AdvancedMath is a modern C++ library for advanced mathematical computations, providing convenient and efficient tools for working with complex numbers, linear algebra, mathematical analysis, and computational geometry.
· Complex numbers (algebraic + trigonometric forms) · Affine transformations · Homothety transformations · High-performance operations
· Matrices and Linear Algebra - matrix operations, determinants, inverse matrices · Mathematical Analysis - numerical integration, differentiation · Computational Geometry - barycentric coordinates, geometric transformations · Additional Mathematical Structures - quaternions, tensors
- Dual Representation: Algebraic form (
Complex) and trigonometric form (ComplexTrigonometric) - High Performance: Optimized operations for each representation
- Full Arithmetic: All basic operations (+, -, *, /) with operator overloading
- Mathematical Functions: Magnitude, phase, conjugate, roots, exponentiation
- Seamless Conversion: Easy switching between representations
- Affine Transformations: Translation, rotation, scaling, shearing
- Homothety: Scaling transformations with custom centers
- Composition: Combine multiple transformations
- Inverse Operations: Compute reverse transformations
- Efficient Application: Apply to both algebraic and trigonometric forms
- Trigonometric Form: O(1) multiplication, division, exponentiation
- Matrix Operations: Efficient affine transformation composition
- Minimal Overhead: Optimized for scientific computing
- Dual Representation: Choose the best form for your use case
· Pure C++17 - modern language features · Template-based design - support for various numeric types · High performance - minimal overhead, optimized operations · Dual representation - choose the best form for your use case · Header-only (planned) - easy integration into projects · Fully documented code - clear API · Mathematical constants - built-in support for π and other constants
· Create a universal mathematical library for scientific computations · Provide intuitive API for complex mathematical operations · Ensure high performance for resource-intensive calculations · Support multiple mathematical representations · Become a useful tool for students, researchers, and developers · Optimize operations by choosing the most efficient representation
The trigonometric form is particularly useful for:
The trigonometric form is particularly useful for: ·Signal processing: working with phases and amplitudes ·Electrical engineering: AC circuit analysis ·Physics: wave functions and oscillations ·Computer graphics: rotations and transformations ·Control systems: frequency domain analysis
Homothety transformations are essential for: ·Computer graphics: image scaling and zoom operations ·Geometric modeling: shape transformation and morphing ·Fractal geometry: self-similar transformations ·Computer vision: perspective corrections ·Game development: camera zoom and scaling effects