iShapeTriangulation

Complex polygon triangulation, tessellation and split into convex polygons. A fast O(n*log(n)) algorithm based on "Triangulation of monotone polygons". The result can be represented as a Delaunay triangulation.

Delaunay triangulation

Breaking into convex polygons

Triangulation with extra points

Tessellation

Centroid net

Important Update: Check Out My New Library!

I'm excited to introduce iTriangle, the latest evolution of this project. Not only does it retain most of the fantastic features of iShapeTriangulation, but it also brings significant improvements, including better support for self-intersection cases. Additionally, it offers more precise adherence to the Delaunay condition. I'll be dedicating my future efforts to this new library, so I highly recommend trying it out for the most up-to-date features and enhancements. Your feedback is always appreciated!

Features

💡 Fast O(n*log(n)) algorithm based on "Triangulation of monotone polygons"

💡 All code is written to suit "Data Oriented Design". No reference type like class, just structs.

💡 Supports polygons with holes

💡 Supports plain and Delaunay triangulation

💡 Supports tesselation

💡 Supports breaking into convex polygons

💡 Supports building centroid net

💡 Same points is not restricted

💡 Polygon must not have self intersections

💡 Use integer geometry for calculations

💡 More then 100 tests

Basic Usage

Add import:

import iGeometry
import iShapeTriangulation

After that you need represent your polygon as an array of vertices listed in a clockwise direction. Let's have a look for an example of a cheese polygon.

    let path = [
        // vertices listed in clockwise direction
        Point(x: 0, y: 20),       // 0
        Point(x: 8, y: 10),       // 1
        Point(x: 7, y: 6),        // 2
        Point(x: 9, y: 1),        // 3
        Point(x: 13, y: -1),      // 4
        Point(x: 17, y: 1),       // 5
        Point(x: 26, y: -7),      // 6
        Point(x: 14, y: -15),     // 7
        Point(x: 0, y: -18),      // 8
        Point(x: -14, y: -15),    // 9
        Point(x: -25, y: -7),     // 10
        Point(x: -18, y: 0),      // 11
        Point(x: -16, y: -3),     // 12
        Point(x: -13, y: -4),     // 13
        Point(x: -8, y: -2),      // 14
        Point(x: -6, y: 2),       // 15
        Point(x: -7, y: 6),       // 16
        Point(x: -10, y: 8)       // 17
    ]

Then get an instance of a Triangulator class and triangulate your polygon. As the result you will get an array of indices on your vertices array. Where each triple are represent an indices of a triangle vertices.

    let triangulator = Triangulator()
    if let triangles = try? triangulator.triangulateDelaunay(points: path) {
        for i in 0..<triangles.count / 3 {
            let ai = triangles[3 * i]
            let bi = triangles[3 * i + 1]
            let ci = triangles[3 * i + 2]
            print("triangle \(i): (\(ai), \(bi), \(ci))")
        }
    }

The triple are always list vertices in a clock wise direction.

Lets look another example for a polygon with a hole. Now you need represent a hole as an array of vertices listed in counterclockwise direction

    let hole = [
        // vertices listed in counterclockwise direction
        Point(x: 2, y: 0),    // 18
        Point(x: -2, y: -2),  // 19
        Point(x: -4, y: -5),  // 20
        Point(x: -2, y: -9),  // 21
        Point(x: 2, y: -11),  // 22
        Point(x: 5, y: -9),   // 23
        Point(x: 7, y: -5),   // 24
        Point(x: 5, y: -2)    // 25
    ]
    
    let points = path + hole
    if let triangles = try? triangulator.triangulateDelaunay(points: points, hull: points[0..<path.count], holes: [points[path.count..<points.count]], extraPoints: nil) {
        for i in 0..<triangles.count / 3 {
            let ai = triangles[3 * i]
            let bi = triangles[3 * i + 1]
            let ci = triangles[3 * i + 2]
            print("triangle \(i): (\(ai), \(bi), \(ci))")
        }
    }

Installation

add imports:

import iGeometry
import iShapeTriangulation

CocoaPods

Add the following to your Podfile:

pod 'iShapeTriangulation'

Cartage

Add the following to your Cartfile:

github "iShape-Swift/iShapeTriangulation"

Package Manager

Add the following to your Package.swift:

let package = Package(
    name: "[your name]",
    products: [
        dependencies: [
            .package(url: "https://github.com/iShape-Swift/iShapeTriangulation", from: "1.0.2")
        ],
        targets: [
            .target(
                name: "[your target]",
                dependencies: ["iShapeTriangulation"])
        ]
    ]
)

Or add it directly throw .xcodeproj