C++, UE4, AI developer
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 
and torsion 
, the Frenet equation relates the tangent, normal, and binormal vector of the curve at each position.
![\[ \begin{cases} T'_{\alpha} & =\kappa_{\alpha}N_{\alpha}\\ N'_{\alpha} & =-\tau T_{\alpha}-\kappa_{\alpha}B_{\alpha}\\ B'_{\alpha} & =\tau N_{\alpha} \end{cases} \]](https://sp-ao.shortpixel.ai/client/q_glossy,ret_img,w_180,h_75/http://dprogrammer.org/wp-content/ql-cache/quicklatex.com-7000df5f526ddebeb1a9082b16224dc9_l3.png "Rendered by QuickLaTeX.com")
Simplex Algorithm
I have coded recently the simplex algorithm. It is an algorithm that solves the optimizations of a problem of linear programming. It gives a function to minimize and constrains the variables with an inequality form.
It can be proven that the simplex algorithm solves this problem in Non-Polynomial time.
We usually want to know the shortest/fastest route between two points. This is a well-known problem in graph theory. There are several algorithms that solve this problem: A*, Dijkstra, etc.
I have implemented in C++ those algorithms and a graph of the roads in California.
Recurrent algorithms C++ and Python
I have been working on recurrent algorithms. They’re a bunch of examples in which you can implement these algorithms. However, we usually see that they are efficient.
Connect 4 is a simple game that can be easily programmed and solved to win every time. I have made in Python an AI that solves and wins. It is not programmed in C++ because I wanted a GUI.
N-Order Linear Systems
I have done a project for my math class where we analyze the linear systems. We have classified the first and second-order linear systems and give a general formula for an n-linear system. We have used algebra notation and we have encountered with the companion matrix power to the n problem.
The n-linear systems are used widely in finance for loans, interests, etc.
PDF download: N-LinearDynamicSystem
GitHub repository: DynamicSystem
