first commit

.gitignore

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+build
+bin
+scripts/*.dat
+doc/*.pdf

CMakeLists.txt

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+#***********************************************************
+#
+#***********************************************************
+cmake_minimum_required(VERSION 3.10)
+project(TQMesh
+        LANGUAGES CXX
+        VERSION   1.0)
+
+# Set C++ flags
+set(CMAKE_CXX_STANDARD 17)
+set(CMAKE_CXX_STANDARD_REQUIRED ON)
+#set(CMAKE_CXX_FLAGS         "${CMAKE_CXX_FLAGS} -Wunused-variable -std=c++17 -O3 -DNDEBUG -pg")
+set(CMAKE_CXX_FLAGS         "${CMAKE_CXX_FLAGS} -Wunused-variable -std=c++17 -O3 -DNDEBUG")
+#set(CMAKE_CXX_FLAGS         "${CMAKE_CXX_FLAGS} -std=c++17 -O0 -g -pg")
+#set(CMAKE_CXX_FLAGS         "${CMAKE_CXX_FLAGS} -Wunused-variable -std=c++17 -O0 -g")
+
+
+set( BIN ${CMAKE_SOURCE_DIR}/bin )
+
+
+add_subdirectory( src/utils )
+add_subdirectory( src/algorithm )
+add_subdirectory( src/tests )
+add_subdirectory( src/app )

LICENSE.md

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+MIT License
+
+Copyright (c) 2022 Florian Setzwein
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.
+

README.md

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+# TQMesh
+-----------------------
+<img src="doc/TQM_banner.png" alt="TQMesh-Grid" width="750"/>
+
+**TQMesh** is a simple C++ program for the generation of two-dimensional 
+meshes, that consist of triangles and quadrilaterals.
+The application is intended for learning purposes, for example to create two-dimensional 
+grids for Computational Fluid Dynamics or Finite Element Methods without much effort.
+The elements are generated with an advancing-front method, where the user must 
+define the edge segments that define the boundary of the domain to tesselate. 
+A user-defined size function makes it very easy to adjust the element size locally.
+**TQMesh** also offers the possibility to treat the near boundary region explicitly 
+by quadrilateral elements, which can be especially interesting for discretizing 
+Computational Fluid Dynamics problems.
+<img src="doc/ExampleMesh.png" alt="TQMesh-Example" width="500"/>
+
+
+## Installation
+**TQMesh** is basically a header-only library, which requires the files in the directories
+*src/algorithm* and *src/utils*.
+The directory *src/app* contains the code for the **TQMesh** application, that is described below.
+To its installation, simply create a build directory and run 
+```sh
+cmake ..
+make install
+```
+
+## Usage of TQMesh
+The **TQMesh** application requires a parameter file as input for the mesh generation.
+There are some sample files given in the *input/* directory.
+Basically, one only needs to define a few global parameters and the mesh boundaries in terms
+of boundary nodes and edges. 
+There is the possibility to assign markers to each defined boundary-edge. These markers 
+are then assigned to the final mesh boundary edges.
+Here is a simple example to create the shown mesh of a cylinder in a two-dimensional channel.
+<img src="doc/RectangleMesh_Tri.png" alt="TQMesh-Grid-Tri" width="750"/>
+``` sh
+#-----------------------------------------------------------
+#                          TQMESH     
+#-----------------------------------------------------------
+Element size: 0.05 
+Element type: Triangle 
+
+#-----------------------------------------------------------
+#                         VERTICES     
+# Arguments:
+#   1) X-coordinate
+#   2) Y-coordinate
+#   3) Scale parameter
+#   3) Range parameter
+#-----------------------------------------------------------
+Define vertices
+  0.0,   0.0,   1.0,  1.0     # 0
+  4.0,   0.0,   1.0,  1.0     # 1
+  4.0,   1.0,   1.0,  1.0     # 2
+  0.0,   1.0,   1.0,  1.0     # 3
+  0.35,  0.35,  1.0,  1.0     # 4
+  0.35,  0.65,  1.0,  1.0     # 5
+  0.65,  0.65,  1.0,  1.0     # 6
+  0.65,  0.35,  1.0,  1.0     # 7
+End vertices
+
+#-----------------------------------------------------------
+#                        BOUNDARIES     
+# Arguments:
+#   1) Index of starting vertex
+#   2) Index of ending vertex
+#   3) Boundary marker
+#
+# > All boundaries must be closed 
+# > Exterior boundaries must be defined counter-clockwise
+# > Interior boundaries must be defined clockwise
+#-----------------------------------------------------------
+Define exterior boundary
+ 0,  1,  2  # Domain Wall 
+ 1,  2,  3  # Outlet
+ 2,  3,  2  # Domain Wall
+ 3,  0,  1  # Inlet
+End exterior boundary
+
+Define interior boundary
+ 4,  5,  4  # Rectangle Wall
+ 5,  6,  4  # Rectangle Wall
+ 6,  7,  4  # Rectangle Wall
+ 7,  4,  4  # Rectangle Wall
+End interior boundary
+
+#-----------------------------------------------------------
+#                       QUAD-LAYERS     
+# Arguments: 
+#   1) Starting vertex
+#   2) Ending vertex
+#   3) Number of layers
+#   4) First layer height
+#   5) Growth ratio
+#
+# > The given start and ending vertices must be connected
+#   by boundary edges
+# > A closed layer of quadrilateral elements will be
+#   generated if the same start and ending vertex is 
+#   provided
+#-----------------------------------------------------------
+Add quad layers: 0, 1, 2, 0.02, 1.5
+Add quad layers: 2, 3, 2, 0.02, 1.5
+Add quad layers: 4, 4, 2, 0.02, 1.5
+```
+The mesh is created with 
+```sh
+./bin/TQMesh input/RectangleMesh.para > Mesh.dat
+```
+The mesh will be written to the file `Mesh.dat` in a simple ASCII format.
+
+It is even possible to provide simple size function expressions 
+through the input file by simply passing it through the element size
+parameter:
+``` sh
+Element size: 0.02 + 0.075 * sqrt( (x-0.5)*(x-0.5) ) 
+``` 
+The effect of the refinement is shown here:
+<img src="doc/RectangleMesh_TriRefined.png" alt="TQMesh-Grid-TriRefined" width="750"/>
+
+
+It is possible to define vertices with corresponding element sizings in the domain. 
+This can for example also be used to refine the field locally.
+``` sh
+#-----------------------------------------------------------
+#                      FIXED VERTICES     
+# Arguments:
+#   1) X-coordinate
+#   2) Y-coordinate
+#   3) Scale parameter
+#   4) Range parameter
+#-----------------------------------------------------------
+
+Define fixed vertices
+    1.00,     0.50,   0.3,  0.75
+    1.50,     0.50,   0.3,  0.75
+    2.00,     0.50,   0.3,  0.75
+End fixed vertices
+
+``` 
+<img src="doc/RectangleMesh_FixedVertex.png" alt="TQMesh-Grid-FixedVertex" width="750"/>
+
+
+Of course, we can also discretize the domain with Quadrilateral elements. 
+Simply change the element type in the input file to:
+``` sh
+Element type: Quadrilateral 
+``` 
+<img src="doc/RectangleMesh_Quad.png" alt="TQMesh-Grid-Qua-Quadd" width="750"/>
+
+## Output format
+Currently, **TQMesh** only features a simple output format,
+which is defined in the following way:
+``` sh
+VERTICES 5741            # The total number of mesh vertices
+-22.00000, 9.72407       # Coordinates of vertex 1
+-22.00000, 9.43624       # Coordinates of vertex 2
+...
+INTERIOREDGES 13575      # The total number of interior mesh edges
+976, 43, -1              # The edge connects vertex 976 & 43 and has marker -1
+...
+BOUNDARYEDGES 975        # The total number of boundary mesh edges
+41, 42, 1                # The edge connects vertex 41 & 42 and has marker 1
+733, 734, 2              # The edge connects vertex 733 & 734 and has marker 2
+...
+FRONT 0                  # Remaining advancing front edges after a failed meshing attempt
+QUADS 1700               # The total number of quadrilateral elements
+42, 43, 976, 975         # Quadrilateral made up of vertices 42, 43, 976 & 975
+...
+TRIANGLES 7111           # The total number of triangular elements
+40, 41, 42               # Triangle made up of vertices 40, 41 & 42
+...
+QUADNEIGHBORS 1700       # 
+1, 709, 358, -1          # Element indices of the neighbors of quadrilateral 1
+2, 359, 0, -1            # The index -1 indicates a mesh boundary adjacency
+TRIANGLENEIGHBORS 7111   # 
+197, 550, 196            # Element indices of the neighbors of triangle 1
+1377, 2492, -1           # The index -1 indicates a mesh boundary adjacency 
+...                      # 
+SIZE-FUNCTION 0.00000 0.00000 14.00000 10.00000 100 100 
+0.20519,0.22794,0.25070,0.27346,0.29623,0.31902,0.34182,0.36466,0.38754,0.41050
+...
+```
+For the adjacency lists, quadrilateral and triangular elements are indexed together. 
+This means, for example, if the mesh consists of 400 triangles and 300 quads, then quad 1 
+has element index 1 and triangle 1 has element index 401.
+At the end of the mesh output, the size function is returned. In the example above, it
+is resolved over a rectangular area (0,0) x (14,10) with 100 x 100 points.
+The floating point numbers below represent the corresponding entries of the size function array.
+
+## Plot your meshes
+A simple python script to plot your mesh is provided under `scripts/plot_mesh.py`.
+Run the script with
+```sh
+python scipts/plot_mesh.py Mesh.dat
+```
+You can use the script with the optional flag `-s` in order to plot the 
+underlying size function of the mesh.
+
+<img src="doc/ExampleMesh_SizeFunction.png" alt="TQMesh-Example-SizeFunction" width="350"/>
+
+## Usage of the TQMesh library
+Several examples on how to use the **TQMesh**-library functions are given in 
+*src/tests/mesh_test.cpp*.
+
+## Tests / Benchmarks
+**TQMesh** uses a customized QuadTree container structure to store and access 
+all mesh entities. 
+The following plots show some performance statistics that have been gathered with 
+the test functions `run_qtree_tests()` and `run_mesh_tests()`.
+
+<img src="doc/BenchmarkPlot_QTree.png" alt="TQMesh-QTree-Benchmark" width="400"/> <img src="doc/BenchmarkPlot_Mesh.png" alt="TQMesh-Mesh-Benchmark" width="400"/>
+
+## Libraries used
+* [exprtk.h - C++ Mathematical Expression Toolkit Library](http://www.partow.net/programming/exprtk/index.html)
+
+## Sources
+* o'Rourke, Joseph. Computational geometry in C. Cambridge university press, 1998.
+* [Shewchuk, Jonathan R. Lecture Notes on Delaunay Mesh Generation, February 5, 2012](https://people.eecs.berkeley.edu/~jrs/meshpapers/delnotes.pdf)
+* [Jonathan R. Shewchuk's free course material on Mesh Generation and Geometry Processing in Graphics, Engineering, and Modeling ](https://people.eecs.berkeley.edu/~jrs/mesh/)
+* Lo, Daniel SH. Finite element mesh generation. CRC Press, 2014
+* Blazek, Jiri. Computational fluid dynamics: principles and applications. Butterworth-Heinemann, 2015
+* Zed A. Shaw, Learn C the Hard Way (this is where the testing structure and the list functions are coming from)
+* [Zhou and Shimada, An Angle-Based Approach to Two-Dimensional Mesh Smoothing, IMR 2000, 373-384, 2000](https://www.researchgate.net/profile/Kenji-Shimada-2/publication/221561796_An_Angle-Based_Approach_to_Two-Dimensional_Mesh_Smoothing/links/0deec53988e9f560ec000000/An-Angle-Based-Approach-to-Two-Dimensional-Mesh-Smoothing.pdf) 
+
+## Licences
+The project is licensed under the MIT License - see the LICENSE file for details.
+
+

input/Example.para

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+#-----------------------------------------------------------
+#                          TQMESH     
+#-----------------------------------------------------------
+Element size: 0.5 #0.5-0.43*exp(-0.03*((1.-x)*(2.-x)+(9.-y)*(9.-y)))
+Element type: Triangle
+
+#-----------------------------------------------------------
+#                         VERTICES     
+# Arguments:
+#   1) X-coordinate
+#   2) Y-coordinate
+#   3) Scale parameter
+#-----------------------------------------------------------
+Define vertices
+  0.0,   0.0,   1.0,   1.0     # 0
+  1.0,   0.0,   1.0,   1.0     # 1
+  1.0,   2.0,   0.5,   1.5     # 2
+  2.0,   2.0,   0.5,   1.5     # 3
+  2.0,   1.0,   0.5,   1.2     # 4
+  3.0,   1.0,   0.5,   1.2     # 5
+  3.0,   3.0,   1.0,   1.0     # 6
+  0.0,   3.0,   1.0,   1.0     # 7
+End vertices
+
+#-----------------------------------------------------------
+#                        BOUNDARIES     
+# Arguments:
+#   1) Index of starting vertex
+#   2) Index of ending vertex
+#   3) Boundary marker
+#
+# > All boundaries must be closed 
+# > Exterior boundaries must be defined counter-clockwise
+# > Interior boundaries must be defined clockwise
+#-----------------------------------------------------------
+Define exterior boundary
+ 0,  1,  1
+ 1,  2,  1
+ 2,  3,  1
+ 3,  4,  1
+ 4,  5,  1
+ 5,  6,  1
+ 6,  7,  1
+ 7,  0,  1
+End exterior boundary
+
+#-----------------------------------------------------------
+#                       QUAD-LAYERS     
+# Arguments: 
+#   1) Starting vertex
+#   2) Ending vertex
+#   3) Number of layers
+#   4) First layer height
+#   5) Growth ratio
+#
+# > The given start and ending vertices must be connected
+#   by boundary edges
+# > A closed layer of quadrilateral elements will be
+#   generated if the same start and ending vertex is 
+#   provided
+#-----------------------------------------------------------
+Add quad layers: 0, 0, 3, 0.05, 1.5
+
+#-----------------------------------------------------------
+#                      FIXED VERTICES     
+# Arguments:
+#   1) X-coordinate
+#   2) Y-coordinate
+#   3) Scale parameter
+#   4) Range parameter
+#-----------------------------------------------------------
+Define fixed vertices
+    0.50,     1.00,   0.1,  0.5
+End fixed vertices
+