zalo/MathUtilities

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.

Star history