205 lines
6.3 KiB
Markdown
205 lines
6.3 KiB
Markdown
## Spherical Triangular Tessellation (STT) Generator
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### Introduction
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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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### Technical Details
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#### Core Algorithm
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1. **Base Structure**
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- Starts with an icosahedron (20 triangular faces)
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- Uses quad-tree data structure for adaptive refinement
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- Each face of the icosahedron becomes the root of a quad-tree
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2. **Refinement Process**
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- Adaptive refinement based on various constraints
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- Uses vector calculations for spherical geometry
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- Supports multiple levels of refinement (controlled by depth parameter)
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3. **Constraint Types**
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- Point constraints: Refines mesh around specific points
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- Line constraints: Refines along great circle paths
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- Polygon constraints: Refines within or around polygon boundaries
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- Circle constraints: Refines within spherical caps
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- Topographic constraints: Refines based on elevation data
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4. **Coordinate Systems**
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- Supports multiple reference systems:
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* WGS84 ellipsoid
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* Spherical Earth
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* Lunar sphere
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* Custom ellipsoid
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* Custom flattened sphere
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- Configurable orientation of the base icosahedron
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### Algorithm Details
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1. **Initialization**
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- Creates base icosahedron
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- Sets up coordinate system and orientation
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- Initializes quad-tree structure
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2. **Refinement Process**
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- Reads constraint files
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- For each triangle:
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* Tests intersection with constraints
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* Subdivides if needed based on depth and resolution
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* Maintains neighbor relationships
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3. **Output Generation**
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- Generates final mesh
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- Computes vertex locations
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- Creates neighbor lists
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- Exports in various formats
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4. **Memory Management**
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- Uses dynamic allocation for tree structures
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- Automatically cleans up temporary data
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- Efficient handling of large datasets
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### Files and folders
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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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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> [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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Example: -d3/7 for refinement from depth 3 to 7
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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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Default: 0/90 (North Pole)
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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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### Input File Formats
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#### Point Control Format
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Controls refinement around specific points. Each point is defined by its location and refinement parameters:
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```bash
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# <longitude> <latitude> <maximal-depth> <minimal-resolution> <physical-group>
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# longitude, latitude: Coordinates in degrees
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# maximal-depth: Maximum refinement depth for this point
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# minimal-resolution: Minimum cell size in degrees
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# physical-group: Group identifier for the refined region
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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 Control Format
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Controls refinement around spherical caps. Each circle is defined by its center, radius, and refinement parameters:
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```bash
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# <longitude> <latitude> <spherical-cap-degree> <maximal-depth> <minimal-resolution> <physical-group>
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# spherical-cap-degree: Angular radius of the cap in degrees
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45 60 30 5 0.1 12
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-20 -45 20 6 0.1 13
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```
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#### Line/Polygon Control Format
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Controls refinement along lines or around polygons. Each shape is defined by a sequence of points and refinement parameters:
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```bash
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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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# Points are connected in sequence, last point connects to first for polygons
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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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60 55
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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. The refinement is based on elevation variation within triangles:
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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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# maximum-STD: Maximum allowed standard deviation of elevation within a triangle
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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. A triangle will be refined if the elevation variation within it exceeds this threshold.
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### Examples
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1. Multi-resolution STT with geometric constraints:
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```bash
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# Creates a mesh with depth range 3-7, refined around lines, polygons and circles
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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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# Creates a mesh with depth range 6-10, refined based on topography data
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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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### Contact
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For any bug reports or you need some help. Please contact Dr. Yi Zhang ([yizhang-geo@zju.edu.cn](yizhang-geo@zju.edu.cn)).
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