Differential Geometry

Fundamental Theorem of Space Curves Visualization

In differential geometry, the fundamental theorem of space curves states that every regular curve in three-dimensional space, with non-zero curvature, has its shape (and size) completely determined by its curvature and torsion.

Given curvature \kappa and torsion \tau, the Frenet equation relates the tangent, normal, and binormal vector of the curve at each position.

    \[ \begin{cases} T'_{\alpha} & =\kappa_{\alpha}N_{\alpha}\\ N'_{\alpha} & =-\tau T_{\alpha}-\kappa_{\alpha}B_{\alpha}\\ B'_{\alpha} & =\tau N_{\alpha} \end{cases} \]

Continue reading “Differential Geometry”

3D Neural Network Simulator

Neural Network implementation in UE4

Our neural network implementation in Unreal Engine 4 can have different purposes, educational or as a tool for data scientist developers.

This tool is really easy to be used: you can change the number of layers and the neurons per layer. In the example showed I have used the MNIST dataset for number recognition, furthermore, I can use different datasets.

If you want to use this tool for educational purposes, you can debug and see how the neural networks work. It is really practical and I recommend whoever wants to start AI. This application is progress, although you would be able to see the advances.

Continue reading “3D Neural Network Simulator”