Projects sharing features with MathUtilities

Rapier is a cross-platform physics engine and rigid body dynamics solver designed for 2D and 3D simulations. It functions as a collision detection system and a robotics simulation framework, providing a consistent API for calculating physical interactions across different environments. The engine distinguishes itself with specialized robotics capabilities, including a toolkit for importing URDF and STL models to control multibody chains. It supports precise mechanical movement through inverse kinematics calculations and the application of PID controllers for dynamic body control. The simulat

Matter-js is a 2D rigid body physics engine written in JavaScript for simulating realistic physical interactions, collisions, and dynamics in web browsers. It functions as a web physics simulation library that calculates motion, gravity, and constraints for objects rendered on a web canvas. The library includes a built-in canvas physics visualizer to draw physical bodies, joints, and constraints for debugging and gameplay. It distinguishes itself through a plugin system that supports recursive dependency resolution and internal method patching to inject custom logic into the engine's executio

LiquidFun is a 2D physics engine and game physics framework designed to calculate movement and collisions for rigid bodies and particle systems. It functions as a simulation tool for integrating real-time physical interactions and dynamics into interactive applications. The framework specifically provides a particle-based fluid simulator to model liquid dynamics, including splashing, displacement, and surface tension. It also includes a soft body physics simulator for creating deformable and elastic objects that react to physical forces. The engine covers a broad range of physical interactio

Newton is a GPU-accelerated physics engine and robotics simulation platform designed for high-performance modeling of rigid bodies and complex articulations. It functions as a differentiable physics engine, calculating gradients to enable mathematical optimization and machine learning. The platform is distinguished by its ability to execute multiple parallel physics worlds on a single GPU, which accelerates data collection for reinforcement learning. It also supports the simulation of deformable bodies, such as cloth and cables, using particle-based methods and multi-physics coupling. Newton

This library is a JavaScript-based numerical analysis tool designed to perform complex mathematical operations directly within web browser environments. It provides a comprehensive suite of algorithms for linear algebra, matrix manipulation, and equation solving, enabling data-intensive computations to occur locally without requiring server-side processing. The project distinguishes itself by offering a specialized computational engine that handles advanced mathematical tasks such as gradient-based function optimization and iterative numerical approximation. By utilizing quadrature-based inte

LibGDX is a Java-based framework designed for cross-platform game development, enabling the creation and deployment of 2D and 3D games across desktop, mobile, and web environments from a single codebase. It functions as a comprehensive library that abstracts hardware-accelerated graphics, audio, input, and file system access, providing a unified interface for developers to manage game logic and application lifecycles. The framework distinguishes itself through a high-performance architecture that prioritizes efficiency and native interoperability. It utilizes a batch-oriented graphics pipelin

This repository is a comprehensive collection of functional 2D and 3D demo projects and implementation samples for the Godot Game Engine. It serves as an interactive tutorial and reference library, providing a working codebase to demonstrate how to apply engine features in real-world scenarios. The collection focuses on practical implementation guides, covering a wide array of technical capabilities from basic engine fundamentals to advanced rendering and scripting techniques. It allows users to study the application of node-based composition, asset pipelines, and game logic through direct ex

ammo.js is a JavaScript port of the Bullet physics engine, compiled via Emscripten to provide a high-performance physics library for the browser. It functions as a 3D rigid body engine and an Emscripten compiled library that enables complex physical computations using WebAssembly and JavaScript. The project provides specialized simulation capabilities for soft body physics, modeling the deformation of flexible materials like cloth and rubber, and a vehicle dynamics engine for calculating the mechanics of wheeled vehicles. The simulation surface also covers rigid body dynamics for non-deforma

This project is a scientific computing framework for the .NET ecosystem, providing a comprehensive suite of libraries for numerical analysis, statistics, and mathematical optimization. It serves as a foundational toolkit for developing applications in machine learning, digital signal processing, and computer vision. The framework provides specialized toolkits for training and deploying predictive models, including neural networks, support vector machines, and decision trees. It further distinguishes itself with deep integrations for real-time visual analysis, such as object tracking and facia

Fornjot is a CAD modeling kernel and 3D geometry engine designed for the creation and manipulation of precise mechanical shapes. It functions as a B-Rep 3D modeling kernel, using boundary representation to define the shapes and topologies of three-dimensional models. The project provides a B-Rep geometry visualizer to render 3D models in a windowed environment for visual verification. It also includes a pipeline to export internal geometric representations into external data formats for compatibility with other software. The engine covers geometric modeling through primitive-based constructi

This project is a Java-based toolkit that integrates the OpenCV computer vision library into the Processing creative coding environment. It provides a programming interface designed to facilitate the inclusion of real-time image analysis and computer vision algorithms within interactive art installations and visual design projects. The library distinguishes itself by wrapping low-level C++ routines into a managed environment, allowing users to perform complex visual tasks through a simplified interface. It supports high-performance operations by sharing raw pixel data between the host environ

This project is an educational resource and toolkit for implementing Bayesian estimation and Kalman filters in Python. It provides a framework for constructing linear and non-linear filters to estimate the state of dynamic systems by combining noisy sensor data with mathematical process models. The library focuses on probabilistic state estimation, utilizing recursive Bayesian updating and state-space mathematical modeling to refine beliefs about system states. It includes utilities for simulating dynamic systems, allowing users to generate synthetic trajectories and sensor observations to va

filterpy is a toolkit for Bayesian state estimation, Gaussian statistical analysis, and time-series noise reduction. It provides a library of linear and non-linear Kalman filters, as well as routines for non-Gaussian state estimation and signal smoothing. The project implements a variety of estimation methods, including particle filtering using Markov Chain Monte Carlo and resampling, and discrete Bayes filtering. It also includes a suite of algorithms for refining historical state estimates through backward and fixed-lag smoothing. Additional capabilities cover multivariate Gaussian analysi

This project is a collection of optional, community-contributed algorithms and specialized vision tools that extend the core OpenCV framework. It serves as a comprehensive library of extra modules for computer vision research, providing advanced toolsets for image processing, visual data analysis, and object detection. The library includes specialized frameworks for augmented reality tracking, biometric face recognition, and three-dimensional pose estimation. It provides distinct capabilities for identifying AR markers, tracking 3D object silhouettes, and performing neural network vulnerabili

GoCV is a computer vision library and Go language binding for OpenCV. It serves as an image processing toolkit and deep learning inference engine, providing programmatic access to a wide range of algorithms for image manipulation, object detection, and video analysis. The project differentiates itself through high-performance native bindings and hardware acceleration. It utilizes a foreign function interface to map Go calls to C++ functions and includes a hardware-agnostic backend dispatch to route neural network tasks to computation engines such as CUDA and OpenVINO. The library covers a br

This project is a Python wrapper for the OpenCV computer vision library, providing a bridge that exposes high-performance C++ functions to the Python programming language. It serves as a collection of tools for real-time image processing, object detection, and machine learning on visual data. The project provides precompiled binary distributions, allowing for the integration of vision capabilities into Python applications without requiring a local C++ compiler. It offers multi-variant package distributions, including headless versions designed for server or cloud environments where a graphica

JavaCV provides a Java-based interface for native computer vision and video processing libraries. It functions as a wrapper for native vision libraries, allowing Java applications to perform image analysis, object detection, and video stream processing. The project integrates comprehensive computer vision capabilities, including facial recognition, image segmentation, and optical flow analysis for motion tracking. It also provides tools for hardware geometry calibration and projector-camera alignment to ensure accurate spatial representation. The system covers high-performance media renderin

This project is a collection of neural network models and geometric tools designed for image feature matching, spatial alignment, and visual localization. It provides a pre-trained neural network model for identifying high-accuracy correspondences between sparse image features without requiring local training. The system utilizes a graph neural network matcher that employs attention mechanisms and message passing to learn spatial relationships between image feature points. It integrates a RANSAC camera pose estimator to filter feature matches and calculate the relative spatial transformation

Box2D is a 2D physics engine and rigid body simulator designed to compute collisions, forces, and joints in a two-dimensional plane. It functions as a collision detection library and a constraint-based physics solver that calculates the movement and interaction of solid objects using mass, friction, and restitution properties. The engine ensures consistency across different hardware architectures through a deterministic trigonometry implementation. It prevents high-speed objects from passing through boundaries using continuous collision detection and time-of-impact interpolation. The system

opencv4nodejs is a set of JavaScript wrappers and a C++ native addon that provides Node.js bindings for the OpenCV library. It functions as a computer vision library and image processing framework, exposing high-performance C++ algorithms to a JavaScript environment. The project enables the execution of vision algorithms for detecting faces, tracking objects, and analyzing visual data using deep neural networks. It includes capabilities for data pattern classification, text pattern recognition, and the identification of facial landmarks and gestures. The framework covers a broad capability s

Kornia is a differentiable computer vision library and cross-framework tensor vision toolset. It implements vision operations as differentiable tensors to enable integration into deep learning pipelines and supports the transpilation of operations across PyTorch, TensorFlow, JAX, and NumPy. The project provides specialized toolsets for geometric vision and stereo depth, including algorithms for 3D scene reconstruction, camera calibration, and pose estimation. It further distinguishes itself as a differentiable image augmentation framework, applying random geometric and color transformations w

node-opencv is a high-performance C++ native addon and bridge that connects Node.js applications to the OpenCV library. It serves as an image processing toolkit and computer vision library, allowing JavaScript code to execute vision algorithms and image manipulation operations through native bindings. The project provides specialized capabilities for face and shape detection, as well as face identity recognition using trained models. It includes tools for object motion tracking through optical flow and background subtraction, along with the ability to identify specific patterns and analyze sh

COLMAP is a 3D scene reconstruction suite and C++ geometry library that implements a full structure-from-motion pipeline. It functions as a GPU-accelerated photogrammetry tool and multi-view stereo framework designed to produce dense 3D geometry and watertight meshes from collections of 2D images. The project distinguishes itself through hardware-accelerated feature extraction and a modular camera modeling system that supports perspective, fisheye, and equirectangular lens types. It employs vocabulary tree image retrieval to efficiently identify similar images in large datasets and provides P

OpenCV is an open-source computer vision library and visual analysis toolkit. It provides a framework for processing static images and dynamic video frames to analyze visual data and extract information using deep learning. The project functions as a real-time image processing framework, enabling the execution of vision algorithms on live video streams for immediate analysis and data processing. The toolkit covers a broad range of capabilities including image pattern recognition, real-time video analysis, and visual data extraction. It also supports automated visual inspection for detecting

OR-Tools is a software suite for combinatorial optimization, constraint programming, and mathematical modeling. It provides a framework for defining complex problems involving variables and logical constraints, enabling the systematic search for feasible or optimal solutions. The project features a high-performance core engine written in C++ that utilizes branch and bound search and local search metaheuristics to navigate large solution spaces. A language-agnostic wrapper layer allows these optimization capabilities to be accessed through idiomatic interfaces in multiple high-level programmin

PaddleDetection is an object detection framework designed for the end-to-end development, training, and deployment of computer vision models. It provides a comprehensive library of modular neural network architectures and pipelines that support object detection, instance segmentation, and multi-object tracking tasks. The project distinguishes itself through a configuration-driven approach that decouples model components like backbones and heads, allowing for the flexible assembly of custom vision workflows. It incorporates advanced techniques such as anchor-free detection logic, joint detecti

This project is a comprehensive software framework for autonomous robot navigation, providing a collection of algorithms for path planning, motion control, and trajectory generation. It serves as a toolkit for implementing and researching navigation logic, enabling the calculation of collision-free routes and the execution of precise movement commands for autonomous mobile agents. The library distinguishes itself by integrating both global pathfinding and real-time reactive control strategies. It supports diverse planning methodologies, including graph-based heuristic searches and sampling-ba