Wassily Geometry

Advanced geometric operations and spatial data structures for generative art. This crate provides sophisticated tools for working with curves, grids, spatial data structures, and subdivision algorithms essential for creating complex geometric patterns and algorithmic art.

Key Features

Parametric Curves: Arc-length parameterized paths with interpolation and refinement
Spatial Data Structures: Efficient quadtree implementation for point queries
Subdivision Algorithms: Recursive quadrilateral and triangle subdivision with noise
Matrix Operations: Generic matrix with convolution, multiplication, and linear algebra
Specialized Lines: Artistic line effects including fade, sand, and stipple textures
Grid Systems: Structured point grids with quadrilateral extraction

Quick Start

use wassily_geometry::*;
use wassily_core::points::pt;

// Create a parametric curve
let points = vec![pt(0.0, 0.0), pt(100.0, 50.0), pt(200.0, 0.0)];
let curve = ParametricPath::new(points);
let midpoint = curve.point_at(0.5);  // Get point at 50% along curve

// Subdivision example
let quad = Quad::new(pt(0.0, 0.0), pt(0.0, 100.0), pt(100.0, 100.0), pt(100.0, 0.0));
let (left, right) = quad.split_v(0.3, 0.7);

// Quadtree for spatial queries
let mut qtree = QNode::new(vec![pt(10.0, 10.0), pt(90.0, 90.0)], pt(0.0, 0.0), pt(100.0, 100.0));
let nearby = qtree.points_in_circle(pt(0.0, 0.0), pt(100.0, 100.0), pt(50.0, 50.0), 25.0);

Core Components

Curves and Paths

[ParametricPath]: Arc-length parameterized curves with uniform sampling
[curve]: Generate smooth curves from mathematical functions
[refine]: Adaptive curve refinement for optimal approximation quality

Spatial Data Structures

[QNode]: Quadtree for efficient spatial queries and nearest neighbor searches
[Grid]: Structured point grids with quadrilateral mesh extraction

Subdivision Algorithms

[Quad]: Quadrilateral subdivision with customizable split strategies
[Tri]: Triangle subdivision for triangular mesh generation
[warp_points]: Noise-based point perturbation for organic distortion

Matrix and Linear Algebra

[Matrix]: Generic matrix operations including convolution and multiplication
Zero-indexed, row-major storage with comprehensive operation support

Artistic Line Effects

[FadeLine]: Lines with variable opacity subdivisions
[SandLine]: Textured lines with grain-like appearance
[DotLine]: Stippled lines with noise-based dot placement

Applications

Algorithmic Art: Recursive subdivision patterns and fractal-like structures
Mesh Generation: Quadrilateral and triangular mesh creation with organic distortion
Spatial Queries: Efficient point location and nearest neighbor operations
Curve Manipulation: Smooth interpolation and adaptive curve approximation
Pattern Generation: Grid-based patterns with artistic line rendering

Examples

Recursive Subdivision

use wassily_geometry::*;
use wassily_core::points::pt;

// Create initial quad
let quad = Quad::new(pt(0.0, 0.0), pt(0.0, 100.0), pt(100.0, 100.0), pt(100.0, 0.0));
let mut quads = vec![quad];

// Recursively subdivide
for _ in 0..5 {
    quads = quad_divide_vec(
        &quads,
        |q| q.best_dir(),           // Split along longest dimension
        |_| (0.4, 0.6),             // Split ratios
    );
}

Parametric Curve Interpolation

use wassily_geometry::*;
use wassily_core::points::pt;

// Define control points
let points = vec![
    pt(0.0, 50.0),
    pt(25.0, 100.0),
    pt(75.0, 0.0),
    pt(100.0, 50.0),
];

let path = ParametricPath::new(points);

// Sample points uniformly along curve length
let samples: Vec<_> = (0..=20)
    .map(|i| path.point_at(i as f32 / 20.0))
    .collect();

Spatial Indexing with Quadtree

use wassily_geometry::*;
use wassily_core::points::pt;

// Build quadtree with scattered points
let points = vec![
    pt(10.0, 10.0), pt(25.0, 80.0), pt(90.0, 30.0),
    pt(45.0, 45.0), pt(70.0, 15.0), pt(30.0, 90.0),
];

let qtree = QNode::new(points, pt(0.0, 0.0), pt(100.0, 100.0));

// Find all points within radius of query point
let query_center = pt(50.0, 50.0);
let radius = 30.0;
let nearby = qtree.points_in_circle(
    pt(0.0, 0.0), pt(100.0, 100.0),
    query_center, radius
);

wassily-geometry 0.2.0