Below is the list of algorithms and mathematical concepts involved, from fundamental vector geometry to state-of-the-art neural networks in software development with vector mathematics:
- Bezier Polynomials (Quadratic and Cubic): The mathematical foundation for generating smooth SVG paths using control points.
- Casteljau Algorithm: A recursive method used for curve subdivision and robust geometric construction.
- Affine Transformations: 3x3 matrix operations enabling translation, rotation, scaling, and skewing of objects.
- Curve Tessellation: Adaptive subdivision algorithms converting smooth parametric curves into discrete pixel segments.
- Spiro Splines: Used in Inkscape to create curves that minimize curvature variation through clothoid segments.
- Boolean Operations (Union, Intersection, Difference, XOR): Based on computational geometry for combining complex shapes.
- Bentley–Ottmann Algorithm: Used to detect line‑segment intersections during boolean path operations.
- Winding Number Calculation: Determines whether a point lies inside or outside a path.
- Arc‑Length Parameterization: Essential for placing text on a path and for uniform motion animations.
- Potrace Algorithm: Converts bitmap images into vector paths through decomposition, polygon optimization, and least‑squares curve fitting.
- Sobel Operator: Edge‑detection algorithm computing gradient magnitude and direction in raster images.
- Ramer–Douglas–Peucker Algorithm: Simplifies paths by reducing intermediate points while preserving shape fidelity.
- Schneider Algorithm: Optimizes Bézier curve fitting using Newton–Raphson iteration.
- DeepSVG (Hierarchical Generative Networks): Enables vector graphics reconstruction and animation through latent‑space operations.
- SVGformer (Transformer Architectures): Captures complex patterns and dependencies in large SVG datasets.
- GANs (Generative Adversarial Networks): Produce professional vector outputs through adversarial training.
- CVAEs (Convolutional Variational Autoencoders): Learn to encode and decode graphic data such as fonts or icons into latent spaces.
- L‑Systems (Lindenmayer Systems): Use formal grammar rules and recursion to generate organic shapes.
- Perlin Noise: Produces mathematically controlled random variations for organic patterns.
- Verlet Integration: Used in force‑based simulations (Coulomb attraction, Hooke elasticity) for data visualization.
- Convolution Mathematics: Implements SVG filters (such as Gaussian Blur) using discrete convolution matrices.
