wtsnz / Triangle

Swift wrapper for Triangle.c https://www.cs.cmu.edu/~quake/triangle.html

Swift wrapper for triangle

This package is a wrapper for the Triangle library originally written in C by Jonathan Shewchuk, and heavily inspired by the golang port.

Features:

• constrained & conforming Delaunay triangulation (with support for holes)

for points in 2D.

Usage

There is two version of API for each Delaunay function. One that is higher-level that takes [CGPoint] and returns [Triangle], and another that takes points as [Double] (as x1, y1, x2, y2, x3, y3, ...), segments as an [Int] (seg1Start, seg1End, seg2Start, seg2End, ...) and holes as [Double] (x1, y1, x2, y2, ...).

Use either based on preference, the higher level is easier when dealing with UIKit drawing.

Delaunay triangulation of points

The Delaunay function takes a slice of 2D points represented as [CGPoint].

let points = [
    CGPoint(x: 0, y: 0),
    CGPoint(x: 10, y: 0),
    CGPoint(x: 10, y: 10),
    CGPoint(x: 0, y: 10)
]

Triangulate.Delaunay(points: ) returns an array of Triangles`.

let triangles = Triangulate.Delaunay(points: points)
dump(triangles)
// ▿ 2 elements
//  ▿ Triangle.Triangle #0
//    ▿ a: (0.0, 10.0)
//    ▿ b: (0.0, 0.0)
//    ▿ c: (10.0, 0.0)
//  ▿ Triangle.Triangle #1
//    ▿ a: (10.0, 0.0)
//    ▿ b: (10.0, 10.0)
//    ▿ c: (0.0, 10.0)

Constrained and conforming Delaunay triangulation of PSLGs

Functions ConformingDelaunay() and ConstrainedDelaunay() accept a PSLG as input. PSLGs are planar straight line graphs defined by a set of points, segments (pair of indices into the points slice), and holes (single point somewhere within each hole).

// Points forming the shape of letter "A"

let points = [
    0.200000, -0.776400, // x1, y1
    0.220000, -0.773200, // x2, y2
    0.245600, -0.756400, // .., .. (and so on)
    0.277600, -0.702000,
    0.488800, -0.207600,
    0.504800, -0.207600,
    0.740800, -0.7396,
    0.756000, -0.761200,
    0.774400, -0.7724,
    0.800000, -0.776400,
    0.800000, -0.792400,
    0.579200, -0.792400,
    0.579200, -0.776400,
    0.621600, -0.771600,
    0.633600, -0.762800,
    0.639200, -0.744400,
    0.620800, -0.684400,
    0.587200, -0.604400,
    0.360800, -0.604400,
    0.319200, -0.706800,
    0.312000, -0.739600,
    0.318400, -0.761200,
    0.334400, -0.771600,
    0.371200, -0.776400,
    0.371200, -0.792400,
    0.374400, -0.570000,
    0.574400, -0.5700,
    0.473600, -0.330800,
    0.200000, -0.792400
]

// Segments connecting the points
let segments = [
    28, 0, // p28 -> p0
    0, 1,  // p0 -> p1
    1, 2,  // p1 -> p2
    2, 3,  // .. -> .. (and so on)
    3, 4,
    4, 5,
    5, 6,
    6, 7,
    7, 8,
    8, 9,
    9, 10,
    10, 11,
    11, 12,
    12, 13,
    13, 14,
    14, 15,
    15, 16,
    16, 17,
    17, 18,
    18, 19,
    19, 20,
    20, 21,
    21, 22,
    22, 23,
    23, 24,
    24, 28,
    25, 26,
    26, 27,
    27, 25
]

// Hole represented by a point lying inside it 
let holes = [
    0.47, -0.5, // x1, y1
]

ConstrainedDelaunay() computes a constrained Delaunay triangulation of a PSLG, where the given segments are retained as such in the resulting triangulation. As a result, not all triangles are Delaunay. (left image below)

let (trianglePoints, triangleIndicies) = Triangulate.ConstrainedDelaunay(points: points, segments: segments, holes: holes)

ConformingDelaunay() computes a conforming Delaunay triangulation of a PSLG, where each triangle in the result is Delaunay. This is acheived by inserting vertices inbetween the given segments. (right image below)

let (trianglePoints, triangleIndicies) = Triangulate.ConformingDelaunay(points: points, segments: segments, holes: holes)

Constrained Delaunay	Conforming Delaunay

Constrained Delaunay	Conforming Delaunay