dimforge/nalgebra

Features

• No-Std Mathematical Frameworks - Designed to run in resource-constrained embedded environments by eliminating dependencies on the Rust standard library.
• Linear Algebra Libraries - A comprehensive linear algebra library for Rust supporting both compile-time and runtime dimensions for matrices and vectors.
• 3D Graphics Pipelines - Calculates projections, rotations, and transformations for rendering 3D scenes and objects using Rust.
• Perspective Projections - Combines object orientation, camera position, and perspective projection to map 3D scenes.
• Embedded Mathematics Libraries - Provides a complete mathematical framework capable of running in embedded environments without the Rust standard library.
• Mathematical Frameworks - Offers a mathematical framework specifically designed to run in WebAssembly and embedded environments without the standard library.
• Generic Scalar Abstractions - Implements mathematical operations over generic types to support diverse numeric formats like floats and integers.
• Scalar Abstractions - Implements matrix and vector operations using generic types to support various floating-point and integer formats.
• No-Standard-Library Modes - Avoids dependencies on the standard library to enable execution in embedded systems and WebAssembly.
• Scientific & Mathematical Computing - Implements a comprehensive set of tools and methods for scientific research and numerical analysis.
• Algebraic Dimension Definitions - Creates matrices and vectors with dimensions specified at compile-time for performance or runtime for flexibility.
• Compile-Time Dimension Checking - Uses the type system to statically verify matrix and vector dimensions, preventing runtime shape mismatches.
• Coordinate Transformations - Implements mathematical operations to transform points and vectors between different 3D reference frames.
• Geometric Transformation Routines - Provides routines for applying linear transformations such as scaling, rotation, and projections to typed points and vectors.
• Rotation Calculators - Provides utilities to construct rotation matrices and unit quaternions from axis-angle or Euler angle representations.
• Numerical Libraries - Provides optimized algorithms for matrix operations and a wide variety of numerical decompositions.
• Compressed Sparse Storage - Supports large-scale datasets using compressed sparse row and column formats to optimize memory usage.
• Vector Operations - Provides fundamental mathematical primitives for performing operations on vectors and matrices.
• Homogeneous Transformation Utilities - Uses four-by-four matrices to unify translations and rotations into single transformation operations.
• Object Transformation Matrices - Applies scaling, rotation, and translation to 3D objects using isometry types or homogeneous matrices.
• Array View Creation - Provides non-owning references to submatrices, rows, or columns using strides for non-consecutive elements.
• Strided - Provides non-owning references to matrix sub-sections using memory offsets to avoid data copying.
• Game Development Engines - Provides the spatial transformation and camera matrix logic essential for building game development engines.
• Graphics API Data Export - Converts matrices and vectors into column-major arrays or raw pointers for compatibility with graphics APIs.
• Orthographic Projections - Implements orthographic projection matrices to render 3D scenes without perspective distortion.
• Ray-Casting Picking Logic - Converts 2D screen-space coordinates back into 3D view-space lines for ray casting and object picking.
• Algebraic Dispatch - Uses generic traits to provide a consistent interface for different matrix decompositions and linear solvers.
• WebAssembly - Supports execution in browser environments by providing a WebAssembly-compatible compilation target.
• Algebraic Type Conversions - Provides mechanisms to transform data between different matrix and vector types and scaling precisions.
• Cholesky Decomposition Utilities - Decomposes Hermitian positive-definite matrices into lower-triangular factors for solving linear systems.
• Geometric Point Representations - Defines points as distinct entities from vectors to correctly support translation and displacement operations.
• Isometry Computations - Combines rotations and translations into isometries to preserve distance and orientation for objects and cameras.
• Eigendecomposition Routines - Computes eigenvalues and eigenvectors of square matrices through eigendecomposition.
• Similarity Transformations - Implements uniform scaling combined with rotation and translation to preserve angles and parallel lines.
• Linear System Solvers - Provides direct linear solvers and eigen-solvers to find solutions for systems of linear equations.
• Matrix and Vector Construction - Constructs matrices using row slices, iterators, closures, identity patterns, or random values.
• Matrix Component Accessors - Updates individual components or entire rows and columns within a mutable matrix.
• Matrix Decompositions - Factors rectangular matrices into singular values and vectors to determine matrix rank and pseudo-inverses.
• LU Decompositions - Factors matrices into lower and upper triangular components to compute determinants and solve linear systems.
• QR Decompositions - Decomposes general matrices into unitary and upper triangular matrices to facilitate the computation of inverses.
• Matrix Resizing - Adds or removes rows and columns from a matrix using fixed-size or dynamic-size adjustments.
• Sparse Matrix Storage - Provides memory-efficient data structures that store only non-zero elements for large datasets.
• Unit-Norm Type Wrapping - Wraps vectors and quaternions in specific types to guarantee a magnitude of one through the type system.
• View Matrix Calculators - Provides utilities for calculating camera view matrices based on position and orientation for 3D scenes.

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