update readme

README.md

@@ -12,6 +12,61 @@ The spherical triangular tessellation (STT) is a method to partition a spherical
 2. Topographic refinement based on elevation data
 3. Customizable exterior and interior boundaries
 
+### Technical Details
+
+#### Core Algorithm
+
+1. **Base Structure**
+   - Starts with an icosahedron (20 triangular faces)
+   - Uses quad-tree data structure for adaptive refinement
+   - Each face of the icosahedron becomes the root of a quad-tree
+
+2. **Refinement Process**
+   - Adaptive refinement based on various constraints
+   - Uses vector calculations for spherical geometry
+   - Supports multiple levels of refinement (controlled by depth parameter)
+
+3. **Constraint Types**
+   - Point constraints: Refines mesh around specific points
+   - Line constraints: Refines along great circle paths
+   - Polygon constraints: Refines within or around polygon boundaries
+   - Circle constraints: Refines within spherical caps
+   - Topographic constraints: Refines based on elevation data
+
+4. **Coordinate Systems**
+   - Supports multiple reference systems:
+     * WGS84 ellipsoid
+     * Spherical Earth
+     * Lunar sphere
+     * Custom ellipsoid
+     * Custom flattened sphere
+   - Configurable orientation of the base icosahedron
+
+### Algorithm Details
+
+1. **Initialization**
+   - Creates base icosahedron
+   - Sets up coordinate system and orientation
+   - Initializes quad-tree structure
+
+2. **Refinement Process**
+   - Reads constraint files
+   - For each triangle:
+     * Tests intersection with constraints
+     * Subdivides if needed based on depth and resolution
+     * Maintains neighbor relationships
+
+3. **Output Generation**
+   - Generates final mesh
+   - Computes vertex locations
+   - Creates neighbor lists
+   - Exports in various formats
+
+4. **Memory Management**
+   - Uses dynamic allocation for tree structures
+   - Automatically cleans up temporary data
+   - Efficient handling of large datasets
+
 ### Files and folders
 
 1. **CMakeLists.txt**: CMake project configuration file
@@ -22,7 +77,7 @@ The spherical triangular tessellation (STT) is a method to partition a spherical
 
 ### Installation
 
-This program is developed and maintained by Dr. Yi Zhang (yizhang-geo@zju.edu.cn). To compile and install using [CMake](https://cmake.org):
+To compile and install using [CMake](https://cmake.org):
 
 ```shell
 mkdir build
@@ -39,6 +94,7 @@ Usage: stt -d<minimal-depth>/<maximal-depth> [options]
 
 Required:
   -d<min>/<max>    Minimal and maximal depths of the quad-tree structure
+                   Example: -d3/7 for refinement from depth 3 to 7
 
 Optional:
   -r<ref>          Coordinate reference system:
@@ -48,6 +104,7 @@ Optional:
                    - <eq-rad>/<pole-rad>: Custom ellipsoid
                    - <eq-rad>,<flat-rate>: Custom flattened sphere
   -o<lon>/<lat>    Orientation of icosahedron top vertex
+                   Default: 0/90 (North Pole)
   
 Output options:
   -m<file>         Output Gmsh(.msh) mesh file
@@ -72,29 +129,35 @@ Help:
 ### Input File Formats
 
 #### Point Control Format
-Controls refinement around specific points:
+Controls refinement around specific points. Each point is defined by its location and refinement parameters:
 
 ```bash
 # <longitude> <latitude> <maximal-depth> <minimal-resolution> <physical-group>
+# longitude, latitude: Coordinates in degrees
+# maximal-depth: Maximum refinement depth for this point
+# minimal-resolution: Minimum cell size in degrees
+# physical-group: Group identifier for the refined region
 -45 -45 5 1.0 7
 45 -45 5 1.0 7
 ```
 
 #### Circle Control Format
-Controls refinement around spherical caps:
+Controls refinement around spherical caps. Each circle is defined by its center, radius, and refinement parameters:
 
 ```bash
 # <longitude> <latitude> <spherical-cap-degree> <maximal-depth> <minimal-resolution> <physical-group>
+# spherical-cap-degree: Angular radius of the cap in degrees
 45 60 30 5 0.1 12
 -20 -45 20 6 0.1 13
 ```
 
 #### Line/Polygon Control Format
-Controls refinement along lines or around polygons:
+Controls refinement along lines or around polygons. Each shape is defined by a sequence of points and refinement parameters:
 
 ```bash
 # First line: <number-of-points> <maximal-depth> <minimal-resolution> <physical-group>
 # Following lines: <longitude> <latitude> of each point
+# Points are connected in sequence, last point connects to first for polygons
 4 6 0.1 5
 -10 10
 50 15
@@ -103,31 +166,39 @@ Controls refinement along lines or around polygons:
 ```
 
 #### Topography Control Format
-Controls refinement based on elevation data:
+Controls refinement based on elevation data. The refinement is based on elevation variation within triangles:
 
 ```bash
 # First line: <maximum-STD> <maximal-depth> <minimal-resolution> <physical-group>
 # Following lines: <longitude> <latitude> <elevation(meters)>
+# maximum-STD: Maximum allowed standard deviation of elevation within a triangle
 200.0 10 -1 5
 -179.95 89.95 -4203.20
 -179.85 89.95 -4203.07
 -179.75 89.95 -4203.47
 ```
 
-Note: maximum-STD represents the maximum standard deviation of elevation allowed in a triangle.
+Note: maximum-STD represents the maximum standard deviation of elevation allowed in a triangle. A triangle will be refined if the elevation variation within it exceeds this threshold.
 
 ### Examples
 
 1. Multi-resolution STT with geometric constraints:
 
 ```bash
+# Creates a mesh with depth range 3-7, refined around lines, polygons and circles
 stt -d 3/7 -m example.msh -l doc/control_lines.txt -g doc/control_poly.txt -c doc/control_circle.txt
 ```
+
 ![stt-example](doc/stt-example.png)
 
 2. Topography-constrained STT:
 
 ```bash
+# Creates a mesh with depth range 6-10, refined based on topography data
 stt -d 6/10 -m topo_example.msh -t doc/control_topo.txt
 ```
+
 ![topo-example](doc/topo_constraint.png)
+
+### Contact
+For any bug reports or you need some help. Please contact Dr. Yi Zhang ([yizhang-geo@zju.edu.cn](yizhang-geo@zju.edu.cn)).