Description
flattenjs is a javascript library for manipulating abstract geometrical shapes like point, vector, line, ray, segment, circle, arc and polygon. Shapes may be organized into Planar Set  searchable container which support spatial queries.
flattenjs provides a lot of useful methods and algorithms like finding intersections, checking inclusion, calculating distance, applying affine transformations, performing boolean operations and more.
Packages are distributed in 3 formats: commonjs, umd and es6 modules. Package.json file
provides various entry points suitable for different targets.
TypeScript users may take advantage of static type checking with typescript definition file index.d.ts included into the package.
flattenjs does not concern too much about visualization. Anyway, all classes implement svg() method, that returns a string which may be inserted into SVG container.
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README
Javascript library for 2d geometry
flattenjs is a javascript library for manipulating abstract geometrical shapes like point, vector, line, ray, segment, circle, arc and polygon. Shapes may be organized into Planar Set  searchable container which support spatial queries.
flattenjs provides a lot of useful methods and algorithms like finding intersections, checking inclusion, calculating distance, applying affine transformations, performing boolean operations and more.
Packages are distributed in 3 formats: commonjs, umd and es6 modules. Package.json file provides various entry points suitable for different targets.
TypeScript users may take advantage of static type checking with typescript definition file index.d.ts included into the package.
flattenjs does not concern too much about visualization. Anyway, all classes implement svg() method, that returns a string which may be inserted into SVG container. It works pretty well together with d3js library, but it is definitely possible to create bridges to other graphic libraries.
The best way to start working with FlattenJS is to use awesome Observable javascript interactive notebooks. Check out collection of Tutorials published in Observable Notebooks.
Full documentation may be found here: https://alexbol99.github.io/flattenjs/index.html
Contacts
Follow me on Twitter @alex_bol_
Installation
npm install save @flattenjs/core
Usage
import {Point, Vector, Circle, Line, Ray, Segment, Arc, Box, Polygon, Matrix, PlanarSet} from '@flattenjs/core';
It is possible to import Flatten namespace as default import, and then destruct all classes from it.
import Flatten from '@flattenjs/core'
const {Point, Vector, Circle, Line, Ray, Segment, Arc, Box, Polygon, Matrix, PlanarSet} = Flatten;
Some classes have shortcuts to avoid annoying new constructor:
import {point, vector, circle, line, ray, segment, arc, polygon, matrix} from '@flattenjs/core';
Example
After module imported, it is possible to create some construction:
// extract object creators
import {point, circle, segment} from '@flattenjs/core';
// make some construction
let s1 = segment(10,10,200,200);
let s2 = segment(10,160,200,30);
let c = circle(point(200, 110), 50);
let ip = s1.intersect(s2);
You may test the code above also in NPM RunKit
You may also check out examples section in the code which illustrate different use cases:
 in nodejs
 in a browser using
<script>
tag with unpkg.com loader  in a React application
Content of the library
Basic shapes
flattenjs library implements following basic shapes:
Polygon
Polygon in flattenjs library is actually a multipolygon. Polygon is a collection of faces  closed oriented chains of edges, which may be of type Segment or Arc. The most external face called island, a face included into it is called hole. Holes in turn may have inner islands, number of inclusion levels is unlimited.
Orientation of islands and holes is matter for calculation
of relationships and boolean operations, holes should have orientation opposite to islands.
It means that for proper results faces in a polygon should be orientable: they should not have selfintersections.
Faces also should not overlap each other. Method isValid()
checks if polygon fit these rules.
Constructor of the polygon object accept various inputs:
 Array of shapes (instances of Flatten.Segment or Flatten.Arc) that represent closed chains
 Array of shapes as json objects that represent closed chains
 Array of points (Flatten.Point) that represent vertices of the polygon
 Array of numeric pairs [x,y] that represent vertices of the polygon
 Instances of Circle or Box
Polygon provides various useful methods:
area
 calculate area of a polygonaddFace
 add a new face to polygondeleteFace
 removes face from polygonaddVertex
 split an edge of polygon adn create new vertexcut
 cut polygon with multiline into subpolygonsfindEdgeByPoint
 find edge in polygoncontains
 test if polygon contains shape (point, segment or arc)transform
 transform polygon using affine transformation matrixreverse
 revert orientation of facessplitToIslands
 split to array of islands with holes
Multiline
Multiline represent an unclosed chain of edges of type Segment or Arc
Planar Set
Planar Set is a container of shapes that enables spatial seach by rectangular query.
Affine transformations
Affine transformation matrix is a 3x3 matrix of the form
[ a c tx
A = b d ty
0 0 1 ]
Where a, b, c, d, represent rotation and scaling, tx, ty represent translation.
Matrix constructor without parameters creates an identity matrix, and then
resulted matrix may be composed by chaining basic operations,
like translate
, rotate
and scale
, like this:
// Rotate segment by 45 deg around its center
let {point,segment,matrix} = Flatten;
let s = segment(point(20,30), point(60,70));
let center = s.box.center;
let angle = 45.*Math.PI/180.;
let m = matrix()
.translate(center.x, center.y)
.rotate(angle)
.translate(center.x, center.y);
let t_s = s.transform(m);
Intersection points
All classes have method intersect(otherShape)
that return array of intersection points,
if two shapes intersect each other, or empty array otherwise. The is no predefined order
of intersection points in the array.
Please don't be confused, there are another two methods BooleanOperations.intersect()
that performs boolean intersection of polygons and logical predicate Relations.intersect()
that check if two shapes intersected or not.
Distance between shapes
All basic classes and polygon have method distanceTo(othershape)
that calculate distance to other shape. Together with the distance function returns the shortest segment
between two shapes  segment between two closest point, where the first point lays
on this
shape, and the second  on the other shape, see example:
let s = segment(point(10,30), point(150, 40));
let c = circle(point(75,75),10);
let [dist,shortest_segment] = s.distanceTo(c);
Intersection model (DE9IM)
The Dimensionally Extended nineIntersection Model (DE9IM) is a topological model and a standard used to describe the spatial relations of two geometries in 2dimensional plane.
First, for every shape we define:
 An interior
 A boundary
 An exterior
For polygons, the interior, boundary and exterior are obvious, other types have some exclusions:
 Point has no interior
 Line has no boundary
The DE9IM model based on a 3ร3 intersection matrix with the form:
[ I(a) ^ I(b) B(a) ^ I(b) E(a) ^ I(b)
de9im = I(a) ^ B(b) B(a) ^ B(b) E(a) ^ B(b)
I(a) ^ E(b) B(a) ^ E(b) E(a) ^ E(b) ]
where a
and b
are two shapes (geometries),
I(), B(), E()
denotes interior, boundary and exterior operator and
^
denotes operation of intersection.
Dimension of intersection result depends on the dimension of shapes, for example,
 intersection between an interior of the line and an interior of the polygon is an array of segments
 intersection between an interior of the line and boundary polygon is an array of points (may include segments in case of touching)
 intersection between interiors of two polygons (if exists) will be a polygon.
DE9IM matrix describes any possible relationships between two shapes on the plane.
DE9IM matrix is available via method relate
under namespace Relations
.
Each element of DE9IM matrix is an array of the objects representing corresponding intersection. Empty array represents case of no intersection. If intersection is not applicable (i.e. intersection with a boundary for a line which has no boundary), correspondent cell left undefined.
Intersection between two exteriors not calculated because usually it is meaningless.
let {relate} = Flatten.Relations;
//
// define two shapes: polygon1, polygon2
//
let de9im = relate(polygon1, polygon2);
//
// explore 8 of 9 fields of the de9im matrix:
// de9im.I2I de9im.B2I de9im.E2I
// de9im.I2B de9im.B2B de9im.E2B
// de9im.I2E de9im.B2E N/A
Another common way to represent DE9IM matrix is a string where
T
represent intersection where array is not imptyF
represent intersection where array is empty.
means not relevant or not applicable
String may be obtained with de9im.toString()
method.
Relationship predicates
The spatial relationships between two shapes exposed via namespace Relations
.
The spatial predicates return true
if relationship match and false
otherwise.
let {intersect, disjoint, equal, touch, inside, contain, covered, cover} = Flatten.Relations;
// define shape a and shape b
let p = intersect(a, b);
console.log(p) // true / false
intersect
 shapes a and b have at least one common pointdisjoint
 opposite tointersect
equal
 shapes a and b are topologically equaltouch
 shapes a and b have at least one point in common but their interiors not intersectinside
 shape a lies in the interior of shape bcontain
 shape b lies in the interior of shape bcovered
 every point of a lies or in the interior or on the boundary of shape bcovered
 every point of b lies or in the interior or on the boundary of shape a
Boolean operations
Boolean operations on polygons available via namespace BooleanOperations. Polygons in boolean operation should be valid: both operands should have same meaning of face orientation, faces should not overlap each other and should not have selfintersections.
User is responsible to provide valid polygons, boolean operation methods do not check validity.
let {unify, subtract, intersect, innerClip, outerClip} = BooleanOperations;
unify
 unify two polygons and return resulted polygonsubtract
 subtract second polygon from the first and return resulted polygonintersect
 intersect two polygons and return resulted polygoninnerClip
 intersect two polygons and return boundary of intersection as 2 arrays. The first aray contains edges of the first polygon, the second  the edges of the secondouterClip
 clip boundary of the first polygon with the interior of the second polygon
Implementation based on WeilerAtherton clipping algorithm, described in the article Hidden Surface Removal Using Polygon Area Sorting
Serialization
All flattenjs shape objects may be serialized using JSON.stringify()
method.
JSON.stringify
transforms object to string using .toJSON()
formatter implemented in the class.
JSON.parse
restore object from a string, and then constructor can use this object to create Flatten object.
let {lint, point} = Flatten;
let l = line(point(4, 0), point(0, 4));
// Serialize
let str = JSON.stringify(l);
// Parse and reconstruct
let l_json = JSON.parse(str);
let l_parsed = line(l_json);
Visualization
All classes provide svg()
method, that create svg string that may be inserted into svg container element
in a very straightforward way:
<body>
<svg id="stage" width="500" height="500"></svg>
<script>
const Flatten = window["@flattenjs/core"];
const {point, circle, segment} = Flatten;
// make some construction
let s1 = segment(10,10,200,200);
let s2 = segment(10,160,200,30);
let c = circle(point(200, 110), 50);
let ip = s1.intersect(s2);
document.getElementById("stage").innerHTML = s1.svg() + s2.svg() + c.svg() + ip[0].svg();
</script>
</body>
Method svg()
may accept as a parameter an object that enables to define
several basic attributes of svg element:
stroke
, strokeWidth
, fill
, fillRule
, fillOpacity
, id
and className
.
If attributes not provided, method svg()
use default values.
Other packages
Other packages, published under scope @flattenjs/:
Name  Description 

@flattenjs/intervaltree  Interval binary search tree 
@flattenjs/booleanop  Boolean operations (deprecated, use this functionality from the core package) 
@flattenjs/polygonoffset  Polygon offset 