darkeclipz / calcupy

Calculus powered graphical calculator.

Hello, and welcome to my GitHub repository! 👋

I have lots of repositories with completed projects, uncompleted projects, proof-of-concepts, ideas, and course notes.

To make this a bit more navigatable, this is a list of my most interesting projects. Not all projects are finished, and actually, when is software really finished?

C#

• Wave function collapse demo
• Min-conflict CSP solver for N-Queens (N = 128)
• Prototype of a CSP solver that solves expressions
• Solving Sudoku as a CSP with Forward Propagation
• Physics Light 2D
• Google Proxy
• Simple CSP solver
• Procedural mesh editor in Unity
• Newtonian Physics in Unity
• Raytracing
• Graph Theory Algorithms
• Flappy Bird VR with Unity
• 2D Platform game with Unity
• Computing System with Logical Gates
• Maze generator with Kruskal's algorithm

Python

• Sudoku solver using OpenCV and a neural network for digit extraction
• Project Euler Problem Solving Library
• Funny graph theory problem
• Image to polygon
• Calcupy
• CSP solver
• Gradient descent
• Probability Analysis of Monopoly (Approximated)
• Probability Analysis of Monopoly (Analytical)
• Modeling endemic diseases with ODE's
• Strategy Backtesting for Algorithmic Trading
• Technical Analysis library for Algorithmic Trading

JavaScript/TypeScript

• Dungeon generation with Newton's law of gravitation
• Equirectangular to cubemap projection
• HTML5 TypeScript Template
• 3D L-systems
• Procedural generation
• 3D engine with Canvas
  • Simple perspective projection
• Binary search tree algorithm (BST)
• Convex hull algorithm

GLSL

My ShaderToy profile contain many more GLSL doodles.

• Fractal Shaders
• 2D Fractals

Machine Learning/Statistics

• Principle Component Analysis with R
• Applying PCA on a heart disease dataset with R (dutch)
• k-Means clustering

C++

• OpenGL game engine for learning C++/OpenGL
• Virtual Machine (CPU emulator) in C++
• CTF challenge - Reverse engineering
• Sudoku solver

Other

• Age of Empires II - AI

Other

• Blender
• 8K Fractals
• Sudoku solver in Delphi

Competitions

• Participated in Google Hash Code 2020 and got rank 366 out of 10,724 participants world wide and rank 6 out of 141 participants in The Netherlands, with a total score of 26,883,344.

calcupy's Issues

Parametric curves

Support for two and three dimensional parametric curves.

A paramatric curve can be recognized if the expression is a 2x1 or 3x1 matrix with a single variable.

Matrix shorthand notation

Parse [[1,2],[3,4]] to Matrix(...).

Degree matrix

The function that creates the degree matrix counts self-loops as 1 degree, this should be 2.

Extensions

• csp solver
• lp solver
• gradient descent (1+ var)
• graph theory
• mst
• tsp

Support for statistics

Add basic functionality for statistics. No support for categorical data.

If an expression is 1,2,3,4,5,6,7 it is a list X.
If an expression is [1,2,3,4], [5,6,7,8] it is a list of pairs X and Y.
If an expression is [1,2,3], [4,5,6], [7,8,9] is a list of pairs X, Y, and Z.

• Box plot (1, 2, or 3 boxplots)
• Scatter plots (2D/3D)
• Histogram (only for X)
• Summary (mean, sd, ...)
• Correlation between X and Y (or X~Y, X~Z, Y~Z)
• Linear regression
• Quad. regression
• Testing distributions (normal, exp, pois, ...)
• Other tests...

Step-by-step solutions

Add step-by-step solutions for some of the main functionality that is used from SymPy. Initially only for Algebra and Calculus operations.

Some information about extracting the steps from SymPy:

• https://stackoverflow.com/questions/39359220/is-there-any-way-to-get-the-step-by-step-solution-in-sympy
• https://sympygamma.com/input/?i=x%5E2+%2B+y%5E2

List generators

There should be a few functions that generate a list of elements.

See: https://stackoverflow.com/questions/27960965/parsing-an-equation-with-custom-functions-in-python

Possible generators are:

• Range(a,b,n,step)
• Random(a,b,n)
• Repeat(what, n)
• Normal(mean, sd, n)
• Exp(a, n)
• Poisson(lambda, n)
• Bin(pi, n)

Either the generator is expanded client-side (with javascript), but preferable the API should be able to evaluate custom functions. In the latter case, this also makes it possible to support other functions such as statistical distributions, e.g. InvNorm(0.95, mean, lambda), NormalCdf(-inf, 10, mean, sd), ...

Transformation plot of 2x2 matrices

Create an (animated?) plot that visualized the transformation of the 2x2 matrix.

Characteristic polynomial

For square matrices with 0? variables.

Action in does not reset

Repeatedly open graph info:

2x2 matrix

Directional derivatives

Support for directional derivatives. For functions of two variables.

1. Select point and a direction (angle, vector, or use gradient).
2. Draw a surface plot with the directional derivative.
3. Find the line and create a line plot.

Mobile friendly equations

Make it easier for mobile devices to enter equations.

Stable state of Markov matrices

Find the stable state of a Markov matrix.

Vector fields

Support for vector fields. Create a plot of the vector field.

Support for systems of equations

Solving systems of equations Ax=b. Syntax could be:

[2x+1, x+y, y] = [1,2,3]

Line plot of tan is weird

https://stackoverflow.com/questions/21204740/drawing-tangent-plot-in-python-matplotlib

Extremas

Find extremas (minima/maxima) of a function. For function with one or two variable(s).

• For functions with one variable, an interval should be defined for the global extrema.
• For functions with two variables, a region should be defined for the global extrema.
• Create a plot (line plot / contour plot) and mark the extremas.

Matrices

Add support for matrices.

• Gaussian elimination to solve the system.
• Find the transpose.
• Find the inverse.
• Find the determinant.
• Find the eigenvectors and eigenvalues.
• For 2x2 matrices: create a plot to show the transformation.
• Detection and methods for markov matrices?

Plot interval/region

Add the UI components to set the xlim and ylim for the plots.

Support for linear programming models

First do some research to see what solvers there are available, and how this should be implemented.

Integrate partials with respect to one variable

see title

Matrix heatmap

For 3x3 matrices and larger with no variables.

Support for graphs

Add support for graphs.

A graph G can be represented with an adjacency matrix of G. If the matrix is symmetrical the graph is undirected. If the coefficients of the matrix are only 0 or 1, then G is an unweighted graph.

Determine basic properties from Graph Theory:

• Degrees of G, diameter of G, connected components of G, Cycles, Bipartite, Eulerian cycles, semi-Eulerian cycles, Hamilton cycles, semi-Hamilton cycles, trees (MST), shortest path heuristic.
• Plotting can be with a spectral graph plot, or try to implement a visualization with GraphViz.

Gradient search procedure (optimization)

Implement a gradient search procedure which requires any function of 1 or more variables, and a starting point. Then find the local minima or maxima for that point with the gradient descent procedure.