iOverlay

iOverlay is a high-performance polygon overlay engine for Rust. It solves robust boolean operations on complex polygons for GIS, CAD, and graphics workflows, built for developers who need reliable geometry at scale across integer and floating-point APIs.

iOverlay powers polygon boolean operations in geo.

Why iOverlay?

Built for robust polygon overlays where precision matters (GIS, CAD, graphics).
High performance with predictable results across complex inputs.
Supports both integer and floating-point APIs for flexible pipelines.
OGC-valid output is available when strict topology is required.
Core overlay engine used in geo.

Features

Boolean Operations: union, intersection, difference, and exclusion.
Spatial Predicates: intersects, disjoint, interiors_intersect, touches, within, covers with early-exit optimization.
Polyline Operations: clip and slice.
Polygons: with holes, self-intersections, and multiple contours.
Simplification: removes degenerate vertices and merges collinear edges.
Buffering: offsets paths and polygons.
Fill Rules: even-odd, non-zero, positive and negative.
Data Types: Supports i16/i32/i64 integer APIs and f32/f64 floating-point APIs.

Demo

Performance

iOverlay supports:

i16/i32/i64 math solvers
on/off multithreading feature

For bigger data sets, the math engine and multithreading mode have a larger impact on runtime.

See the detailed reports: Performance Comparison and Rust Solver Benchmarks

Getting Started

Add the following to your Cargo.toml:

[dependencies]
i_overlay = "^7.0"

Read full documentation

Quick Start

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::single::SingleFloatOverlay;

let subj = [[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0]];
let clip = [[2.0, 2.0], [6.0, 2.0], [6.0, 6.0], [2.0, 6.0]];

let result = subj.overlay(&clip, OverlayRule::Intersect, FillRule::EvenOdd);
println!("result: {:?}", result);

Boolean Operations

Simple Example

Here's an example of performing a union operation between two polygons:

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::single::SingleFloatOverlay;

// Define the subject "O"
let subj = [
    // main contour
    vec![
      [1.0, 0.0],
      [4.0, 0.0],
      [4.0, 5.0],
      [1.0, 5.0], // the contour is auto closed!
    ],
    // hole contour
    vec![
      [2.0, 1.0],
      [2.0, 4.0],
      [3.0, 4.0],
      [3.0, 1.0], // the contour is auto closed!
    ],
];

// Define the clip "-"
let clip = [
    // main contour
    [0.0, 2.0],
    [5.0, 2.0],
    [5.0, 3.0],
    [0.0, 3.0], // the contour is auto closed!
];

let result = subj.overlay(&clip, OverlayRule::Union, FillRule::EvenOdd);

println!("result: {:?}", result);

The result is a vec of shapes:

[
    // first shape
    [
        // main contour (counterclockwise order)
        [
            [0.0, 3.0], [0.0, 2.0], [1.0, 2.0], [1.0, 0.0], [4.0, 0.0], [4.0, 2.0], [5.0, 2.0], [5.0, 3.0], [4.0, 3.0], [4.0, 5.0], [1.0, 5.0], [1.0, 3.0]
        ],
        // first hole (clockwise order)
        [
            [2.0, 1.0], [2.0, 2.0], [3.0, 2.0], [3.0, 1.0]
        ],
        // second hole (clockwise order)
        [
            [2.0, 3.0], [2.0, 4.0], [3.0, 4.0], [3.0, 3.0]
        ]
    ]
    // ... other shapes if present
]

The overlay function returns a Vec<Shapes>:

Vec<Shape>: A collection of shapes.
Shape: Represents a shape made up of:
- Vec<Contour>: A list of contours.
- The first contour is the outer boundary (counterclockwise), and subsequent contours represent holes (clockwise).
Contour: A sequence of points (Vec<P: FloatPointCompatible>) forming a closed contour.

Note: By default, outer boundaries are counterclockwise and holes are clockwise—unless main_direction is set. More information about contours.

Overlay Rules

A,B	A ∪ B	A ∩ B	A - B	B - A	A ⊕ B

Edge Attributes and Provenance

Use EdgeOverlay when the result boundary needs to keep data from the original input edges: source ids, layer ids, material ids, constraints, styles, or any other edge provenance. The regular Overlay API remains optimized for plain geometry; this API is opt-in and works with user-defined payloads.

When an input edge is split by intersections, its data is copied by default. When coincident edges are merged, your OverlayEdgeData implementation decides what the resulting data means. A common policy is to keep identical values and mark conflicts as Undefined.

use i_overlay::core::edge_data::{EdgeDataMerge, OverlayEdgeData};
use i_overlay::core::edge_overlay::{EdgeOverlay, InputEdge};
use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay::ShapeType;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::i_float::int::point::IntPoint;
use i_overlay::segm::boolean::ShapeCountBoolean;

#[derive(Clone, Copy, Debug, PartialEq, Eq)]
enum EdgeKind {
    Red,
    Green,
    Undefined,
}

impl OverlayEdgeData for EdgeKind {
    fn merge(ctx: EdgeDataMerge<ShapeCountBoolean, Self>) -> Self {
        match (ctx.lhs_data, ctx.rhs_data) {
            (EdgeKind::Red, EdgeKind::Red) => EdgeKind::Red,
            (EdgeKind::Green, EdgeKind::Green) => EdgeKind::Green,
            _ => EdgeKind::Undefined,
        }
    }
}

let mut overlay = EdgeOverlay::new(8);

let red_square = [
    [0, 0], [4, 0], [4, 4], [0, 4],
];
let green_square = [
    [2, 0], [6, 0], [6, 4], [2, 4],
];

for edge in red_square.windows(2).map(|w| (w[0], w[1]))
    .chain([(red_square[3], red_square[0])])
{
    overlay.add_edge(InputEdge {
        a: IntPoint::new(edge.0[0], edge.0[1]),
        b: IntPoint::new(edge.1[0], edge.1[1]),
        data: EdgeKind::Red,
    }, ShapeType::Subject);
}

for edge in green_square.windows(2).map(|w| (w[0], w[1]))
    .chain([(green_square[3], green_square[0])])
{
    overlay.add_edge(InputEdge {
        a: IntPoint::new(edge.0[0], edge.0[1]),
        b: IntPoint::new(edge.1[0], edge.1[1]),
        data: EdgeKind::Green,
    }, ShapeType::Clip);
}

let shapes = overlay.build_vector_shapes(OverlayRule::Union, FillRule::NonZero);

// The result is grouped as shapes -> contours -> edges.
// Each output edge contains geometry, fill, and the propagated user data.
assert_eq!(shapes.len(), 1);
assert!(shapes[0][0].iter().any(|edge| edge.data == EdgeKind::Undefined));

This API currently targets integer boolean operations and exports the result as vector shapes. It keeps the same contour structure as the regular polygon API, but each contour item is an edge with propagated data. Collinear edges are simplified only when their data is equal, so attribute boundaries are preserved.

Spatial Predicates

When you only need to know whether two shapes have a spatial relationship—not compute their intersection geometry—use spatial predicates for better performance:

use i_overlay::float::relate::FloatRelate;

let outer = vec![[0.0, 0.0], [0.0, 20.0], [20.0, 20.0], [20.0, 0.0]];
let inner = vec![[5.0, 5.0], [5.0, 15.0], [15.0, 15.0], [15.0, 5.0]];
let adjacent = vec![[20.0, 0.0], [20.0, 10.0], [30.0, 10.0], [30.0, 0.0]];
let distant = vec![[100.0, 100.0], [100.0, 110.0], [110.0, 110.0], [110.0, 100.0]];

// intersects: shapes share any point (interior or boundary)
assert!(outer.intersects(&inner));
assert!(outer.intersects(&adjacent));  // edge contact counts

// disjoint: shapes share no points (negation of intersects)
assert!(outer.disjoint(&distant));

// interiors_intersect: interiors overlap (stricter than intersects)
assert!(outer.interiors_intersect(&inner));
assert!(!outer.interiors_intersect(&adjacent));  // edge-only contact

// touches: boundaries intersect but interiors don't
assert!(outer.touches(&adjacent));
assert!(!outer.touches(&inner));  // interiors overlap

// within: first shape completely inside second
assert!(inner.within(&outer));
assert!(!outer.within(&inner));

// covers: first shape completely contains second
assert!(outer.covers(&inner));
assert!(!inner.covers(&outer));

These methods use early-exit optimization, returning as soon as the predicate can be determined without processing remaining segments.

Fixed-Scale Predicates

For consistent precision across operations, use FixedScaleFloatRelate:

use i_overlay::float::scale::FixedScaleFloatRelate;

let square = vec![[0.0, 0.0], [0.0, 10.0], [10.0, 10.0], [10.0, 0.0]];
let other = vec![[5.0, 5.0], [5.0, 15.0], [15.0, 15.0], [15.0, 5.0]];

let scale = 1000.0;  // or 1.0 / grid_size

let result = square.intersects_with_fixed_scale(&other, scale);
assert!(result.unwrap());

For more control, use FloatPredicateOverlay directly:

use i_overlay::float::relate::FloatPredicateOverlay;

let square = vec![[0.0, 0.0], [0.0, 10.0], [10.0, 10.0], [10.0, 0.0]];
let clip = vec![[5.0, 5.0], [5.0, 15.0], [15.0, 15.0], [15.0, 5.0]];

// Use fixed-scale constructor
let mut overlay = FloatPredicateOverlay::with_subj_and_clip_fixed_scale(
    &square, &clip, 1000.0
).unwrap();

assert!(overlay.intersects());

Custom Point Type Support

iOverlay allows users to define custom point types, as long as they implement the FloatPointCompatible trait.

use i_overlay::i_float::float::compatible::FloatPointCompatible;
use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::single::SingleFloatOverlay;

#[derive(Clone, Copy, Debug)]
struct CustomPoint {
  x: f32,
  y: f32,
}

impl FloatPointCompatible for CustomPoint {
  type Scalar = f32;

  fn from_xy(x: f32, y: f32) -> Self {
    Self { x, y }
  }

  fn x(&self) -> f32 {
    self.x
  }

  fn y(&self) -> f32 {
    self.y
  }
}

let subj = [
    CustomPoint { x: 0.0, y: 0.0 },
    CustomPoint { x: 0.0, y: 3.0 },
    CustomPoint { x: 3.0, y: 3.0 },
    CustomPoint { x: 3.0, y: 0.0 },
];

let clip = [
    CustomPoint { x: 1.0, y: 1.0 },
    CustomPoint { x: 1.0, y: 2.0 },
    CustomPoint { x: 2.0, y: 2.0 },
    CustomPoint { x: 2.0, y: 1.0 },
];

let result = subj.overlay(&clip, OverlayRule::Difference, FillRule::EvenOdd);

println!("result: {:?}", result);

Slicing & Clipping

Slicing a Polygon with a Polyline

use i_overlay::core::fill_rule::FillRule;
use i_overlay::float::slice::FloatSlice;

let polygon = [
    [1.0, 1.0],
    [1.0, 4.0],
    [4.0, 4.0],
    [4.0, 1.0],
];

let slicing_line = [
    [3.0, 5.0],
    [2.0, 2.0],
    [3.0, 3.0],
    [2.0, 0.0],
];

let result = polygon.slice_by(&slicing_line, FillRule::NonZero);

println!("result: {:?}", result);

Clipping a Polyline by a Polygon

use i_overlay::core::fill_rule::FillRule;
use i_overlay::float::clip::FloatClip;
use i_overlay::string::clip::ClipRule;

let polygon = [
    [1.0, 1.0],
    [1.0, 4.0],
    [4.0, 4.0],
    [4.0, 1.0],
];

let string_line = [
    [3.0, 5.0],
    [2.0, 2.0],
    [3.0, 3.0],
    [2.0, 0.0],
];

let clip_rule = ClipRule { invert: false, boundary_included: false };
let result = string_line.clip_by(&polygon, FillRule::NonZero, clip_rule);

println!("result: {:?}", result);

Buffering

Offsetting a Path

use i_overlay::mesh::stroke::offset::StrokeOffset;
use i_overlay::mesh::style::{LineCap, LineJoin, StrokeStyle};

let path = [
    [ 2.0, 1.0],
    [ 5.0, 1.0],
    [ 8.0, 4.0],
    [11.0, 4.0],
    [11.0, 1.0],
    [ 8.0, 1.0],
    [ 5.0, 4.0],
    [ 2.0, 4.0],
];

let style = StrokeStyle::new(1.0)
    .line_join(LineJoin::Miter(1.0))
    .start_cap(LineCap::Round(0.1))
    .end_cap(LineCap::Square);

let shapes = path.stroke(style, false);

println!("result: {:?}", shapes);

Offsetting a Polygon

use i_overlay::mesh::outline::offset::OutlineOffset;
use i_overlay::mesh::style::{LineJoin, OutlineStyle};

let shape = vec![
    vec![
        [2.0, 1.0],
        [4.0, 1.0],
        [5.0, 2.0],
        [13.0, 2.0],
        [13.0, 3.0],
        [12.0, 3.0],
        [12.0, 4.0],
        [11.0, 4.0],
        [11.0, 3.0],
        [10.0, 3.0],
        [9.0, 4.0],
        [8.0, 4.0],
        [8.0, 3.0],
        [5.0, 3.0],
        [5.0, 4.0],
        [4.0, 5.0],
        [2.0, 5.0],
        [1.0, 4.0],
        [1.0, 2.0]
    ],
    vec![
        [2.0, 4.0],
        [4.0, 4.0],
        [4.0, 2.0],
        [2.0, 2.0]
    ],
];

let style = OutlineStyle::new(0.2).line_join(LineJoin::Round(0.1));
let shapes = shape.outline(&style);

println!("shapes: {:?}", &shapes);

Note:

Offsetting a polygon works reliably only with valid polygons. Ensure that:
- No self-intersections.
- Outer boundaries are counterclockwise, holes are clockwise—unless main_direction is set.
If polygon validity cannot be guaranteed, it is recommended to apply the simplify_shape operation before offsetting.
More information on contour orientation.

LineCap

Butt	Square	Round	Custom

LineJoin

Bevel	Miter	Round

FAQ

1. When should I use `FloatOverlay`, `SingleFloatOverlay`, or `FloatOverlayGraph`?

Use FloatOverlay when you perform repeated overlay operations:

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::overlay::FloatOverlay;

let subj = vec![[0.0, 0.0], [0.0, 5.0], [5.0, 5.0], [5.0, 0.0]];
let clip = vec![[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [4.0, 2.0]];
let next_clip = vec![[1.0, 1.0], [1.0, 3.0], [3.0, 3.0], [3.0, 1.0]];

let mut overlay = FloatOverlay::with_subj_and_clip(&subj, &clip);
let result = overlay.overlay(OverlayRule::Difference, FillRule::EvenOdd);

overlay.reinit_with_subj_and_clip(&subj, &next_clip);
let next_result = overlay.overlay(OverlayRule::Difference, FillRule::EvenOdd);
// ...

Use SingleFloatOverlay trait for one-shot operations.
Use FloatOverlayGraph if you need to extract multiple boolean results (e.g. union and intersection) from the same input geometry without recomputing.

2. I need to union many shapes at once. What's the most efficient way?

Use the simplify_shape operation:

use i_overlay::core::fill_rule::FillRule;
use i_overlay::float::simplify::SimplifyShape;

let shapes = vec![
    vec![[0.0, 0.0], [0.0, 2.0], [2.0, 2.0], [2.0, 0.0]],
    vec![[2.0, 0.0], [2.0, 2.0], [4.0, 2.0], [4.0, 0.0]],
];

let result = shapes.simplify_shape(FillRule::EvenOdd);

It internally merges shapes efficiently and is typically faster and more robust than chaining many overlay() calls manually.

3. How do I use a fixed grid size (fixed precision) for float overlays?

Use FixedScaleFloatOverlay or FloatOverlay::with_subj_and_clip_fixed_scale. The scale is scale = 1.0 / grid_size.

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::scale::FixedScaleFloatOverlay;

let subj = vec![[0.0, 0.0], [0.0, 5.0], [5.0, 5.0], [5.0, 0.0]];
let clip = vec![[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [4.0, 2.0]];

let grid_size = 0.001;
let scale = 1.0 / grid_size;

let result = subj
    .overlay_with_fixed_scale(&clip, OverlayRule::Difference, FillRule::EvenOdd, scale)
    .expect("scale does not fit input bounds");

If you need more control, use FloatPointAdapter::with_scale and FloatOverlay::with_adapter.

4. How do I select the integer engine for float overlays?

If you need control over the float-to-integer precision range, select the integer engine at compile time with the from_* constructors. The supported engines are i16, i32, and i64. The default engine is i32; use i64 when the input bounds need a wider integer range.

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::overlay::FloatOverlay;

let subj = vec![[0.0, 0.0], [0.0, 5.0], [5.0, 5.0], [5.0, 0.0]];
let clip = vec![[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [4.0, 2.0]];

let mut overlay = FloatOverlay::<[f64; 2], i64>::from_subj_and_clip(&subj, &clip);
let result = overlay.overlay(OverlayRule::Difference, FillRule::EvenOdd);

The sugar traits also use i32 by default. Use the *_as::<I> methods when you want to keep the shorthand API and still select the integer engine explicitly:

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::single::SingleFloatOverlay;

let subj = vec![[0.0, 0.0], [0.0, 5.0], [5.0, 5.0], [5.0, 0.0]];
let clip = vec![[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [4.0, 2.0]];

let result = subj.overlay_as::<i64>(&clip, OverlayRule::Difference, FillRule::EvenOdd);

5. How do I enable OGC-valid output?

Set the ogc flag in OverlayOptions.

use i_overlay::core::fill_rule::FillRule;
use i_overlay::core::overlay_rule::OverlayRule;
use i_overlay::float::overlay::{FloatOverlay, OverlayOptions};

//     0   1   2   3   4   5
//   5 ┌───────────────────┐
//     │                   │
//   4 │   ┌───────┐       │
//     │   │ ░   ░ │       │   Two L-shaped holes share vertices at (2,2) and (3,3)
//   3 │   │   ┌───●───┐   │
//     │   │ ░ │   │ ░ │   │   ░ = holes
//   2 │   └───●───┘   │   │
//     │       │ ░   ░ │   │   The shared edge disconnects the interior
//   1 │       └───────┘   │
//     │                   │
//   0 └───────────────────┘
//
// OGC Simple Feature Specification (ISO 19125-1) states:
// "The interior of every Surface is a connected point set."

let subj = vec![vec![[0.0, 0.0], [5.0, 0.0], [5.0, 5.0], [0.0, 5.0]]];
let clip = vec![
    vec![[1.0, 2.0], [1.0, 4.0], [3.0, 4.0], [3.0, 3.0], [2.0, 3.0], [2.0, 2.0]],
    vec![[2.0, 1.0], [2.0, 2.0], [3.0, 2.0], [3.0, 3.0], [4.0, 3.0], [4.0, 1.0]],
];

let options = OverlayOptions::<f64>::ogc();
let mut overlay = FloatOverlay::with_subj_and_clip_custom(&subj, &clip, options, Default::default());
let result = overlay.overlay(OverlayRule::Difference, FillRule::EvenOdd);

assert_eq!(result.len(), 2);

License

Licensed under either of:

MIT license (LICENSE-MIT)
Apache License, Version 2.0 (LICENSE-APACHE)

Name		Name	Last commit message	Last commit date
Latest commit History 825 Commits
.github		.github
examples		examples
iOverlay		iOverlay
performance/rust_app		performance/rust_app
readme		readme
.gitattributes		.gitattributes
.gitignore		.gitignore
CONTRIBUTING.md		CONTRIBUTING.md
LICENSE-APACHE		LICENSE-APACHE
LICENSE-MIT		LICENSE-MIT
README.md		README.md

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iOverlay

Table of Contents

Why iOverlay?

Features

Demo

Performance

Getting Started

Quick Start

Boolean Operations

Simple Example

Overlay Rules

Edge Attributes and Provenance

Spatial Predicates

Fixed-Scale Predicates

Custom Point Type Support

Slicing & Clipping

Slicing a Polygon with a Polyline

Clipping a Polyline by a Polygon

Buffering

Offsetting a Path

Offsetting a Polygon

LineCap

LineJoin

FAQ

1. When should I use FloatOverlay, SingleFloatOverlay, or FloatOverlayGraph?

2. I need to union many shapes at once. What's the most efficient way?

3. How do I use a fixed grid size (fixed precision) for float overlays?

4. How do I select the integer engine for float overlays?

5. How do I enable OGC-valid output?

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1. When should I use `FloatOverlay`, `SingleFloatOverlay`, or `FloatOverlayGraph`?

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