The application takes the coordinates of points or planes as input (given by inequalities) and calculates with which vertices (planes) it is possible to create a convex polyhedron of maximum volume.
Output: a graphical representation of the polyhedron and a textual representation of the vertices (coordinates)
Example of work:
OpenGL and freeglut are used.
It is advisable to work in Visual Studio with vcpkg installed.
Installation instructions can be found here: https://vcpkg.io/en/getting-started.html
Next, install OpenGL, freeglut
vcpkg install freeglut:x64-windows
vcpkg install integrate
Everything will be implemented automatically in visual studio and no additional settings need to be made.
In the command line, run the command:
Convex_poly.exe input.txt
Or without an argument input.txt, then the points will need to be entered manually.
where input is the name of the data file input.txt:
V
9
0 0 2
2 0 2
0 2 2
1 0 0
2 0 0
0 1 0
0 2 0
2 2 0
1st row - data type, V - vertices, H - Inequalities (planes)
2nd line - number of points
The remaining rows are the rows of vertex coordinates (x, y, z) - integer if the data type is V.
If the data type is H, then inequalities are introduced, similarly:
input.txt:
H
7
0 0 1 2
0 -1 0 0
-1 0 0 0
-2 -2 -1 -2
1 0 0 2
0 1 0 2
0 0 -1 0
The data can be interpreted as a system of inequalities:
The program will display the following data:
- All vertices of the desired convex polyhedron (coordinates and their naming)
- Adjacency matrix, which tells how the vertices are connected
1 - Vertices are connected by a straight line, 0 - not - The face defined by the inequality
- And straight lines belonging to this face
- Graphical representation of the convex hull in the form of a 3D graph along the XYZ axes
- To display the graphics, you need to open a full-screen window with a polyhedron.
- You can run a graph or move away, LCM - zoom in, PCM - move away
- The rotation of the graph is set at the very beginning of the application