \text{object surface} \\
+ * -d & \text{orthogonal distance to the closest surface of a point lying outside the object} \\
+ * \end{cases} @f]
+ *
+ * Once we have received the Phi_SDF from the redistancing, particles can be placed on narrow band around the interface.
+ *
+ * * Creates filled 2D circle with -1/+1 indicator function
+ * * Runs gaussian filter if gradient at interface too steep or if user sets redist_options.sigma >= 1
+ * * Runs Sussman redistancing (see @ref RedistancingSussman.hpp)
+ * * Places particles on narrow band around interface
+ *
+ * Output:
+ * print on promt : Iteration, Change, Residual (see: #DistFromSol::change, #DistFromSol::residual)
+ * writes vtk and hdf5 files of:
+ * 1.) 2D grid with circle pre-redistancing and post-redistancing (Phi_0 and Phi_SDF, respectively)
+ * 2.) particles on narrow band around interface
+ */
+
+/**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Include ## {#e2d_c_include}
+ *
+ * These are the header files that we need to include:
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Include
+ *
+ */
+//! @cond [Include] @endcond
+// Include standard library header files
+#include <iostream>
+#include <typeinfo>
+#include <cmath>
+#include <cstdio>
+
+// Include header files from other libraries
+#include <boost/log/core.hpp>
+#include <boost/log/trivial.hpp>
+#include <boost/log/expressions.hpp>
+#include <boost/log/utility/setup/file.hpp>
+#include <boost/log/utility/setup/common_attributes.hpp>
+
+// Include OpenFPM header files
+#include "Vector/vector_dist.hpp"
+#include "Grid/grid_dist_id.hpp"
+#include "data_type/aggregate.hpp"
+#include "Decomposition/CartDecomposition.hpp"
+
+// Include Redistancing header files
+#include "util/PathsAndFiles.hpp"
+#include "level_set/redistancing_Sussman/RedistancingSussman.hpp"
+#include "level_set/redistancing_Sussman/NarrowBand.hpp"
+#include "Draw/DrawCircle.hpp"
+//! @cond [Include] @endcond
+
+/**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Initialization and output folder ## {#e2d_c_init}
+ *
+ * We start with
+ * * Initializing OpenFPM
+ * * Setting the output path and creating an output folder
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Initialization and output folder
+ *
+ */
+//! @cond [Initialization and output folder] @endcond
+int main(int argc, char* argv[])
+{
+ // initialize library
+ openfpm_init(&argc, &argv);
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Set current working directory, define output paths and create folders where output will be saved
+ std::string cwd = get_cwd();
+ const std::string path_output = cwd + "/output_circle";
+
+ create_directory_if_not_exist(path_output);
+ //! @cond [Initialization and output folder] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Indices for the grid ## {#e2d_c_indices}
+ *
+ * Optionally, we can define the grid dimensionality and some indices for better code readability later on.
+ * * \p x: First dimension
+ * * \p y: Second dimension
+ * * \p Phi_0_grid: Index of property that stores the initial level-set-function
+ * * \p Phi_SDF_grid: Index of property where the redistancing result should be written to
+ * @snippet examples/example_sussman_circle/main.cpp Indices grid
+ *
+ */
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Indices grid] @endcond
+ // Grid dimension
+ const unsigned int grid_dim = 2;
+ // Some indices for the grid / grid properties
+ const size_t x = 0;
+ const size_t y = 1;
+
+ const size_t Phi_0_grid = 0;
+ const size_t Phi_SDF_grid = 1;
+ //! @cond [Indices grid] @endcond
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Create the grid ## {#e2d_c_grid}
+ *
+ * In order to get a grid, we
+ * * Define the grid size in terms of number of grid points per dimension
+ * * Create a Box that defines our domain
+ * * Create a Ghost object that will define the extension of the ghost part
+ * * Create a 2D grid with two properties of type double, one for the pre-redistancing Phi_initial and one, where
+ * the post-redistancing Phi_SDF should be written to.
+ * * Set some property names (optionally. These names show up when opening the grid vtk in Paraview.)
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Grid creation
+ *
+ */
+ //! @cond [Grid creation] @endcond
+ // Here we create a 2D grid that stores 2 properties:
+ // Prop1: store the initial Phi;
+ // Prop2: here the re-initialized Phi (signed distance function) will be written to in the re-distancing step
+ size_t sz[grid_dim] = {128, 128}; // Grid size in terms of number of grid points per dimension
+ Box<grid_dim, double> box({0.0, 0.0}, {5.0, 5.0}); // 2D
+ Ghost<grid_dim, long int> ghost(0);
+ typedef aggregate<double, double> props;
+ typedef grid_dist_id<grid_dim, double, props > grid_in_type;
+ grid_in_type g_dist(sz, box, ghost);
+ g_dist.setPropNames({"Phi_0", "Phi_SDF"});
+ //! @cond [Grid creation] @endcond
+
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Get filled circle on the grid ## {#e2d_c_getcircle}
+ *
+ *
+ * On the grid that we have just created, we can now initialize Phi_0 as a filled circle of defined radius.
+ * The center of the circle is passed as x_center and y_center (see @ref Circle.hpp). Phi_0 will then be:
+ *
+ * @f[ \phi_{\text{indicator}} = \begin{cases}
+ * +1 & \text{point lies inside the object} \\
+ * 0 & \text{object surface} \\
+ * -1 & \text{point lies outside the object} \\
+ * \end{cases} @f]
+ *
+ * Optionally, we can save this initial grid as a vtk file, if we want to visualize and check it in Paraview.
+ * @snippet examples/example_sussman_circle/main.cpp Get circle
+ */
+ //! @cond [Get circle] @endcond
+ // Now we initialize the grid with a filled circle. Outside the circle, the value of Phi_0 will be -1, inside +1.
+ double radius = 1.0; // Radius of the circle
+ init_grid_with_circle<Phi_0_grid>(g_dist, radius, 2.5, 2.5); // Initialize circle onto grid, centered at (2.5, 2.5)
+
+ g_dist.write(path_output + "/grid_circle_preRedistancing_radius" + std::to_string((int)radius) , FORMAT_BINARY); // Save the circle as vtk file
+ //! @cond [Get circle] @endcond
+
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Set the redistancing options ## {#e2d_c_redistoptions}
+ *
+ * For the redistancing, we can choose some options. These options will then be passed bundled as a structure to
+ * the redistancing function. Setting these options is optional, since they all have a Default value as well. In
+ * particular the following options can be set by the user:
+ * * \p sigma: Sigma of the gaussian kernel, which is used for gaussian smooting Phi_0. If the initial gradient of
+ * phi_0 at the interface is too large and no sigma is chosen or chosen too small, gauss smoothing will
+ * automatically be applied until phi gradient magnitude <= 12, regardless of which sigma is chosen by
+ * the user. Default = 0.
+ * * \p min_iter: Minimum number of iterations before steady state in narrow band will be checked (Default: 100).
+ * * \p max_iter: Maximum number of iterations you want to run the redistancing, even if steady state might not yet
+ * have been reached (Default: 1e6).
+ * * \p convTolChange.value: Convolution tolerance for the normalized total change of Phi in the narrow band between
+ * two consecutive iterations (Default: 1e-6).
+ * * \p convTolChange.check: Set true, if you want to use the normalized total change between two iterations as
+ * measure of how close you are to the steady state solution. Redistancing will then stop
+ * if convTolChange.value is reached or if the current iteration is bigger than max_iter.
+ * * \p convTolResidual.value: Convolution tolerance for the residual, that is abs(magnitude gradient of phi - 1) of
+ * Phi in the narrow band (Default 1e-1).
+ * * \p convTolResidual.check: Set true, if you want to use the residual of the current iteration as measure of how
+ * close you are to the steady state solution. Redistancing will then stop if
+ * convTolResidual.value is reached or if the current iteration is bigger than max_iter.
+ * * \p interval_check_convergence: Interval of #iterations at which convergence to steady state is checked
+ * (Default: 100).
+ * * \p width_NB_in_grid_points: Width of narrow band in number of grid points. Must be at least 4, in order to
+ * have at least 2 grid points on each side of the interface. Is automatically set
+ * to 4, if a value smaller than 4 is chosen (Default: 4).
+ * * \p print_current_iterChangeResidual: If true, the number of the current iteration, the corresponding change
+ * w.r.t the previous iteration and the residual is printed (Default: false).
+ * * \p print_steadyState_iter: If true, the number of the steady-state-iteration, the corresponding change
+ * w.r.t the previous iteration and the residual is printed (Default: false).
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Redistancing options
+ */
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Redistancing options] @endcond
+ // Now we want to convert the initial Phi into a signed distance function (SDF) with magnitude of gradient = 1.
+ // For the initial re-distancing we use the Sussman method. First of all, we can set some redistancing options.
+ Redist_options redist_options;
+ redist_options.sigma = 0;
+ redist_options.min_iter = 100;
+ redist_options.max_iter = 10000;
+
+ redist_options.convTolChange.value = 1e-12;
+ redist_options.convTolChange.check = true;
+ redist_options.convTolResidual.value = 1e-6;
+ redist_options.convTolResidual.check = true;
+
+ redist_options.interval_check_convergence = 1;
+ redist_options.width_NB_in_grid_points = 6;
+ redist_options.print_current_iterChangeResidual = true;
+ redist_options.print_steadyState_iter = true;
+ //! @cond [Redistancing options] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Run the redistancing ## {#e2d_c_runredist}
+ *
+ * Now, we can instantiate the Sussman-redistancing class using the redist_options we have just set (or use the
+ * defaults) and run the redistancing. If we are interested in the time-step that was automatically computed
+ * internally according to the CFL-condition, we can access it with #RedistancingSussman::get_time_step(). If, for
+ * whatever reason, we wish to change this timestep, we can do that with #RedistancingSussman::set_user_time_step
+ * (T dt). However, be careful when setting your own timestep: if chosen too large, the CFL-condition may be no
+ * longer fulfilled and the method can become unstable. For the #RedistancingSussman::run_redistancing we need to
+ * provide two template parameters. These are the indices of the respective property that: 1.) contains the
+ * initial Phi, 2.) should
+ * contain the output of the redistancing. You can use the same index twice, if you want that your input will be
+ * overwritten by the output. This time, it makes sense, to save the output grid, since this is already our grid
+ * containing the signed distance function in Prop. 2. The vtk-file can be opened in Paraview. If we want, we can
+ * further save the result as hdf5 file that can be reloaded onto an openFPM grid.
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Run redistancing
+ */
+ //! @cond [Run redistancing] @endcond
+ RedistancingSussman<grid_in_type> redist_obj(g_dist, redist_options); // Instantiation of Sussman-redistancing class
+ // std::cout << "dt = " << redist_obj.get_time_step() << std::endl;
+ // Run the redistancing. In the <> brackets provide property-index where 1.) your initial Phi is stored and 2.)
+ // where the resulting SDF should be written to.
+ redist_obj.run_redistancing<Phi_0_grid, Phi_SDF_grid>();
+
+ g_dist.write(path_output + "/grid_circle_postRedistancing", FORMAT_BINARY); // Save the result as vtk file
+ g_dist.save(path_output + "/grid_circle_postRedistancing" + ".bin"); // Save the result as hdf5 file that can be
+ // reloaded onto an openFPM grid
+ //! @cond [Run redistancing] @endcond
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Initialize empty vector for narrow band particles ## {#e2d_c_initnbvector}
+ *
+ * Next, we want to place particles in a narrow band around the interface. For this, we need to create an empty
+ * vector in the same domain as our grid from before. We therefore re-use the \p box and \p ghost that we defined
+ * during grid creation. This time, we have to set the boundary conditions (see general OpenFPM vector_dist
+ * documentation for details.) We also have to choose now, how many properties our particle should store. Minimum is
+ * one, but you can have particles with arbitrary many properties, depending on what you want to use them for
+ * later on. Here, we exemplarily define 3 properties.
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Initialize narrow band
+ */
+ //! @cond [Initialize narrow band] @endcond
+ // Get narrow band: Place particles on interface (narrow band width e.g. 2 grid points on each side of the interface)
+ size_t bc[grid_dim] = {PERIODIC, PERIODIC};
+ // Create an empty vector to which narrow-band particles will be added. You can choose, how many properties you want.
+ // Minimum is 1 property, to which the Phi_SDF can be written
+ // In this example we chose 3 properties. The 1st for the Phi_SDF, the 2nd for the gradient of phi and the 3rd for
+ // the magnitude of the gradient
+ typedef aggregate<double, double[grid_dim], double> props_nb;
+ typedef vector_dist<grid_dim, double, props_nb> vd_type;
+ vd_type vd_narrow_band(0, box, bc, ghost);
+ vd_narrow_band.setPropNames({"Phi_SDF", "Phi_grad", "Phi_magnOfGrad"});
+ //! @cond [Initialize narrow band] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Instantiate narrow band ## {#e2d_c_instnarrowband}
+ *
+ * Before we fill the empty vector that we just created with particles, we define how thick the narrow band
+ * around the interface should be.
+ * This is independent of the redist_options.width_NB_in_grid_points that we chose before. However, it makes
+ * sense to use a width during redistancing which is at least as large as the width that we want to place the
+ * particles in. The reason is that convergence criteria were checked for that part of the grid only, which
+ * belonged to the narrow band.
+ *
+ * Depending on the type of the variable which you define, the width can be either set in terms of number of
+ * grid points (size_t), physical width (double) or extension of narrow band as physical width inside of object
+ * and outside the object (double, double).
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Instantiate narrow band
+ */
+ //! @cond [Instantiate narrow band] @endcond
+ size_t thickness_of_narrowBand_in_grid_points = 6;
+ NarrowBand<grid_in_type> narrowBand(g_dist, thickness_of_narrowBand_in_grid_points); // Instantiation of NarrowBand class
+ //! @cond [Instantiate narrow band] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Indices for the narrow band vector ## {#e2d_c_indices}
+ *
+ * Again, we can define some indices for better code readability. This is just an example, you may want to choose
+ * different names and have a different number of properties thus different number of indices.
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Indices narrow band
+ *
+ */
+ //////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Indices narrow band] @endcond
+ // Some indices
+ const size_t Phi_SDF_vd = 0;
+ const size_t Phi_grad_vd = 1;
+ const size_t Phi_magnOfGrad_vd = 2;
+ //! @cond [Indices narrow band] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Fill the vector with particles placed within a narrow band around the interface ## {#e2d_c_getnarrowband}
+ *
+ * Now, we finally fill the vector with particles placed in a narrow band around the interface. The first
+ * template parameter that we pass, must always be the index of the grid property that contains the Phi_SDF.
+ *
+ * Then you can decide between the following options, what you want to copy from the grid to the particles:
+ * * Only copy the Phi_SDF: \p narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ * * Copy Phi_SDF as well as the first order upwind gradient of Phi_SDF: \p narrowBand
+ * .get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd>(g_dist, vd_narrow_band);
+ * * Copy Phi_SDF as well as the first order upwind gradient of Phi_SDF and the corresponding gradient magnitude:
+ * \p narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist,
+ * vd_narrow_band);
+ * * Copy an arbitrary property: \p narrowBand.get_narrow_band_copy_specific_property<Phi_SDF_grid,
+ * Prop_index_grid, Prop_index_vector>(g_dist, vd_narrow_band);
+ *
+ * We save the particles in a vtk file (open in Paraview) and as hdf5 file (can be loaded back on particles).
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Get narrow band
+ */
+ // Get the narrow band. You can decide, if you only want the Phi_SDF saved to your particles or
+ // if you also want the gradients or gradients and magnitude of gradient.
+ // The function will know depending on how many property-indices you provide in the <> brackets.
+ // First property-index must always be the index of the SDF on the grid!
+ // E.g.: The following line would only write only the Phi_SDF from the grid to your narrow-band particles
+ // narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ // Whereas this will give you the gradients and magnOfGrad of Phi as well:
+ //! @cond [Get narrow band] @endcond
+ narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist, vd_narrow_band);
+
+ vd_narrow_band.write(path_output + "/vd_narrow_band_circle", FORMAT_BINARY); // Save particles as vtk file
+ vd_narrow_band.save(path_output + "/vd_narrow_band_circle.bin"); // Save particles as hdf5 file -> can be reloaded as particles
+ //! @cond [Get narrow band] @endcond
+
+ /**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Terminate ## {#e2d_c_terminate}
+ *
+ * We end with terminating OpenFPM
+ *
+ * @snippet examples/example_sussman_circle/main.cpp Terminate
+ */
+ //! @cond [Terminate] @endcond
+ openfpm_finalize(); // Finalize openFPM library
+ return 0;
+}
+//! @cond [Terminate] @endcond
+
+/**
+ * @page example_sussman_circle Circle 2D
+ *
+ * ## Full code ## {#e2d_c_full}
+ *
+ * @include examples/example_sussman_circle/main.cpp
+ */
+
+
+
+
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_2D/Makefile b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/Makefile
new file mode 100644
index 000000000..54c26c019
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/Makefile
@@ -0,0 +1,24 @@
+include ../../../example.mk
+
+CC=mpic++
+
+LDIR =
+
+OBJ = main.o
+
+%.o: %.cpp
+ $(CC) -O3 -c --std=c++11 -o $@ $< $(INCLUDE_PATH)
+
+example_sussman_images: $(OBJ)
+ $(CC) -o $@ $^ $(CFLAGS) $(LIBS_PATH) $(LIBS)
+
+all: example_sussman_images
+
+run: all
+ mpirun -np 2 ./example_sussman_images
+
+.PHONY: clean all run
+
+clean:
+ rm -f *.o *~ core example_sussman_images
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_2D/config.cfg b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/config.cfg
new file mode 100644
index 000000000..1b7a0bcbd
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/config.cfg
@@ -0,0 +1,2 @@
+[pack]
+files = input/circle.bin input/dolphin.bin input/face.bin input/triangle.bin input/size_circle.csv input/size_dolphin.csv input/size_face.csv input/size_triangle.csv main.cpp Makefile
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/circle.bin b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/circle.bin
new file mode 100644
index 000000000..d23679b80
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/circle.bin
@@ -0,0 +1 @@
+ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
\ No newline at end of file
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/dolphin.bin b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/dolphin.bin
new file mode 100644
index 000000000..f48bd5663
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/dolphin.bin
@@ -0,0 +1 @@
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+ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
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+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/input/triangle.bin
@@ -0,0 +1 @@
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diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_2D/main.cpp b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/main.cpp
new file mode 100644
index 000000000..a6e63c959
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_2D/main.cpp
@@ -0,0 +1,278 @@
+//
+// Created by jstark on 2020-05-18.
+//
+/**
+ * @file example_sussman_images_2D/main.cpp
+ * @page example_sussman_images_2D Images 2D
+ *
+ * # Load the geometrical object from a binary 2D image #
+ * In this example, we will:
+ * * Read a 2D binary image from a binary file (for a 2D image volume see @ref example_sussman_images_2D)
+ * * Build a 2D cartesian OpenFPM grid with same dimensions as the image (1 particle for each pixel in x and y) or
+ * refined by arbitrary factor in dimension of choice (e.g. to get a isotropic grid)
+ * * Assign pixel value to a grid node property
+ * * Run the Sussman Redistancing and get the narrow band around the interface (see also: @ref example_sussman_circle
+ * and example_sussman_sphere)
+ *
+ * Output:
+ * print on promt : Iteration, Change, Residual (see: #DistFromSol::change, #DistFromSol::residual)
+ * writes vtk and hdf5 files of:
+ * 1.) 2D grid with geometrical object pre-redistancing and post-redistancing (Phi_0 and Phi_SDF, respectively)
+ * 2.) particles on narrow band around interface.
+ **/
+
+/**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Include ## {#e2d_img_include}
+ *
+ * These are the header files that we need to include:
+ *
+ * @snippet examples/example_sussman_images_2D/main.cpp Include
+ *
+ */
+//! @cond [Include] @endcond
+// Include standard library header files
+#include <iostream>
+#include <typeinfo>
+#include <cmath>
+#include <cstdio>
+
+// Include header files from other libraries
+#include <boost/log/core.hpp>
+#include <boost/log/trivial.hpp>
+#include <boost/log/expressions.hpp>
+#include <boost/log/utility/setup/file.hpp>
+#include <boost/log/utility/setup/common_attributes.hpp>
+
+// Include OpenFPM header files
+#include "Vector/vector_dist.hpp"
+#include "Grid/grid_dist_id.hpp"
+#include "data_type/aggregate.hpp"
+#include "Decomposition/CartDecomposition.hpp"
+
+// Include redistancing header files
+#include "util/PathsAndFiles.hpp"
+#include "level_set/redistancing_Sussman/RedistancingSussman.hpp"
+#include "level_set/redistancing_Sussman/NarrowBand.hpp"
+#include "RawReader/InitGridWithPixel.hpp"
+//! @cond [Include] @endcond
+
+
+/**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Initialization, indices and output folder ## {#e2d_img_init}
+ *
+ * Again we start with
+ * * Initializing OpenFPM
+ * * Setting the output path and creating an output folder
+ * This time, we also set the input path and name of the binary image that we want to load onto the grid. For this
+ * example we provide 3 simple example images. The binary images have been converted into -1 / +1 values.
+ * A jupyter notebook how to do this can be found here:
+ * Optionally, we can define the grid dimensionality and some indices for better code readability later on.
+ * * \p x: First dimension
+ * * \p y: Second dimension
+ * * \p Phi_0_grid: Index of property that stores the initial level-set-function
+ * * \p Phi_SDF_grid: Index of property where the redistancing result should be written to
+ *
+ * @snippet examples/example_sussman_images_2D/main.cpp Initialization
+ *
+ */
+//! @cond [Initialization] @endcond
+
+int main(int argc, char* argv[])
+{
+// std::string image_name = "circle";
+// std::string image_name = "triangle";
+// std::string image_name = "face";
+ std::string image_name = "dolphin";
+
+
+ // initialize library
+ openfpm_init(&argc, &argv);
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Set current working directory, define output paths and create folders where output will be saved
+ std::string cwd = get_cwd();
+ const std::string path_output = cwd + "/output_" + image_name;
+// const std::string path_output = cwd + "/output_face";
+
+ create_directory_if_not_exist(path_output);
+
+ //////////////////////////////////////////////////////////////////////////////////////////////
+ // Now we set the input paths. We need a binary file with the pixel values and a csv file with the
+ // size of the stack (in #pixels / dimension)
+ const std::string path_input ="../input/";
+ const std::string path_to_image = path_input + image_name + ".bin";
+ const std::string path_to_size = path_input + "size_" + image_name + ".csv";
+
+ /*
+ * in case of 2D (single image):
+ */
+ const unsigned int grid_dim = 2;
+ // some indices
+ const size_t x = 0;
+ const size_t y = 1;
+
+ const size_t Phi_0_grid = 0;
+ const size_t Phi_SDF_grid = 1;
+
+ const size_t Phi_SDF_vd = 0;
+ const size_t Phi_grad_vd = 1;
+ const size_t Phi_magnOfGrad_vd = 2;
+ //! @cond [Initialization] @endcond
+
+
+ /**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Set refinement factor ## {#e2d_img_refine}
+ *
+ * If we want that the grid has a different resolution as the image, we can set a refinement factor. In the
+ * refinement array, we define by which factor the grid resolution should be changed w.r.t. the image resolution.
+ * This can be useful for example when you want to have an isotropic grid but the underlying image is
+ * anisotropic (as it often happens for microcsopic z-stacks rather than 2D images).
+ *
+ * @snippet examples/example_sussman_images_2D/main.cpp Refinement
+ *
+ */
+ //! @cond [Refinement] @endcond
+ const double refinement [] = {0.5, 0.5}; // (2D) factor by which grid should be finer / coarser as
+ // underlying image in each dimension (e.g. to get isotropic grid from anisotropic image resolution)
+ //! @cond [Refinement] @endcond
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // read the stack size (number of pixel values per dimension) from a binary file
+ // alternatively, you can directly define the stack size as: std::vector<size_t> stack_size {#pixels in x, #pixels in y}
+ /**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Get size from image_size.csv ## {#e2d_img_size}
+ *
+ * Here we read the image size (number of pixel values per dimension) from a csv file. Alternatively, you can
+ * directly define the image size as: \p std::vector<size_t> \p stack_size \p {#pixels \p in \p x, \p #pixels \p in
+ * \p y}.
+ * We use this image size and the refinement factor to set the grid size \p sz.
+ *
+ *
+ * @snippet examples/example_sussman_images_2D/main.cpp Size
+ *
+ */
+ //! @cond [Size] @endcond
+ std::vector<size_t> stack_size = get_size(path_to_size);
+ auto & v_cl = create_vcluster();
+ if (v_cl.rank() == 0)
+ {
+ for(std::vector<int>::size_type i = 0; i != stack_size.size(); i++)
+ {
+ std::cout << "#Pixel in dimension " << i << " = " << stack_size[i] << std::endl;
+ std::cout << "original refinement in dimension " << i << " = " << refinement[i] << std::endl;
+ }
+ }
+
+ // Array with grid dimensions after refinement. This size-array will be used for the grid creation.
+ const size_t sz[grid_dim] = {(size_t)std::round(stack_size[x] * refinement[x]), (size_t)std::round(stack_size[y] * refinement[y])}; // 2D
+ //! @cond [Size] @endcond
+ // Here we create a 2D grid that stores 2 properties:
+ // Prop1: store the initial Phi;
+ // Prop2: here the re-initialized Phi (signed distance function) will be written to in the re-distancing step
+ /**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Run Sussman redistancing and get narrow band ## {#e2d_img_redist}
+ *
+ * Once we have loaded the geometrical object from the 2D image onto the grid, we can perform Sussman
+ * redistancing and get the narrow band the same way as it is explained in detail here: @ref
+ * example_sussman_circle and here: @ref example_sussman_sphere.
+ *
+ *
+ * @snippet examples/example_sussman_images_2D/main.cpp Redistancing
+ *
+ */
+ //! @cond [Redistancing] @endcond
+ Box<grid_dim, double> box({0.0, 0.0}, {5.0, 5.0}); // 2D
+
+ Ghost<grid_dim, long int> ghost(0);
+ typedef aggregate<double, double> props;
+ typedef grid_dist_id<grid_dim, double, props > grid_in_type;
+ grid_in_type g_dist(sz, box, ghost);
+ g_dist.setPropNames({"Phi_0", "Phi_SDF"});
+
+ // Now we can initialize the grid with the pixel values from the image stack
+ load_pixel_onto_grid<Phi_0_grid>(g_dist, path_to_image, stack_size);
+ g_dist.write(path_output + "/grid_from_images_initial", FORMAT_BINARY); // Save the initial grid as vtk file
+
+
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Now we want to convert the initial Phi into a signed distance function (SDF) with magnitude of gradient = 1
+ // For the initial re-distancing we use the Sussman method
+ // 1.) Set some redistancing options
+ Redist_options redist_options;
+ redist_options.sigma = 0; // if the initial gradient of phi at the interface is too large, gauss smoothing will automatically be applied until phi gradient magnitude <= 12, regardless of the given sigma in the main
+ redist_options.min_iter = 100; // min. number of iterations before steady state in narrow band will be checked (default: 100)
+ redist_options.max_iter = 10000; // max. number of iterations you want to run the
+ // redistancing, even if steady state might not yet have been reached (default: 1e6)
+
+ redist_options.convTolChange.value = 1e-6; // convolution tolerance for the normalized total change of Phi in the narrow band between two consecutive iteratins (default: 1e-6)
+ redist_options.convTolChange.check = true; // define here which of the convergence criteria above should be used. If both are true, termination only occurs when both are fulfilled or when iter > max_iter
+ redist_options.convTolResidual.value = 1e-1; // convolution tolerance for the normalized total residual of Phi versus the SDF (aka the error). Don't choose too small to not run forever. (default: 1e-1)
+ redist_options.convTolResidual.check = false; // (default: false)
+
+ redist_options.interval_check_convergence = 1; // interval of #iterations at which convergence is checked (default: 100)
+ redist_options.width_NB_in_grid_points = 6; // width of narrow band in number of grid points.
+ // Must be at least 4, in order to have at least 2 grid points on each side of the interface. (default: 4)
+ redist_options.print_current_iterChangeResidual = true; // if true, prints out every current iteration + corresponding change from the previous iteration + residual from SDF (default: false)
+ redist_options.print_steadyState_iter = true; // if true, prints out the final iteration number when steady state was reached + final change + residual (default: true)
+
+ RedistancingSussman<grid_in_type> redist_obj(g_dist, redist_options); // Instantiation of Sussman-redistancing class
+// std::cout << "dt = " << redist_obj.get_time_step() << std::endl;
+ // Run the redistancing. in the <> brackets provide property-index where 1.) your initial Phi is stored and 2.) where the resulting SDF should be written to.
+ redist_obj.run_redistancing<Phi_0_grid, Phi_SDF_grid>();
+
+ g_dist.write(path_output + "/grid_images_post_redistancing", FORMAT_BINARY); // Save the result as vtk file
+
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Get narrow band: Place particles on interface (narrow band width e.g. 2 grid points on each side of the interface)
+ size_t bc[grid_dim] = {PERIODIC, PERIODIC};
+ // Create an empty vector to which narrow-band particles will be added. You can choose, how many properties you want.
+ // Minimum is 1 property, to which the Phi_SDF can be written
+ // In this example we chose 3 properties. The 1st for the Phi_SDF, the 2nd for the gradient of phi and the 3rd for
+ // the magnitude of the gradient
+ typedef aggregate<double, double[grid_dim], double> props_nb;
+ typedef vector_dist<grid_dim, double, props_nb> vd_type;
+ vd_type vd_narrow_band(0, box, bc, ghost);
+ vd_narrow_band.setPropNames({"Phi_SDF", "Phi_grad", "Phi_magnOfGrad"});
+
+ NarrowBand<grid_in_type> narrowBand(g_dist, redist_options.width_NB_in_grid_points); // Instantiation of NarrowBand class
+
+ // Get the narrow band. You can decide, if you only want the Phi_SDF saved to your particles or
+ // if you also want the gradients or gradients and magnitude of gradient.
+ // The function will know depending on how many property-indices you provide in the <> brackets.
+ // First property-index must always be the index of the SDF on the grid!
+ // E.g.: The following line would only write only the Phi_SDF from the grid to your narrow-band particles
+ // narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ // Whereas this will give you the gradients and magnOfGrad of Phi as well:
+ narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist, vd_narrow_band);
+
+ vd_narrow_band.write(path_output + "/vd_narrow_band_images", FORMAT_BINARY); // Save particles as vtk file
+
+ openfpm_finalize(); // Finalize openFPM library
+ return 0;
+}
+//! @cond [Redistancing] @endcond
+
+/**
+ * @page example_sussman_images_2D Images 2D
+ *
+ * ## Full code ## {#e2d_img_full}
+ *
+ * @include examples/example_sussman_images_2D/main.cpp
+ */
+
+
+
+
+
+
+
+
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_3D/Makefile b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/Makefile
new file mode 100644
index 000000000..54c26c019
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/Makefile
@@ -0,0 +1,24 @@
+include ../../../example.mk
+
+CC=mpic++
+
+LDIR =
+
+OBJ = main.o
+
+%.o: %.cpp
+ $(CC) -O3 -c --std=c++11 -o $@ $< $(INCLUDE_PATH)
+
+example_sussman_images: $(OBJ)
+ $(CC) -o $@ $^ $(CFLAGS) $(LIBS_PATH) $(LIBS)
+
+all: example_sussman_images
+
+run: all
+ mpirun -np 2 ./example_sussman_images
+
+.PHONY: clean all run
+
+clean:
+ rm -f *.o *~ core example_sussman_images
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_3D/config.cfg b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/config.cfg
new file mode 100644
index 000000000..e98e2e1c9
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/config.cfg
@@ -0,0 +1,2 @@
+[pack]
+files = input/sphere.bin input/size_sphere.csv main.cpp Makefile
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_3D/input/sphere.bin b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/input/sphere.bin
new file mode 100644
index 000000000..048ab1f8b
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/input/sphere.bin
@@ -0,0 +1 @@
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ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
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diff --git a/example/Numerics/Sussman_redistancing/example_sussman_images_3D/main.cpp b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/main.cpp
new file mode 100644
index 000000000..ba23b4f88
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_images_3D/main.cpp
@@ -0,0 +1,279 @@
+//
+// Created by jstark on 2020-05-18.
+//
+/**
+ * @file example_sussman_images_3D/main.cpp
+ * @page example_sussman_images_3D Images 3D
+ *
+ * [TOC]
+ *
+ * # Example for loading a 3D object from an image stack (binary) onto a grid and applying Sussman redistancing #
+ *
+ * In this example the image stack is read from a binary file. A 3D cartesian grid with same dimensions as image
+ * stack is constructed. The grid resolution can be either 1 grid node for each pixel in x and y) or the resolution
+ * can be higher/lower as the image stack. This can be achieved by setting the refinement factor to a value of choice in
+ * dimension of choice (e.g. to get a isotropic grid). The pixel value is stored in a property of the grid.
+ *
+ * The initial, image-derived level set function phi (indicator function) is then converted into a signed distance
+ * function by using the Sussman redistancing (see @ref RedistancingSussman.hpp).
+ *
+ * When the grid contains phi as a signed distance function, particles can be placed on narrow band around the
+ * interface.
+ *
+ * Output:
+ * print on promt : Iteration, Change, Residual (see: #DistFromSol::change, #DistFromSol::residual)
+ * writes vtk and hdf5 files of:
+ * 1.) 3D grid with geometrical object pre-redistancing and post-redistancing (Phi_0 and Phi_SDF, respectively)
+ * 2.) particles on narrow band around interface.
+ **/
+
+/**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Include ## {#e2d_img_include}
+ *
+ * These are the header files that we need to include:
+ *
+ * @snippet examples/example_sussman_images_3D/main.cpp Include
+ *
+ */
+//! @cond [Include] @endcond
+// Include standard library header files
+#include <iostream>
+#include <typeinfo>
+#include <cmath>
+#include <cstdio>
+
+// Include header files from other libraries
+#include <boost/log/core.hpp>
+#include <boost/log/trivial.hpp>
+#include <boost/log/expressions.hpp>
+#include <boost/log/utility/setup/file.hpp>
+#include <boost/log/utility/setup/common_attributes.hpp>
+
+// Include OpenFPM header files
+#include "Vector/vector_dist.hpp"
+#include "Grid/grid_dist_id.hpp"
+#include "data_type/aggregate.hpp"
+#include "Decomposition/CartDecomposition.hpp"
+
+// Include redistancing header files
+#include "util/PathsAndFiles.hpp"
+#include "level_set/redistancing_Sussman/RedistancingSussman.hpp"
+#include "level_set/redistancing_Sussman/NarrowBand.hpp"
+#include "RawReader/InitGridWithPixel.hpp"
+//! @cond [Include] @endcond
+
+
+/**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Initialization, indices and output folder ## {#e2d_img_init}
+ *
+ * Again we start with
+ * * Initializing OpenFPM
+ * * Setting the output path and creating an output folder
+ * This time, we also set the input path and name of the binary image stack that we want to load onto the grid. For this
+ * example we provide 1 simple example image stack. The binary image stack have been converted into -1 / +1 values.
+ * A jupyter notebook how to do this can be found here:
+ * Optionally, we can define the grid dimensionality and some indices for better code readability later on.
+ * * \p x: First dimension
+ * * \p y: Second dimension
+ * * \p Phi_0_grid: Index of property that stores the initial level-set-function
+ * * \p Phi_SDF_grid: Index of property where the redistancing result should be written to
+ *
+ * @snippet examples/example_sussman_images_3D/main.cpp Initialization
+ *
+ */
+//! @cond [Initialization] @endcond
+int main(int argc, char* argv[])
+{
+ // initialize library
+ openfpm_init(&argc, &argv);
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Set current working directory, define output paths and create folders where output will be saved
+ std::string cwd = get_cwd();
+ const std::string path_output = cwd + "/output_3D_sphere";
+ create_directory_if_not_exist(path_output);
+
+ //////////////////////////////////////////////////////////////////////////////////////////////
+ // Now we set the input paths. We need a binary file with the pixel values and a csv file with the
+ // size of the stack (in #pixels / dimension)
+ const std::string path_input ="../input";
+ const std::string path_to_zstack = path_input + "/sphere.bin";
+ const std::string path_to_size = path_input + "/size_sphere.csv";
+ /*
+ * in case of 3D (image volume):
+ */
+ const unsigned int grid_dim = 3;
+ const size_t x = 0;
+ const size_t y = 1;
+ const size_t z = 2;
+
+ const size_t Phi_0_grid = 0;
+ const size_t Phi_SDF_grid = 1;
+
+ const size_t Phi_SDF_vd = 0;
+ const size_t Phi_grad_vd = 1;
+ const size_t Phi_magnOfGrad_vd = 2;
+ //! @cond [Initialization] @endcond
+
+
+ /**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Set refinement factor ## {#e2d_img_refine}
+ *
+ * If we want that the grid has a different resolution as the image stack, we can set a refinement factor. In the
+ * refinement array, we define by which factor the grid resolution should be changed w.r.t. the image stack
+ * resolution.
+ * This can be useful for example when you want to have an isotropic grid but the underlying image stack is
+ * anisotropic (as it often happens for the z-resolution of volumetric microscopy image data).
+ *
+ * @snippet examples/example_sussman_images_3D/main.cpp Refinement
+ *
+ */
+ //! @cond [Refinement] @endcond
+ const double refinement [] = {1.0, 1.0, 1.0}; // without refinement
+// const double refinement [] = {0.8, 1.5, 2.0}; // factors by which grid should be finer as underlying image stack in each dimension (e.g. to get isotropic grid from anisotropic stack resolution)
+ //! @cond [Refinement] @endcond
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // read the stack size (number of pixel values per dimension) from a binary file
+ // alternatively, you can directly define the stack size as: std::vector<size_t> stack_size {#pixels in x, #pixels in y, #pixels in z}
+ /**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Get size from image_size.csv ## {#e2d_img_size}
+ *
+ * Here we read the stack size (number of pixel values per dimension) from a csv file. Alternatively, you can
+ * directly define the stack size as: \p std::vector<size_t> \p stack_size \p {#pixels \p in \p x, \p #pixels \p in
+ * \p y}.
+ * We use this stack size and the refinement factor to set the grid size \p sz.
+ *
+ *
+ * @snippet examples/example_sussman_images_3D/main.cpp Size
+ *
+ */
+ //! @cond [Size] @endcond
+ std::vector<size_t> stack_size = get_size(path_to_size);
+ auto & v_cl = create_vcluster();
+ if (v_cl.rank() == 0)
+ {
+ for(std::vector<int>::size_type i = 0; i != stack_size.size(); i++)
+ {
+ std::cout << "#Pixel in dimension " << i << " = " << stack_size[i] << std::endl;
+ std::cout << "original refinement in dimension " << i << " = " << refinement[i] << std::endl;
+ }
+ }
+
+
+ // Array with grid dimensions after refinement. This size-array will be used for the grid creation.
+ const size_t sz[grid_dim] = {(size_t)std::round(stack_size[x] * refinement[x]), (size_t)std::round(stack_size[y] * refinement[y]), (size_t)std::round(stack_size[z] * refinement[z])}; // 3D
+ //! @cond [Size] @endcond
+ // Here we create a 3D grid that stores 2 properties:
+ // Prop1: store the initial Phi;
+ // Prop2: here the re-initialized Phi (signed distance function) will be written to in the re-distancing step
+ /**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Run Sussman redistancing and get narrow band ## {#e2d_img_redist}
+ *
+ * Once we have loaded the geometrical object from the 3D stack onto the grid, we can perform Sussman
+ * redistancing and get the narrow band the same way as it is explained in detail here: @ref
+ * example_sussman_circle and here: @ref example_sussman_sphere.
+ *
+ *
+ * @snippet examples/example_sussman_images_3D/main.cpp Redistancing
+ *
+ */
+ //! @cond [Redistancing] @endcond
+ Box<grid_dim, double> box({0.0, 0.0, 0.0}, {5.0, 5.0, 5.0}); // 3D
+
+ Ghost<grid_dim, long int> ghost(0);
+ typedef aggregate<double, double> props;
+ typedef grid_dist_id<grid_dim, double, props > grid_in_type;
+ grid_in_type g_dist(sz, box, ghost);
+ g_dist.setPropNames({"Phi_0", "Phi_SDF"});
+
+ // Now we can initialize the grid with the pixel values from the image stack
+ load_pixel_onto_grid<Phi_0_grid>(g_dist, path_to_zstack, stack_size);
+ g_dist.write(path_output + "/grid_from_images_initial", FORMAT_BINARY); // Save the initial grid as vtk file
+
+
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Now we want to convert the initial Phi into a signed distance function (SDF) with magnitude of gradient = 1
+ // For the initial re-distancing we use the Sussman method
+ // 1.) Set some redistancing options
+ Redist_options redist_options;
+ redist_options.sigma = 0; // if the initial gradient of phi at the interface is too large, gauss smoothing will automatically be applied until phi gradient magnitude <= 12, regardless of the given sigma in the main
+ redist_options.min_iter = 100; // min. number of iterations before steady state in narrow band will be checked (default: 100)
+ redist_options.max_iter = 10000; // max. number of iterations you want to run the
+ // redistancing, even if steady state might not yet
+ // have been reached (default: 1e6)
+ redist_options.convTolChange.value = 1e-6; // convolution tolerance for the normalized total change of Phi in the narrow band between two consecutive iteratins (default: 1e-6)
+ redist_options.convTolChange.check = true; // define here which of the convergence criteria above should be used. If both are true, termination only occurs when both are fulfilled or when iter > max_iter
+ redist_options.convTolResidual.value = 1e-1; // convolution tolerance for the normalized total residual of Phi versus the SDF (aka the error). Don't choose too small to not run forever. (default: 1e-1)
+ redist_options.convTolResidual.check = false; // (default: false)
+
+ redist_options.interval_check_convergence = 1; // interval of #iterations at which convergence is checked (default: 100)
+ redist_options.width_NB_in_grid_points = 6; // width of narrow band in number of grid points.
+ // Must be at least 4, in order to have at least 2
+ // grid points on each side of the interface.
+ // (default: 4)
+ redist_options.print_current_iterChangeResidual = true; // if true, prints out every current iteration + corresponding change from the previous iteration + residual from SDF (default: false)
+ redist_options.print_steadyState_iter = true; // if true, prints out the final iteration number when steady state was reached + final change + residual (default: true)
+
+ RedistancingSussman<grid_in_type> redist_obj(g_dist, redist_options); // Instantiation of Sussman-redistancing class
+// std::cout << "dt = " << redist_obj.get_time_step() << std::endl;
+ // Run the redistancing. in the <> brackets provide property-index where 1.) your initial Phi is stored and 2.) where the resulting SDF should be written to.
+ redist_obj.run_redistancing<Phi_0_grid, Phi_SDF_grid>();
+
+ g_dist.write(path_output + "/grid_images_post_redistancing", FORMAT_BINARY); // Save the result as vtk file
+
+ ///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ // Get narrow band: Place particles on interface (narrow band width e.g. 2 grid points on each side of the interface)
+ size_t bc[grid_dim] = {PERIODIC, PERIODIC, PERIODIC};
+ // Create an empty vector to which narrow-band particles will be added. You can choose, how many properties you want.
+ // Minimum is 1 property, to which the Phi_SDF can be written
+ // In this example we chose 3 properties. The 1st for the Phi_SDF, the 2nd for the gradient of phi and the 3rd for
+ // the magnitude of the gradient
+ typedef aggregate<double, double[grid_dim], double> props_nb;
+ typedef vector_dist<grid_dim, double, props_nb> vd_type;
+ vd_type vd_narrow_band(0, box, bc, ghost);
+ vd_narrow_band.setPropNames({"Phi_SDF", "Phi_grad", "Phi_magnOfGrad"});
+
+ NarrowBand<grid_in_type> narrowBand(g_dist, redist_options.width_NB_in_grid_points); // Instantiation of NarrowBand class
+
+ // Get the narrow band. You can decide, if you only want the Phi_SDF saved to your particles or
+ // if you also want the gradients or gradients and magnitude of gradient.
+ // The function will know depending on how many property-indices you provide in the <> brackets.
+ // First property-index must always be the index of the SDF on the grid!
+ // E.g.: The following line would only write only the Phi_SDF from the grid to your narrow-band particles
+ // narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ // Whereas this will give you the gradients and magnOfGrad of Phi as well:
+ narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist, vd_narrow_band);
+
+ vd_narrow_band.write(path_output + "/vd_narrow_band_images", FORMAT_BINARY); // Save particles as vtk file
+
+ openfpm_finalize(); // Finalize openFPM library
+ return 0;
+}
+//! @cond [Redistancing] @endcond
+
+/**
+ * @page example_sussman_images_3D Images 3D
+ *
+ * ## Full code ## {#e2d_img_full}
+ *
+ * @include examples/example_sussman_images_3D/main.cpp
+ */
+
+
+
+
+
+
+
+
+
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_sphere/Makefile b/example/Numerics/Sussman_redistancing/example_sussman_sphere/Makefile
new file mode 100644
index 000000000..714fdcb07
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_sphere/Makefile
@@ -0,0 +1,24 @@
+include ../../../example.mk
+
+CC=mpic++
+
+LDIR =
+
+OBJ = main.o
+
+%.o: %.cpp
+ $(CC) -O3 -c --std=c++11 -o $@ $< $(INCLUDE_PATH)
+
+example_sussman_sphere: $(OBJ)
+ $(CC) -o $@ $^ $(CFLAGS) $(LIBS_PATH) $(LIBS)
+
+all: example_sussman_sphere
+
+run: all
+ mpirun -np 2 ./example_sussman_sphere
+
+.PHONY: clean all run
+
+clean:
+ rm -f *.o *~ core example_sussman_sphere
+
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_sphere/config.cfg b/example/Numerics/Sussman_redistancing/example_sussman_sphere/config.cfg
new file mode 100644
index 000000000..1eecbac35
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_sphere/config.cfg
@@ -0,0 +1,2 @@
+[pack]
+files = main.cpp Makefile
diff --git a/example/Numerics/Sussman_redistancing/example_sussman_sphere/main.cpp b/example/Numerics/Sussman_redistancing/example_sussman_sphere/main.cpp
new file mode 100644
index 000000000..ee744880b
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/example_sussman_sphere/main.cpp
@@ -0,0 +1,446 @@
+//
+// Created by jstark on 2020-05-18.
+//
+/**
+ * @file example_sussman_sphere/main.cpp
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * # Get the signed distance function for a 3D sphere via Sussman Redistancing #
+ *
+ * In this example, we perform Sussman redistancing on a filled 3D sphere. Here, the sphere is constructed via
+ * equation. For image based reconstruction and redistancing see @ref example_sussman_images_3D.
+ *
+ * A filled sphere with center a, b, c can be constructed by the following equation:
+ *
+ *
+ * @f[ (x-a)^2 + (y-b)^2 + (z-c)^2 <= r^2 @f]
+ *
+ * We will create a filled sphere on a 3D grid, where the sphere is represented by a -1/+1 step function
+ * (indicator function) as:
+ *
+ * @f[ \phi_{\text{indicator}} = \begin{cases}
+ * +1 & \text{point lies inside the object} \\
+ * 0 & \text{object surface} \\
+ * -1 & \text{point lies outside the object} \\
+ * \end{cases} @f]
+ *
+ * By Sussman redistancing, this indicator function is transformed into a signed distance function:
+ *
+ * @f[ \phi_{\text{SDF}} = \begin{cases}
+ * +d & \text{orthogonal distance to the closest surface of a point lying inside the object} \\
+ * 0 & \text{object surface} \\
+ * -d & \text{orthogonal distance to the closest surface of a point lying outside the object} \\
+ * \end{cases} @f]
+ *
+ * Once we have received the Phi_SDF from the redistancing, particles can be placed on narrow band around the interface.
+ *
+ * * Creates filled 3D sphere with -1/+1 indicator function
+ * * Runs gaussian filter if gradient at interface too steep or if user sets redist_options.sigma >= 1
+ * * Runs Sussman redistancing (see @ref RedistancingSussman.hpp)
+ * * Places particles on narrow band around interface
+ *
+ * Output:
+ * print on promt : Iteration, Change, Residual (see: #DistFromSol::change, #DistFromSol::residual)
+ * writes vtk and hdf5 files of:
+ * 1.) 3D grid with sphere pre-redistancing and post-redistancing (Phi_0 and Phi_SDF, respectively)
+ * 2.) particles on narrow band around interface
+ *
+ */
+
+/**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Include ## {#e3d_s_include}
+ *
+ * These are the header files that we need to include:
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Include
+ *
+ */
+//! @cond [Include] @endcond
+// Include standard library header files
+#include <iostream>
+#include <typeinfo>
+#include <cmath>
+#include <cstdio>
+
+// Include header files from other libraries
+#include <boost/log/core.hpp>
+#include <boost/log/trivial.hpp>
+#include <boost/log/expressions.hpp>
+#include <boost/log/utility/setup/file.hpp>
+#include <boost/log/utility/setup/common_attributes.hpp>
+
+// Include OpenFPM header files
+#include "Vector/vector_dist.hpp"
+#include "Grid/grid_dist_id.hpp"
+#include "data_type/aggregate.hpp"
+#include "Decomposition/CartDecomposition.hpp"
+
+// Include level-set-method related header files
+#include "util/PathsAndFiles.hpp"
+#include "level_set/redistancing_Sussman/RedistancingSussman.hpp"
+#include "level_set/redistancing_Sussman/NarrowBand.hpp"
+#include "Draw/DrawSphere.hpp"
+//! @cond [Include] @endcond
+
+/**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Initialization and output folder ## {#e2d_s_init}
+ *
+ * We start with
+ * * Initializing OpenFPM
+ * * Setting the output path and creating an output folder
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Initialization and output folder
+ *
+ */
+//! @cond [Initialization and output folder] @endcond
+int main(int argc, char* argv[])
+{
+ // initialize library
+ openfpm_init(&argc, &argv);
+ // Set current working directory, define output paths and create folders where output will be saved
+ std::string cwd = get_cwd();
+ const std::string path_output = cwd + "/output_sphere";
+ create_directory_if_not_exist(path_output);
+ //! @cond [Initialization and output folder] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Indices for the grid ## {#e3d_s_indices}
+ *
+ * Optionally, we can define the grid dimensionality and some indices for better code readability later on.
+ * * \p x: First dimension
+ * * \p y: Second dimension
+ * * \p z: Third dimension
+ * * \p Phi_0_grid: Index of property that stores the initial level-set-function
+ * * \p Phi_SDF_grid: Index of property where the redistancing result should be written to
+ * @snippet examples/example_sussman_sphere/main.cpp Indices grid
+ *
+ */
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Indices grid] @endcond
+ // grid dimension
+ constexpr size_t grid_dim = 3;
+ // Some indices for the grid / grid properties
+ const size_t x = 0;
+ const size_t y = 1;
+ const size_t z = 2;
+
+ const size_t Phi_0_grid = 0;
+ const size_t Phi_SDF_grid = 1;
+ //! @cond [Indices grid] @endcond
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Create the grid ## {#e3d_s_grid}
+ *
+ * In order to get a grid, we
+ * * Define the grid size in terms of number of grid points per dimension
+ * * Create a Box that defines our domain
+ * * Create a Ghost object that will define the extension of the ghost part
+ * * Create a 3D grid with two properties of type double, one for the pre-redistancing Phi_initial and one, where
+ * the post-redistancing Phi_SDF should be written to.
+ * * Set some property names (optionally. These names show up when opening the grid vtk in Paraview.)
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Grid creation
+ *
+ */
+ //! @cond [Grid creation] @endcond
+ // Here we create a 3D grid that stores two properties:
+ // Prop1: store the initial Phi;
+ // Prop2: here the re-initialized Phi (signed distance function) will be written to in the re-distancing step
+ const size_t sz[grid_dim] = {128, 128, 128};
+ Box<grid_dim, double> box({0.0, 0.0, 0.0}, {10.0, 10.0, 10.0});
+ Ghost<grid_dim, long int> ghost(0);
+ typedef aggregate<double, double> props;
+ typedef grid_dist_id<grid_dim, double, props > grid_in_type;
+ grid_in_type g_dist(sz, box, ghost);
+ g_dist.setPropNames({"Phi_0", "Phi_SDF"});
+ //! @cond [Grid creation] @endcond
+
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Get filled sphere on the grid ## {#e3d_s_getsphere}
+ *
+ *
+ * On the grid that we have just created, we can now initialize Phi_0 as a filled sphere of defined radius.
+ * The center of the sphere is passed as x_center and y_center (see @ref Sphere.hpp). Phi_0 will then be:
+ *
+ * @f[ \phi_{\text{indicator}} = \begin{cases}
+ * +1 & \text{point lies inside the object} \\
+ * 0 & \text{object surface} \\
+ * -1 & \text{point lies outside the object} \\
+ * \end{cases} @f]
+ *
+ * Optionally, we can save this initial grid as a vtk file, if we want to visualize and check it in Paraview.
+ * @snippet examples/example_sussman_sphere/main.cpp Get sphere
+ */
+ //! @cond [Get sphere] @endcond
+ // Now we initialize the grid with a filled sphere. Outside the sphere, the value of Phi_0 will be -1, inside +1.
+ double radius = 1.0; // Radius of the sphere
+ init_grid_with_sphere<Phi_0_grid>(g_dist, radius, 5, 5, 5); // Initialize sphere onto grid, centered at (5, 5, 5)
+
+ g_dist.write(path_output + "/grid_initial_sphere_preRedistancing_radius" + std::to_string((int)radius) , FORMAT_BINARY); // Save the sphere as vtk file
+ //! @cond [Get sphere] @endcond
+
+
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Set the redistancing options ## {#e3d_s_redistoptions}
+ *
+ * For the redistancing, we can choose some options. These options will then be passed bundled as a structure to
+ * the redistancing function. Setting these options is optional, since they all have a Default value as well. In
+ * particular the following options can be set by the user:
+ * * \p sigma: Sigma of the gaussian kernel, which is used for gaussian smooting Phi_0. If the initial gradient of
+ * phi_0 at the interface is too large and no sigma is chosen or chosen too small, gauss smoothing will
+ * automatically be applied until phi gradient magnitude <= 12, regardless of which sigma is chosen by
+ * the user. Default = 0.
+ * * \p min_iter: Minimum number of iterations before steady state in narrow band will be checked (Default: 100).
+ * * \p max_iter: Maximum number of iterations you want to run the redistancing, even if steady state might not yet
+ * have been reached (Default: 1e6).
+ * * \p convTolChange.value: Convolution tolerance for the normalized total change of Phi in the narrow band between
+ * two consecutive iterations (Default: 1e-6).
+ * * \p convTolChange.check: Set true, if you want to use the normalized total change between two iterations as
+ * measure of how close you are to the steady state solution. Redistancing will then stop
+ * if convTolChange.value is reached or if the current iteration is bigger than max_iter.
+ * * \p convTolResidual.value: Convolution tolerance for the residual, that is abs(magnitude gradient of phi - 1) of
+ * Phi in the narrow band (Default 1e-1).
+ * * \p convTolResidual.check: Set true, if you want to use the residual of the current iteration as measure of how
+ * close you are to the steady state solution. Redistancing will then stop if
+ * convTolResidual.value is reached or if the current iteration is bigger than max_iter.
+ * * \p interval_check_convergence: Interval of #iterations at which convergence to steady state is checked
+ * (Default: 100).
+ * * \p width_NB_in_grid_points: Width of narrow band in number of grid points. Must be at least 4, in order to
+ * have at least 2 grid points on each side of the interface. Is automatically set
+ * to 4, if a value smaller than 4 is chosen (Default: 4).
+ * * \p print_current_iterChangeResidual: If true, the number of the current iteration, the corresponding change
+ * w.r.t the previous iteration and the residual is printed (Default: false).
+ * * \p print_steadyState_iter: If true, the number of the steady-state-iteration, the corresponding change
+ * w.r.t the previous iteration and the residual is printed (Default: false).
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Redistancing options
+ */
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Redistancing options] @endcond
+ // Now we want to convert the initial Phi into a signed distance function (SDF) with magnitude of gradient = 1.
+ // For the initial re-distancing we use the Sussman method. First of all, we can set some redistancing options.
+ Redist_options redist_options;
+ redist_options.sigma = 0;
+ redist_options.min_iter = 100;
+ redist_options.max_iter = 10000;
+
+ redist_options.convTolChange.value = 1e-12;
+ redist_options.convTolChange.check = true;
+ redist_options.convTolResidual.value = 1e-1;
+ redist_options.convTolResidual.check = false;
+
+ redist_options.interval_check_convergence = 1;
+ redist_options.width_NB_in_grid_points = 6;
+ redist_options.print_current_iterChangeResidual = true;
+ redist_options.print_steadyState_iter = true;
+ //! @cond [Redistancing options] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Run the redistancing ## {#e3d_s_runredist}
+ *
+ * Now, we can instantiate the Sussman-redistancing class using the redist_options we have just set (or use the
+ * defaults) and run the redistancing. If we are interested in the time-step that was automatically computed
+ * internally according to the CFL-condition, we can access it with #RedistancingSussman::get_time_step(). If, for
+ * whatever reason, we wish to change this timestep, we can do that with #RedistancingSussman::set_user_time_step
+ * (T dt). However, be careful when setting your own timestep: if chosen too large, the CFL-condition may be no
+ * longer fulfilled and the method can become unstable. For the #run_redistancing we need to provide two template
+ * parameters. These are the indices of the respective property that: 1.) contains the initial Phi, 2.) should
+ * contain the output of the redistancing. You can use the same index twice, if you want that your input will be
+ * overwritten by the output. This time, it makes sense, to save the output grid, since this is already our grid
+ * containing the signed distance function in Prop. 2. The vtk-file can be opened in Paraview. If we want, we can
+ * further save the result as hdf5 file that can be reloaded onto an openFPM grid.
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Run redistancing
+ */
+ //! @cond [Run redistancing] @endcond
+ RedistancingSussman<grid_in_type> redist_obj(g_dist, redist_options); // Instantiation of Sussman-redistancing class
+ // std::cout << "dt = " << redist_obj.get_time_step() << std::endl;
+ // Run the redistancing. in the <> brackets provide property-index where 1.) your initial Phi is stored and 2.)
+ // where the resulting SDF should be written to.
+ redist_obj.run_redistancing<Phi_0_grid, Phi_SDF_grid>();
+
+ g_dist.write(path_output + "/grid_sphere_postRedistancing", FORMAT_BINARY); // Save the result as vtk file
+ g_dist.save(path_output + "/grid_sphere_postRedistancing" + ".bin"); // Save the result as hdf5 file that can be
+ // reloaded onto an openFPM grid
+ //! @cond [Run redistancing] @endcond
+ ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Initialize empty vector for narrow band particles ## {#e3d_s_initnbvector}
+ *
+ * Next, we want to place particles in a narrow band around the interface. For this, we need to create an empty
+ * vector in the same domain as our grid from before. We therefore re-use the \p box and \p ghost that we defined
+ * during grid creation. This time, we have to set the boundary conditions (see general OpenFPM vector_dist
+ * documentation for details.) We also have to choose now, how many properties our particle should store. Minimum is
+ * one, but you can have particles with arbitrary many properties, depending on what you want to use them for
+ * later on. Here, we exemplarily define 3 properties.
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Initialize narrow band
+ */
+ //! @cond [Initialize narrow band] @endcond
+ // Get narrow band: Place particles on interface (narrow band width e.g. 2 grid points on each side of the interface)
+ size_t bc[grid_dim] = {PERIODIC, PERIODIC, PERIODIC};
+ // Create an empty vector to which narrow-band particles will be added. You can choose, how many properties you want.
+ // Minimum is 1 property, to which the Phi_SDF can be written
+ // In this example we chose 3 properties. The 1st for the Phi_SDF, the 2nd for the gradient of phi and the 3rd for
+ // the magnitude of the gradient
+ typedef aggregate<double, double[grid_dim], double> props_nb;
+ typedef vector_dist<grid_dim, double, props_nb> vd_type;
+ vd_type vd_narrow_band(0, box, bc, ghost);
+ vd_narrow_band.setPropNames({"Phi_SDF", "Phi_grad", "Phi_magnOfGrad"});
+ //! @cond [Initialize narrow band] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Instantiate narrow band ## {#e3d_s_instnarrowband}
+ *
+ * Before we fill the empty vector that we just created with particles, we define how thick the narrow band
+ * around the interface should be.
+ * This is independent of the redist_options.width_NB_in_grid_points that we chose before. However, it makes
+ * sense to use a width during redistancing which is at least as large as the width that we want to place the
+ * particles in. The reason is that convergence criteria were checked for that part of the grid only, which
+ * belonged to the narrow band.
+ *
+ * Depending on the type of the variable which you define, the width can be either set in terms of number of
+ * grid points (size_t), physical width (double) or extension of narrow band as physical width inside of object
+ * and outside the object (double, double).
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Instantiate narrow band
+ */
+ //! @cond [Instantiate narrow band] @endcond
+ size_t thickness_of_narrowBand_in_grid_points = 6;
+ NarrowBand<grid_in_type> narrowBand(g_dist, redist_options.width_NB_in_grid_points); // Instantiation of NarrowBand class
+
+//! @cond [Instantiate narrow band] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Indices for the narrow band vector ## {#e3d_s_indices}
+ *
+ * Again, we can define some indices for better code readability. This is just an example, you may want to choose
+ * different names and have a different number of properties thus different number of indices.
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Indices narrow band
+ *
+ */
+ //////////////////////////////////////////////////////////////////////////////////////////////
+ //! @cond [Indices narrow band] @endcond
+ // Some indices
+ const size_t Phi_SDF_vd = 0;
+ const size_t Phi_grad_vd = 1;
+ const size_t Phi_magnOfGrad_vd = 2;
+ //! @cond [Indices narrow band] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Fill the vector with particles placed within a narrow band around the interface ## {#e3d_s_getnarrowband}
+ *
+ * Now, we finally fill the vector with particles placed in a narrow band around the interface. The first
+ * template parameter that we pass, must always be the index of the grid property that contains the Phi_SDF.
+ *
+ * Then you can decide between the following options, what you want to copy from the grid to the particles:
+ * * Only copy the Phi_SDF: \p narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ * * Copy Phi_SDF as well as the first order upwind gradient of Phi_SDF: \p narrowBand
+ * .get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd>(g_dist, vd_narrow_band);
+ * * Copy Phi_SDF as well as the first order upwind gradient of Phi_SDF and the corresponding gradient magnitude:
+ * \p narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist,
+ * vd_narrow_band);
+ * * Copy an arbitrary property: \p narrowBand.get_narrow_band_copy_specific_property<Phi_SDF_grid,
+ * Prop_index_grid, Prop_index_vector>(g_dist, vd_narrow_band);
+ *
+ * We save the particles in a vtk file (open in Paraview) and as hdf5 file (can be loaded back on particles).
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Get narrow band
+ */
+ // Get the narrow band. You can decide, if you only want the Phi_SDF saved to your particles or
+ // if you also want the gradients or gradients and magnitude of gradient.
+ // The function will know depending on how many property-indices you provide in the <> brackets.
+ // First property-index must always be the index of the SDF on the grid!
+ // E.g.: The following line would only write only the Phi_SDF from the grid to your narrow-band particles
+ // narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd>(g_dist, vd_narrow_band);
+ // Whereas this will give you the gradients and magnOfGrad of Phi as well:
+ //! @cond [Get narrow band] @endcond
+ narrowBand.get_narrow_band<Phi_SDF_grid, Phi_SDF_vd, Phi_grad_vd, Phi_magnOfGrad_vd>(g_dist, vd_narrow_band);
+
+ vd_narrow_band.write(path_output + "/vd_narrow_band_sphere", FORMAT_BINARY); // Save particles as vtk file
+ vd_narrow_band.save(path_output + "/vd_narrow_band_sphere.bin"); // Save particles as hdf5 file -> can be reloaded as particles
+ //! @cond [Get narrow band] @endcond
+
+ /**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Terminate ## {#e3d_s_terminate}
+ *
+ * We end with terminating OpenFPM
+ *
+ * @snippet examples/example_sussman_sphere/main.cpp Terminate
+ */
+ //! @cond [Terminate] @endcond
+ openfpm_finalize(); // Finalize openFPM library
+ return 0;
+}
+//! @cond [Terminate] @endcond
+
+/**
+ * @page example_sussman_sphere Sphere 3D
+ *
+ * ## Full code ## {#e3d_s_full}
+ *
+ * @include examples/example_sussman_sphere/main.cpp
+ */
+
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diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/config.cfg b/example/Numerics/Sussman_redistancing/image_binary_conversion/config.cfg
new file mode 100644
index 000000000..30f4c7c42
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/config.cfg
@@ -0,0 +1,2 @@
+[pack]
+files = image2binary_circle.ipynb image2binary_create_sphere.ipynb image2binary_dolphin.ipynb lib/image_process_and_save.py lib/morphological_operations.py
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_circle.ipynb b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_circle.ipynb
new file mode 100644
index 000000000..43d00508a
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_circle.ipynb
@@ -0,0 +1,153 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from tifffile import imread, imsave\n",
+ "import numpy as np\n",
+ "import os\n",
+ "import matplotlib.pyplot as plt\n",
+ "import cv2\n",
+ "import sys\n",
+ "sys.path.append(\"./lib\")\n",
+ "import morphological_operations as mo\n",
+ "import image_process_and_save as ips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Open and plot image"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "filename = '/Users/jstark/Desktop/image_examples/circle.tiff'\n",
+ "x = imread('%s' % filename)\n",
+ "x = x[:, :, 0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(255, 0, (64, 64))"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.max(x), np.min(x), x.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x, cmap='gray')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Convert binary image: >1 -> -1, 0 -> +1 (indicator function)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "format of stack x_bin = (64, 64) \n",
+ "\n",
+ "minimum pixel value after conversion = -1 \n",
+ "\n",
+ "maximum pixel value after conversion = 1 \n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.where(x > 1, -1, 1)\n",
+ "print(\"format of stack x_bin = \", x_bin.shape, \"\\n\"), \n",
+ "print(\"minimum pixel value after conversion = \", np.amin(x_bin), \"\\n\"), \n",
+ "print(\"maximum pixel value after conversion = \", np.amax(x_bin), \"\\n\")\n",
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x_bin[30], cmap = 'gray')\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# save flat image stack as binary file\n",
+ "path = '/Users/jstark/Desktop/image_examples/'\n",
+ "filename = 'circle'\n",
+ "ips.save_array_toBin(x_bin, path, filename)\n",
+ "\n",
+ "# Save image size in #pixels / axis as csv file\n",
+ "dim = np.asarray(x_bin.shape)\n",
+ "np.savetxt('%s/size_%s.csv' % (path, filename), dim, fmt='%i', delimiter=',')"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_create_sphere.ipynb b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_create_sphere.ipynb
new file mode 100644
index 000000000..3267aaef5
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_create_sphere.ipynb
@@ -0,0 +1,170 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from tifffile import imread, imsave\n",
+ "import numpy as np\n",
+ "import os\n",
+ "import matplotlib.pyplot as plt\n",
+ "import cv2\n",
+ "import sys\n",
+ "sys.path.append(\"./lib\")\n",
+ "import morphological_operations as mo\n",
+ "import image_process_and_save as ips"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "from copy import deepcopy\n",
+ "\n",
+ "''' size : size of original 3D numpy matrix A.\n",
+ " radius : radius of circle inside A which will be filled with ones. \n",
+ "'''\n",
+ "size, radius = 64, 5\n",
+ "\n",
+ "''' A : numpy.ndarray of shape size*size*size. '''\n",
+ "A = np.zeros((size,size, size)) \n",
+ "\n",
+ "''' AA : copy of A (you don't want the original copy of A to be overwritten.) '''\n",
+ "AA = deepcopy(A) \n",
+ "\n",
+ "''' (x0, y0, z0) : coordinates of center of circle inside A. '''\n",
+ "x0, y0, z0 = int(np.floor(A.shape[0]/2)), \\\n",
+ " int(np.floor(A.shape[1]/2)), int(np.floor(A.shape[2]/2))\n",
+ "\n",
+ "\n",
+ "for x in range(AA.shape[0]):\n",
+ " for y in range(AA.shape[1]):\n",
+ " for z in range(AA.shape[2]): \n",
+ " d = radius*radius*radius - (x0-x)**2 - (y0-y)**2 - (z0-z)**2 \n",
+ " if d <= 0: AA[x,y,z] = -1\n",
+ " elif d >= 0: AA[x,y,z] = 1"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(64, 64, 64)"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "AA.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(AA[int(AA.shape[0]/2)], cmap='gray')\n",
+ "None"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# flatten stack to get a 1D array\n",
+ "x_bin = AA.flatten();"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(262144,)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x_bin.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# save flat image stack as binary file\n",
+ "path = '/Users/jstark/Desktop/image_examples/'\n",
+ "filename = 'sphere'\n",
+ "ips.save_array_toBin(x_bin, path, filename)\n",
+ "\n",
+ "# Save image size in #pixels / axis as csv file\n",
+ "dim = np.asarray(AA.shape)\n",
+ "np.savetxt('%s/size_%s.csv' % (path, filename), dim, fmt='%i', delimiter=',')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_dolphin.ipynb b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_dolphin.ipynb
new file mode 100644
index 000000000..3b446e4af
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_dolphin.ipynb
@@ -0,0 +1,181 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from tifffile import imread, imsave\n",
+ "import numpy as np\n",
+ "import os\n",
+ "import matplotlib.pyplot as plt\n",
+ "import cv2\n",
+ "import sys\n",
+ "sys.path.append(\"./lib\")\n",
+ "import morphological_operations as mo\n",
+ "import image_process_and_save as ips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Open and plot image"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "filename = '/Users/jstark/Desktop/image_examples/dolphin.tiff'\n",
+ "x = imread('%s' % filename)\n",
+ "x = x[:, :, 0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(255, 0, (800, 618))"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.max(x), np.min(x), x.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "<matplotlib.image.AxesImage at 0x11e5648d0>"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x, cmap='gray')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Convert binary image: >1 -> -1, 0 -> +1 (indicator function)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "format of stack x_bin = (800, 618) \n",
+ "\n",
+ "minimum pixel value after conversion = -1 \n",
+ "\n",
+ "maximum pixel value after conversion = 1 \n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.where(x > 50, -1, 1)\n",
+ "print(\"format of stack x_bin = \", x_bin.shape, \"\\n\"), \n",
+ "print(\"minimum pixel value after conversion = \", np.amin(x_bin), \"\\n\"), \n",
+ "print(\"maximum pixel value after conversion = \", np.amax(x_bin), \"\\n\")\n",
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x_bin[30], cmap = 'gray')\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# save flat image stack as binary file\n",
+ "path = '/Users/jstark/Desktop/image_examples/'\n",
+ "filename = 'dolphin'\n",
+ "ips.save_array_toBin(x_bin, path, filename)\n",
+ "\n",
+ "# Save image size in #pixels / axis as csv file\n",
+ "dim = np.asarray(x_bin.shape)\n",
+ "np.savetxt('%s/size_%s.csv' % (path, filename), dim, fmt='%i', delimiter=',')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_face.ipynb b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_face.ipynb
new file mode 100644
index 000000000..e0d622f52
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_face.ipynb
@@ -0,0 +1,198 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from tifffile import imread, imsave\n",
+ "import numpy as np\n",
+ "import os\n",
+ "import matplotlib.pyplot as plt\n",
+ "import cv2\n",
+ "import sys\n",
+ "sys.path.append(\"./lib\")\n",
+ "import morphological_operations as mo\n",
+ "import image_process_and_save as ips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Open and plot image"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "filename = '/Users/jstark/Desktop/image_examples/face.tiff'\n",
+ "x = imread('%s' % filename)\n",
+ "x = x[:, :, 0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(255, 0, (64, 58))"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.max(x), np.min(x), x.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x, cmap='gray')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Convert binary image: >1 -> -1, 0 -> +1 (indicator function)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "format of stack x_bin = (64, 58) \n",
+ "\n",
+ "minimum pixel value after conversion = -1 \n",
+ "\n",
+ "maximum pixel value after conversion = 1 \n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.where(x > 1, -1, 1)\n",
+ "print(\"format of stack x_bin = \", x_bin.shape, \"\\n\"), \n",
+ "print(\"minimum pixel value after conversion = \", np.amin(x_bin), \"\\n\"), \n",
+ "print(\"maximum pixel value after conversion = \", np.amax(x_bin), \"\\n\")\n",
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x_bin[30], cmap = 'gray')\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-1, 1)"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.min(x_bin), np.max(x_bin)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.flip(x_bin)\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# save flat image stack as binary file\n",
+ "path = '/Users/jstark/Desktop/image_examples/'\n",
+ "filename = 'face'\n",
+ "ips.save_array_toBin(x_bin, path, filename)\n",
+ "\n",
+ "# Save image size in #pixels / axis as csv file\n",
+ "dim = np.asarray(x_bin.shape)\n",
+ "np.savetxt('%s/size_%s.csv' % (path, filename), dim, fmt='%i', delimiter=',')"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_triangle.ipynb b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_triangle.ipynb
new file mode 100644
index 000000000..7086ce176
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/image2binary_triangle.ipynb
@@ -0,0 +1,241 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from tifffile import imread, imsave\n",
+ "import numpy as np\n",
+ "import os\n",
+ "import matplotlib.pyplot as plt\n",
+ "import cv2\n",
+ "import sys\n",
+ "sys.path.append(\"./lib\")\n",
+ "import morphological_operations as mo\n",
+ "import image_process_and_save as ips"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Open and plot image"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "filename = '/Users/jstark/Desktop/image_examples/triangle.tiff'\n",
+ "x = imread('%s' % filename)\n",
+ "x = x[:, :, 0]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(255, 0, (691, 756))"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.max(x), np.min(x), x.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x, cmap='gray')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# convert binary image: >1 -> -1, 0 -> +1 (indicator function)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {
+ "scrolled": true
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "format of stack x_bin = (691, 756) \n",
+ "\n",
+ "minimum pixel value after conversion = -1 \n",
+ "\n",
+ "maximum pixel value after conversion = 1 \n",
+ "\n"
+ ]
+ },
+ {
+ "data": {
+ "image/png": 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cBOlCDDJJUtcMMm0pZ9SSps0gkyR1zSCT1BWrep3PIJMkdc0g05ZxJi1pFgwySd1xUqRxBpkkqWsGmSSpawaZtoRLQZJmxSCT1CUnR1plkEmSumaQaeacOWtWvLYEBpkkqXMGmWbKGbOkWTPIJHXNyZIMMklS1wwyzYwzZW0Vr7XlZpBJ6l6SobugARlkkrpnRbbcDDJJUtcMMs2EM2RJW8Ugk7QQnDwtL4NMktQ1g0yS1DWDTFPnEo+krWSQSVoYTqKWk0EmSeraREGWZHuSu5N8LcmpJNcnuTLJfUmebI9XtHOT5PYkK0keSbJvtkPQPHFGrKF5DS6fSSuyjwJ/WVVvBH4KOAUcBo5X1V7geNsHuBHY2z4OAXdMtceSJI1ZM8iSXA68DbgToKr+taqeAw4AR9tpR4Gb2/YB4BM18gVge5KdU++5JElMVpFdA/wD8EdJHkrysSSXATuq6ul2zjPAjra9Czg99vlnWpskSVM3SZBtA/YBd1TVm4F/5qVlRABqtCi9roXpJIeSnEhyYj2fp/nlvQlJQ5gkyM4AZ6rqwbZ/N6Nge3Z1ybA9nmvHzwJ7xj5/d2v7PlV1pKr2V9X+jXZeki7ESdVyWTPIquoZ4HSSN7SmdwCPA8eAg63tIHBP2z4G3NpevXgd8PzYEqQkSVO1bcLz/hvwySSXAn8HvI9RCN6V5DbgKeA97dzPATcBK8B327lacM6ANW+qyv9wc0lkHv4BSjJ8J7Qp83AdSeMMsYVwcpLbT76zh6SF5ORqeRhkkqSuGWTaNGe+koZkkElaWE6yloNBJknqmkGmTXHGK2loBpkkqWsGmaSF5qrB4jPIJEldM8i0Yc50Jc0Dg0zSwnPStdgMMklS1wwybYgzXPXGa3ZxGWSSloLvhr+4DDJJS8GKbHEZZJKkrhlkWjdntuqV1+5iMsgkSV0zyCRJXTPIJEldM8i0Lt5jUO+8hhfPtqE7oL74tziS5o0VmSSpawaZJKlrBpkkqWsGmSSpawaZJKlrBpkkqWsGmSSpawaZJKlrBpkkqWsGmSSpawaZJKlrBpkkqWsGmSSpawaZJKlrBpkkqWsGmSSpawaZJKlrBpkkqWsGmSSpawaZJKlr24buQPNPwBNDd2KKXgv849CdmKJFGs8ijQUczzxbpLHAMOP5iUlOmpcge6Kq9g/diWlJcsLxzKdFGgs4nnm2SGOB+R6PS4uSpK4ZZJKkrs1LkB0ZugNT5njm1yKNBRzPPFukscAcjydVNXQfJEnasHmpyCRJ2pDBgyzJDUmeSLKS5PDQ/ZlEko8nOZfk0bG2K5Pcl+TJ9nhFa0+S29v4Hkmyb7ie/6Ake5I8kOTxJI8leX9r73U8r0ryxSRfaeP5zdZ+TZIHW78/k+TS1v7Ktr/Sjl89ZP8vJMklSR5Kcm/b73ks30jy1SQPJznR2rq81gCSbE9yd5KvJTmV5Poex5PkDe13svrxnSQf6GYsVTXYB3AJ8HXg9cClwFeANw3Zpwn7/TZgH/DoWNtvA4fb9mHgw237JuAvgADXAQ8O3f/zxrIT2Ne2XwP8LfCmjscT4NVt+xXAg62fdwG3tPY/AP5z2/4vwB+07VuAzww9hguM6YPAHwP3tv2ex/IN4LXntXV5rbU+HgX+U9u+FNje83haPy8BnmH0N1xdjGXoH9j1wOfH9j8EfGjoX+SEfb/6vCB7AtjZtncy+ts4gD8E3nuh8+bxA7gHeOcijAf4EeDLwH9k9Iec21r7i9cd8Hng+ra9rZ2Xofs+NobdwHHg7cC97R+OLsfS+nWhIOvyWgMuB/7+/J9xr+MZ69fPA3/T01iGXlrcBZwe2z/T2nq0o6qebtvPADvadjdjbEtRb2ZUxXQ7nrYU9zBwDriPUdX/XFW90E4Z7/OL42nHnweu2toev6zfBX4V+F7bv4p+xwJQwF8lOZnkUGvr9Vq7BvgH4I/a0u/HklxGv+NZdQvwqbbdxViGDrKFVKMpSlcvB03yauBPgQ9U1XfGj/U2nqr6t6q6llE18xbgjQN3aUOS/CJwrqpODt2XKXprVe0DbgR+Ocnbxg92dq1tY3SL4Y6qejPwz4yW317U2Xho91vfBfzJ+cfmeSxDB9lZYM/Y/u7W1qNnk+wEaI/nWvvcjzHJKxiF2Cer6s9ac7fjWVVVzwEPMFp+255k9S3Zxvv84nja8cuBb25xVy/mZ4B3JfkG8GlGy4sfpc+xAFBVZ9vjOeCzjCYavV5rZ4AzVfVg27+bUbD1Oh4YTTC+XFXPtv0uxjJ0kH0J2NtehXUpo5L22MB92qhjwMG2fZDRvabV9lvbq3yuA54fK9UHlyTAncCpqvqdsUO9jud1Sba37R9mdL/vFKNAe3c77fzxrI7z3cD9beY5uKr6UFXtrqqrGT037q+qX6LDsQAkuSzJa1a3Gd2LeZROr7WqegY4neQNrekdwON0Op7mvby0rAi9jGUObizexOiVcl8HfmPo/kzY508BTwP/n9Gs7DZG9yKOA08C/we4sp0b4Pfb+L4K7B+6/+eN5a2MlgseAR5uHzd1PJ7/ADzUxvMo8N9b++uBLwIrjJZNXtnaX9X2V9rx1w89houM62d56VWLXY6l9fsr7eOx1ed7r9da6+O1wIl2vf05cEWv4wEuY1TBXz7W1sVYfGcPSVLXhl5alCRpUwwySVLXDDJJUtcMMklS1wwySVLXDDJJUtcMMklS1wwySVLX/h30GOJbc9BzSAAAAABJRU5ErkJggg==\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.where(x > 1, -1, 1)\n",
+ "print(\"format of stack x_bin = \", x_bin.shape, \"\\n\"), \n",
+ "print(\"minimum pixel value after conversion = \", np.amin(x_bin), \"\\n\"), \n",
+ "print(\"maximum pixel value after conversion = \", np.amax(x_bin), \"\\n\")\n",
+ "# fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "# ax.imshow(x_bin[30], cmap = 'gray')\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(-1, 1)"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "np.min(x_bin), np.max(x_bin)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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\n",
+ "text/plain": [
+ "<Figure size 504x504 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "x_bin = np.flip(x_bin)\n",
+ "fig, ax = plt.subplots(figsize=(7, 7))\n",
+ "ax.imshow(x_bin, cmap='gray')\n",
+ "None"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(691, 756)"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "x_bin.shape"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 39,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[691 756]\n"
+ ]
+ }
+ ],
+ "source": [
+ "# save flat image stack as binary file\n",
+ "path = '/Users/jstark/Desktop/image_examples/'\n",
+ "filename = 'triangle'\n",
+ "ips.save_array_toBin(x_bin, path, filename)\n",
+ "\n",
+ "# Save image size in #pixels / axis as csv file\n",
+ "dim = np.asarray(x_bin.shape)\n",
+ "print(dim)\n",
+ "np.savetxt('%s/size_%s.csv' % (path, filename), dim, fmt='%i', delimiter=',')"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.6.5"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/image_process_and_save.py b/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/image_process_and_save.py
new file mode 100644
index 000000000..797227559
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/image_process_and_save.py
@@ -0,0 +1,26 @@
+import os
+import numpy as np
+
+def padding(img, x_pad, y_pad, z_pad):
+ z, y, x = img.shape[0], img.shape[1], img.shape[2]
+ zp, yp, xp = z + 2*z_pad, y + 2*y_pad, x + 2*x_pad
+ x_padded = np.zeros((zp, yp, xp ))
+ x_padded[z_pad:zp-z_pad, y_pad:yp-y_pad, x_pad:xp-x_pad] = img
+ return x_padded
+
+def save_zslices_toBin(numpy_array, filename):
+ import os
+ curdir = os.getcwd()
+ directory = '%s/%s'% (curdir, filename)
+ if not os.path.exists(directory):
+ os.makedirs(directory)
+ # loop through z dim and save every slice as separate binary file bc. savetxt only works for 1d or 2d arrays
+ z_dim = numpy_array.shape[0]
+ for z in range(z_dim):
+ numpy_array[z].astype('int8').tofile('%s/zslice_%d.bin' % (directory, z))
+
+def save_array_toBin(numpy_array, path, filename):
+ if not os.path.exists(path):
+ os.makedirs(path)
+ numpy_array.astype('int8').tofile('%s/%s.bin' % (path, filename))
+
diff --git a/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/morphological_operations.py b/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/morphological_operations.py
new file mode 100644
index 000000000..fc606d0ac
--- /dev/null
+++ b/example/Numerics/Sussman_redistancing/image_binary_conversion/lib/morphological_operations.py
@@ -0,0 +1,40 @@
+import cv2
+import numpy as np
+
+def closure(img, kernel, iterations):
+ lz, ly, lx = img.shape[0], img.shape[1], img.shape[2]
+ erosion = np.zeros((lz, ly, lx))
+ dilation = np.zeros((lz, ly, lx))
+
+ # Closure
+ # -> connects separated regions, increase connectivity
+ i = 0
+ while i < 1:
+
+ for z_slice in range(lz):
+ dilation[z_slice] = cv2.dilate(img[z_slice], kernel, iterations = iterations)
+ img = dilation
+ for z_slice in range(lz):
+ erosion[z_slice] = cv2.erode(img[z_slice], kernel, iterations = iterations)
+ img = erosion
+ i += 1;
+ return img
+
+def opening(img, kernel, iterations):
+ lz, ly, lx = img.shape[0], img.shape[1], img.shape[2]
+ erosion = np.zeros((lz, ly, lx))
+ dilation = np.zeros((lz, ly, lx))
+
+ # Opening
+ # -> removes islands / small regions
+ i = 0
+ while i < 1:
+
+ for z_slice in range(lz):
+ erosion[z_slice] = cv2.erode(img[z_slice], kernel, iterations = iterations)
+ img = erosion
+ for z_slice in range(lz):
+ dilation[z_slice] = cv2.dilate(img[z_slice], kernel, iterations = iterations)
+ img = dilation
+ i += 1;
+ return img
\ No newline at end of file
diff --git a/install b/install
index 76a621005..4b4667dcd 100755
--- a/install
+++ b/install
@@ -414,11 +414,11 @@ fi
echo "INCLUDE_PATH=$cuda_include_dirs -Wno-deprecated-declarations $openmp_flags -I. -I$install_base/openfpm_numerics/include -I$install_base/openfpm_pdata/include/config -I$install_base/openfpm_pdata/include -I$install_base/openfpm_data/include -I$install_base/openfpm_vcluster/include -I$install_base/openfpm_io/include -I$install_base/openfpm_devices/include -I$i_dir/VCDEVEL/include -I$i_dir/METIS/include -I$i_dir/PARMETIS/include -I$i_dir/BOOST/include -I$i_dir/HDF5/include -I$i_dir/LIBHILBERT/include $lin_alg_inc" > example.mk
echo "LIBS_PATH=$openmp_flags -L$install_base/openfpm_devices/lib -L$install_base/openfpm_pdata/lib -L$install_base/openfpm_vcluster/lib -L$i_dir/VCDEVEL/lib -L$i_dir/METIS/lib -L$i_dir/PARMETIS/lib -L$i_dir/BOOST/lib -L$hdf5_lib -L$i_dir/LIBHILBERT/lib $lin_alg_dir " >> example.mk
if [ x"$gpu_support" == x"1" ]; then
- echo "LIBS=-lvcluster -lofpm_pdata -lofpmmemory -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $(cat cuda_lib) $lin_alg_lib -ldl" >> example.mk
- echo "LIBS_SE2=-lvcluster -lofpmmemory_se2 -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $(cat cuda_lib) $lin_alg_lib" >> example.mk
+ echo "LIBS=-lvcluster -lofpm_pdata -lofpmmemory -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $(cat cuda_lib) $lin_alg_lib -ldl -lboost_filesystem -lboost_system" >> example.mk
+ echo "LIBS_SE2=-lvcluster -lofpmmemory_se2 -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $(cat cuda_lib) $lin_alg_lib -lboost_filesystem -lboost_system" >> example.mk
else
- echo "LIBS=-lvcluster -lofpm_pdata -lofpmmemory -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $lin_alg_lib -ldl" >> example.mk
- echo "LIBS_SE2=-lvcluster -lofpmmemory_se2 -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $lin_alg_lib" >> example.mk
+ echo "LIBS=-lvcluster -lofpm_pdata -lofpmmemory -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $lin_alg_lib -ldl -lboost_filesystem -lboost_system" >> example.mk
+ echo "LIBS_SE2=-lvcluster -lofpmmemory_se2 -lparmetis -lmetis -lboost_iostreams -lboost_program_options -lhdf5 -llibhilbert -lVc $lin_alg_lib -lboost_filesystem -lboost_system" >> example.mk
fi
echo "INCLUDE_PATH_NVCC=-Xcompiler="-Wno-deprecated-declarations" $(cat openmp_flags) "$(cat cuda_options)" -I. -I$install_base/openfpm_numerics/include -I$install_base/openfpm_pdata/include/config -I$install_base/openfpm_pdata/include -I$install_base/openfpm_data/include -I$install_base/openfpm_vcluster/include -I$install_base/openfpm_io/include -I$install_base/openfpm_devices/include -I$i_dir/METIS/include -I$i_dir/PARMETIS/include -I$i_dir/BOOST/include -I$i_dir/HDF5/include -I$i_dir/LIBHILBERT/include $lin_alg_inc" >> example.mk
cp example.mk src/example.mk
--
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