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README.md
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README.md
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### Introduction
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The spherical triangular tessellation is a kind of partition of the spherical surface composed by only triangular cells. This program could generate the STT based on an icosahedron. The STT generated by the program could be refined around given points, lines, polygons and circles on the spherical surface. The exterior and interior outlines of the STT could also be customized.
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The spherical triangular tessellation (STT) is a method to partition a spherical surface into triangular cells. This program generates STT based on an icosahedron and provides various refinement options:
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1. Geometric refinement around:
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- Points
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- Lines
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- Polygons
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- Circles
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2. Topographic refinement based on elevation data
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3. Customizable exterior and interior boundaries
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### Files and folders
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1. **CMakeLists.txt** CMake project file;
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2. **\*.h and \*.cpp** Source files;
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3. **README.md** This file;
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4. **stt-example.png** Screen short of an example output;
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5. **archived** Old source files;
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6. **doc** Example files.
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#### Source file lists
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```shell
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head_functions.cc
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head_functions.h
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main.cc
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progress_bar.cc
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progress_bar.h
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struct_functions.cc
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struct_functions.h
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stt_class.h
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stt_close_surface.cc
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stt_create_branch.cc
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stt_create_tree.cc
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stt_cut_hole.cc
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stt_cut_outline.cc
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stt_delete_tree.cc
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stt_get_control_circle.cc
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stt_get_control_line.cc
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stt_get_control_point.cc
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stt_in_poly_outline.cc
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stt_in_triangle_circle.cc
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stt_in_triangle_line.cc
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stt_in_triangle_point.cc
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stt_in_triangle_polygon.cc
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stt_initial_icosahedron.cc
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stt_out_poly_outline.cc
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stt_output_msh_file.cc
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stt_output_neighbor.cc
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stt_output_triangle_center_location.cc
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stt_output_vertex_location.cc
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stt_return_branch_depth.cc
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stt_return_depth.cc
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stt_return_leaf.cc
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stt_routine.cc
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stt_set_command_record.cc
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stt_set_icosahedron_orient.cc
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stt_set_pole_equator_radius.cc
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stt_set_tree_depth.cc
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stt_sort_neighbor.cc
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```
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1. **CMakeLists.txt**: CMake project configuration file
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2. **src/**: Source code directory containing all implementation files
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3. **doc/**: Example files and test cases
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4. **README.md**: Documentation (this file)
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5. **archived/**: Legacy source files (for reference only)
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### Installation
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This program is a toolkit that is developed and maintained by Dr. Yi Zhang (zhangyiss@icloud.com) , which could be compiled and installed using the [CMake](https://cmake.org) software. Follow the instructions bellow to compile this program:
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This program is developed and maintained by Dr. Yi Zhang (yizhang-geo@zju.edu.cn). To compile and install using [CMake](https://cmake.org):
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```shell
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mkdir build
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cd build
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cmake ..
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make
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make install
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```
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### Usage
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```bash
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Usage: stt -d<minimal-depth>/<maximal-depth> [-r'WGS84'|'Earth'|'Moon'|<equator-radius>/<pole-radius>|<equator_radius>,<flat-rate>] [-o<orient-longitude>/<orient-latitude>] [-m<output-msh-filename>] [-v<output-vert-loc-filename>] [-t<output-tri-cen-filename>] [-n<output-tri-neg-filename>] [-p<control-point-filename>] [-l<control-line-filename>] [-g<control-poly-filename>] [-c<control-circle-filename>] [-s<outline-shape-filename>] [-k<hole-shape-filename>] [-h]
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Usage: stt -d<minimal-depth>/<maximal-depth> [options]
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Required:
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-d<min>/<max> Minimal and maximal depths of the quad-tree structure
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Optional:
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-r<ref> Coordinate reference system:
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- 'WGS84': WGS84 ellipsoid
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- 'Earth': Spherical Earth
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- 'Moon': Lunar sphere
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- <eq-rad>/<pole-rad>: Custom ellipsoid
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- <eq-rad>,<flat-rate>: Custom flattened sphere
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-o<lon>/<lat> Orientation of icosahedron top vertex
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Output options:
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-m<file> Output Gmsh(.msh) mesh file
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-v<file> Output vertices' locations
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-t<file> Output triangle centers
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-n<file> Output triangle neighbors
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Refinement control:
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-p<file> Control points file
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-l<file> Control lines file
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-g<file> Control polygons file
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-c<file> Control circles file
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-t<file> Topography control file
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-s<file> Outline shape file
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-k<file> Hole shape file
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-z<file> Topography data file
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Help:
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-h Show this help message
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```
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#### Options
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### Input File Formats
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+ __-d__: Minimal and maximal depths of the quad-tree structures used to construct the STT.
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+ __-r__: Coordinate reference system of the output files.
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+ __-o__: Orientation of the top vertex of the base icosahedron.
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+ __-m__: Output filename of the Gmsh(.msh) file.
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+ __-v__: Output filename of the vertices' location.
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+ __-t__: Output filename of the triangles' center location.
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+ __-n__: Output filename of the triangles' neighbor.
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+ __-p__: Input filename of control points' location.
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+ __-l__: Input filename of control lines' location.
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+ __-g__: Input filename of control polygons' location.
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+ __-c__: Input filename of control circles' location.
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+ __-s__: Input filename of outline shapes' location.
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+ __-k__: Input filename of hole shapes' location.
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+ __-h__: show help information.
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#### Input File Formats
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##### Point format
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The format of the control points' location is a plain text file. Each line of the file has the information of one control point which contains the spherical coordinates, maximal quad-tree depth, minimal resolution and physical group of the point. The program takes both the tree depth and resolution to control the fineness of the refined STT. The refinement of the STT will stop which ever the two conditions has been reached. Note that any line that starts with '#' or any empty line will be skipped. An example file:
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#### Point Control Format
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Controls refinement around specific points:
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```bash
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# <longitude> <latitude> <maximal-depth> <minimal-resolution> <physical-group>
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-45 -45 5 1.0 7
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45 -45 5 1.0 7
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45 45 5 1.0 7
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-45 45 5 1.0 7
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```
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##### Circle format
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The format of the control circles' location is a plain text file. Each line of the file has the information of one control circle which contains the spherical coordinates, spherical cap degree, maximal quad-tree depth, minimal resolution and physical group of the circle. The program takes both the tree depth and resolution to control the fineness of the refined STT. The refinement of the STT will stop which ever the two conditions has been reached. Note that any line that starts with '#' or any empty line will be skipped. An example file:
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#### Circle Control Format
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Controls refinement around spherical caps:
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```bash
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# <longitude> <latitude> <spherical-cap-degree> <maximal-depth> <minimal-resolution> <physical-group>
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@@ -112,15 +89,12 @@ The format of the control circles' location is a plain text file. Each line of t
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-20 -45 20 6 0.1 13
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```
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##### Line format
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The format of the control lines', polygons', outlines', and holes' location is a plain text file. Blocks separated by empty lines contain information of control units. For each block, the first line has the number of the spherical locations, maximal quad-tree depth, minimal resolution and physical group of the unit. Followed by spherical coordinates of the unit.The program takes both the tree depth and resolution to control the fineness of the refined STT. The refinement of the STT will stop which ever the two conditions has been reached. Note that any line that starts with '#' or any empty line will be skipped. An example file:
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#### Line/Polygon Control Format
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Controls refinement along lines or around polygons:
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```bash
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# <number-of-points> <maximal-depth> <minimal-resolution> <physical-group>
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# <longitude> <latitude>
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# <longitude> <latitude>
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# ... ...
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# First line: <number-of-points> <maximal-depth> <minimal-resolution> <physical-group>
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# Following lines: <longitude> <latitude> of each point
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4 6 0.1 5
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-10 10
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50 15
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@@ -128,12 +102,32 @@ The format of the control lines', polygons', outlines', and holes' location is a
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-15 50
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```
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#### Topography Control Format
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Controls refinement based on elevation data:
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```bash
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# First line: <maximum-STD> <maximal-depth> <minimal-resolution> <physical-group>
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# Following lines: <longitude> <latitude> <elevation(meters)>
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200.0 10 -1 5
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-179.95 89.95 -4203.20
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-179.85 89.95 -4203.07
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-179.75 89.95 -4203.47
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```
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Note: maximum-STD represents the maximum standard deviation of elevation allowed in a triangle.
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### Examples
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An example of multi-resolution STT:
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1. Multi-resolution STT with geometric constraints:
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```bash
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stt -d 3/7 -m example.msh -l doc/control_lines.txt -g doc/control_poly.txt -c doc/control_circle.txt
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```
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2. Topography-constrained STT:
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```bash
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stt -d 6/10 -m topo_example.msh -t doc/control_topo.txt
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```
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