zalo/MathUtilities
MathUtilities
MathUtilities es una colección de kits de herramientas especializados que proporcionan motores para geometría, visión artificial, matemáticas, simulación física y procesamiento de señales. Funciona como una biblioteca integral de matemáticas y física centrada en álgebra lineal, optimización numérica y cálculos geométricos para aplicaciones técnicas.
El proyecto se distingue por un kit de herramientas de simulación física y un motor de geometría 3D. Estos proporcionan capacidades para la integración de Verlet, solucionadores de cinemática inversa iterativos, renderizado de campos de distancia mediante raymarching volumétrico y deformación de geometría de malla. También incluye una utilidad de visión artificial para estimar el movimiento relativo de la cámara y generar proyecciones de ojo de pez.
La biblioteca cubre áreas de capacidad amplias, incluyendo sistemas de detección de colisiones utilizando diferencias de Minkowski y hashing espacial, planificación de movimiento robótico y procesamiento de señales para reducción de ruido utilizando filtros de Kalman. La funcionalidad adicional incluye optimización de datos numéricos, operaciones de álgebra lineal para ajuste de conjuntos de puntos y serialización JSON basada en reflexión para jerarquías de objetos.
Features
- 3D Geometry Engines - Provides a comprehensive core for processing 3D geometric data, including mesh deformation and volumetric raymarching.
- Mathematical Libraries and Utilities - Implements fundamental algorithms for linear algebra, numerical optimization, and geometric calculations in a comprehensive utility library.
- Computer Vision Libraries - Provides a comprehensive library for computer vision tasks including camera motion estimation and fisheye projections.
- Computer Vision and Image Processing - Provides utilities for estimating relative camera motion and generating wide fisheye projections from image sources.
- Verlet Integration - Simulates soft and rigid bodies by calculating positions based on previous state and acceleration via Verlet integration.
- Collision Detection - Implements collision detection systems using Minkowski differences and spatial hashing to handle object intersections.
- Physics Simulation Toolkits - Ships a suite of utilities for Verlet integration, rigid body dynamics, and inverse kinematics.
- Soft Body Simulations - Uses Verlet integration to simulate cloth, particle chains, and soft or rigid bodies.
- 3D Mesh Manipulation - Provides tools for creating and warping complex 3D shapes, including solid meshes and flexible deformations.
- Mesh Deformations - Transforms 3D meshes by blending rigid motion with flexible deformation based on configurable ductility and weights.
- Inverse Kinematics - Provides an iterative solver to determine joint configurations for limbs based on distance and rotation constraints.
- Motion Planning Toolkits - Calculates optimal paths and solves inverse kinematics for robotic movement between specific coordinates.
- Signal Processing - Provides algorithms for signal processing, specifically Kalman filters and smoothing splines for noise reduction.
- Geometric Point-Set Fitting - The product solves for the orthogonal lines and planes of best fit for 3D point-sets using matrix-less formulation.
- Linear Algebra Routines - Executes fundamental linear algebra tasks including multiplication, inversion, and Cholesky decomposition.
- Minkowski Difference Intersections - Determines if two shapes overlap by calculating the Minkowski difference to find minimum translation vectors for separation.
- Numerical Data Optimization - Filters noisy sensor data with Kalman filters and minimizes complex cost functions using numerical methods.
- Numerical Function Optimization - Implements the Nelder-Mead simplex-based search to minimize n-dimensional cost functions without requiring derivatives.
- Spatial Hashing - Maps 3D coordinates to a discrete grid to find neighboring objects in constant time for collision detection.
- Kalman Filter Implementations - Fuses information from multiple sources using a Kalman filter to produce a clean real-time signal.
- Stereographic Projections - Concatenates and warps images from multiple cameras into a single 180-degree stereographic projection.
- Soft Body Physics - Simulates deformable objects and cloth using Verlet integration and particle-based dynamics.
- Mesh Generators - Programmatically creates thick tessellated planes and capsules to build complex volumetric geometry.
- Relative Camera - Solves for the relative motion between two images by tracking the movement of feature points.
- Trajectory Interpolation - Implements a rigid-as-possible blossoming interpolation scheme to create smooth paths between discrete trajectory segments.
- Raymarching Renderers - Renders volumetric surfaces by stepping along a ray until a predefined distance threshold is hit.
- Minkowski Difference Intersections - Calculates the Minkowski Difference between shapes to determine intersection and minimum translation for separation.
- Spline Interpolators - Produces a continuous smoothing spline for 6 DoF data using a sliding window weighted average.
- Time-Optimal Movement Control - Computes the most efficient movement trajectory for a double-integrating mass with limited thrust.
