This is a Python library written in C++ for working with Conway polyhedron operators.
If you dont have Python, pip and/or a `C++ compiler installed, follow these steps:
sudo apt install python3 python3-pip build-essential
Install Python 3 and pip. Then install Visual Studio Build Tools and make sure to select the C++ build tools.
Install Python 3 and pip. Then install Xcode and the command line tools.
Open a terminal and run the following command in the root directory of the project:
pip install setuptools pybind11
pip install .
To run the examples, run the following command to install the required dependencies:
pip install imageio opencv-python
- Platonic Solids (Tetrahedron, Cube, Octahedron, Dodecahedron, Icosahedron)
- N-sided Prisms, Antiprisms and Pyramids
- Truncation
- Ambo
- Dual
- Gyration
- Propeller
- Compound operators of the above
Iterative refinement forces are a set of forces that can be applied to a polyhedron to alter its shape. They have in common that their respective energy is not minimized by a single application of the force. So the forces need to be applied iteratively, and the polyhedron is moved to minimize the total energy of the respective forces.
- Move vertices to average of neighbor vertex positions
- Move vertices to average of the centers of the faces they are part of
- Move vertices to equalize edge length over the whole polyhedron
- Move vertices to make edges tangent to unit sphere
- Move vertices to lie in the total least squares planes of the faces they are part of
Spectral realization provides a non-iterative way of optimizing the shape of a polyhedron. It works by finding the eigenvectors of a matrix that is related to the polyhedron, and then assigning certain eigenvectors to the vertex positions.
via the Polyhedron.get_matrix(string name) function:
- Adjacency matrix
- Face-mean-matrix (works best)
- Vertex-mean-matrix
- (Laplacian, but it's broken rn)
Face-mean matrix is the default & equivalent to the minimum energy of moving the vertices to the average of their face centers. The iterative force method is more robust and faster in most cases since it is sparsely computed, so it is especially faster in more complex polyhedra.
- Unskewing using Gram-Schmidt-Orthogonalization
- Scaling and rotating the polyhedron
- Automatic rotational alignment of the polyhedron to the coordinate axes
- Small render engine (WIP) for rendering the polyhedron edges in Orthographic projection (See movie above)
- Saving the polyhedron as an obj file
See the examples folder for examples of how to use the library.
The code below instantiates a cube, then truncates it, dualizes it, and saves it as an obj file.
from polyop import cube
p = cube()
p = p.trunc().dual()
p.save_obj('notacube.obj')This project is licensed under the MIT License - see the LICENSE file for details.