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version](https://badge.fury.io/js/%40flatten-js%2Fcore.svg)](https://badge.fury.io/js/%40flatten-js%2Fcore)\n[![Coverage Status](https://coveralls.io/repos/github/alexbol99/flatten-js/badge.svg?branch=master)](https://coveralls.io/github/alexbol99/flatten-js?branch=master)\n[![](https://data.jsdelivr.com/v1/package/npm/@flatten-js/core/badge)](https://www.jsdelivr.com/package/npm/@flatten-js/core)\n[![@flatten-js/core](https://snyk.io/advisor/npm-package/@flatten-js/core/badge.svg)](https://snyk.io/advisor/npm-package/@flatten-js/core)\n\n# Javascript library for 2d geometry\n\n**flatten-js** is a javascript library for manipulating abstract geometrical shapes like point, vector, line, ray, segment,\ncircle, arc and polygon. Shapes may be organized into Planar Set - searchable container which support spatial queries.\n\n**flatten-js** provides a lot of useful methods and algorithms like finding intersections, checking inclusion, calculating distance, applying\naffine transformations, performing boolean operations and more.\n\nPackages are distributed in 3 formats: commonjs, umd and es6 modules. Package.json file\nprovides various entry points suitable for different targets.\n\nTypeScript users may take advantage of static type checking with typescript definition file index.d.ts included into the package.\n\n**flatten-js** does not concern too much about visualization.\nAnyway, all classes implement svg() method, that returns a string which may be inserted into SVG container. \nIt works pretty well together with  [d3js](https://d3js.org/) library, but it is definitely possible to create bridges to other graphic libraries.\n\nThe best way to start working with FlattenJS is to use awesome [Observable](https://beta.observablehq.com/) javascript interactive notebooks.\nCheck out collection of [Tutorials](https://observablehq.com/collection/@alexbol99/flatten-js-tutorials) published in Observable Notebooks.\n\nFull documentation may be found here: [https://alexbol99.github.io/flatten-js/index.html](https://alexbol99.github.io/flatten-js/index.html)\n\n## Contacts\n\nFollow me on Twitter [@alex_bol_](https://twitter.com/alex_bol_)\n\n## Installation\n\n    npm install --save @flatten-js/core\n\n## Usage\n\n```javascript\nimport {Point, Vector, Circle, Line, Ray, Segment, Arc, Box, Polygon, Matrix, PlanarSet} from '@flatten-js/core';\n```\n\nIt is possible to import Flatten namespace as default import, and then destruct all classes from it. \n```javascript\nimport Flatten from '@flatten-js/core'\nconst {Point, Vector, Circle, Line, Ray, Segment, Arc, Box, Polygon, Matrix, PlanarSet} = Flatten;\n```\n\nSome classes have shortcuts to avoid annoying *new* constructor:\n```javascript\nimport {point, vector, circle, line, ray, segment, arc, polygon, matrix} from '@flatten-js/core';\n```\n\n## Example\n\nAfter module imported, it is possible to create some construction:\n```javascript\n    // extract object creators\n    import {point, circle, segment} from '@flatten-js/core';\n\n    // make some construction\n    let s1 = segment(10,10,200,200);\n    let s2 = segment(10,160,200,30);\n    let c = circle(point(200, 110), 50);\n    let ip = s1.intersect(s2);\n```\n\nYou may test the code above also in [NPM RunKit](https://npm.runkit.com/@flatten-js/core)\n\nYou may also check out examples section in the code which illustrate different use cases:\n* in nodejs\n* in a browser using ```<script>``` tag with **unpkg.com** loader\n* in a React application \n\n## Content of the library\n\n### Basic shapes\n**flatten-js** library implements following basic shapes:\n* [Point](https://alexbol99.github.io/flatten-js/Point.html)\n* [Vector](https://alexbol99.github.io/flatten-js/Vector.html)\n* [Line](https://alexbol99.github.io/flatten-js/Line.html)\n* [Ray](https://alexbol99.github.io/flatten-js/Ray.html)\n* [Segment](https://alexbol99.github.io/flatten-js/Segment.html)\n* [Arc (circular)](https://alexbol99.github.io/flatten-js/Arc.html)\n* [Circle](https://alexbol99.github.io/flatten-js/Circle.html)\n* [Box (may be used as rectangle)](https://alexbol99.github.io/flatten-js/Box.html)\n\n### Polygon\n\n[Polygon](https://alexbol99.github.io/flatten-js/Polygon.html) in **flatten-js** library is actually a multi-polygon.\nPolygon is a collection of faces - \nclosed oriented chains of edges, which may be of type Segment or Arc. The most external face\ncalled island, a face included into it is called hole. Holes in turn may have inner islands,\nnumber of inclusion levels is unlimited.\n \nOrientation of islands and holes is matter for calculation\nof relationships and boolean operations, holes should have orientation opposite to islands.\nIt means that for proper results faces in a polygon should be **orientable**: they should not have self-intersections.\nFaces also should not overlap each other. Method ```isValid()``` checks if polygon fit these rules.\n\nConstructor of the polygon object accept various inputs:\n* Array of shapes (instances of Flatten.Segment or Flatten.Arc) that represent closed chains\n* Array of shapes as json objects that represent closed chains \n* Array of points (Flatten.Point) that represent vertices of the polygon\n* Array of numeric pairs [x,y] that represent vertices of the polygon\n* Instances of Circle or Box\n\nPolygon provides various useful methods:\n* ```area``` - calculate area of a polygon\n* ```addFace``` - add a new face to polygon\n* ```deleteFace``` - removes face from polygon\n* ```addVertex``` - split an edge of polygon adn create new vertex\n* ```cut``` - cut polygon with multiline into sub-polygons\n* ```findEdgeByPoint``` - find edge in polygon\n* ```contains``` - test if polygon contains shape (point, segment or arc)\n* ```transform``` - transform polygon using affine transformation matrix\n* ```reverse``` - revert orientation of faces\n* ````splitToIslands```` - split to array of islands with holes\n\n### Multiline\n\nMultiline represent an unclosed chain of edges of type Segment or Arc\n\n### Planar Set\n\nPlanar Set is a container of shapes that enables spatial seach by rectangular query.\n\n### Transformations\n\nAll the classes have methods ```translate```, ```rotate``` and ```scale``` \nwhich may be chained. \n<br/>Example:\n```javascript\n// Rotate segment by 45 deg around its center\nlet {point,segment,matrix} = Flatten;\nlet s = segment(point(20,30), point(60,70));\nlet center = s.box.center;\nlet angle = 45.*Math.PI/180.;\nlet rotated_segment = s.rotate(angle, center)\n```\n### Intersection points\n\nAll classes have method ```intersect(otherShape)``` that return array of intersection points,\nif two shapes intersect each other, or empty array otherwise. The is no predefined order\nof intersection points in the array.\n\nPlease don't be confused, there are another two methods ```BooleanOperations.intersect()```\nthat performs boolean intersection of polygons and logical predicate ```Relations.intersect()```\nthat check if two shapes intersected or not. \n\n### Distance between shapes\n\nAll basic classes and polygon have method ```distanceTo(othershape)``` \nthat calculate distance to other shape. Together with the distance function returns the shortest segment\nbetween two shapes - segment between two closest point, where the first point lays\non ```this``` shape, and the second - on the other shape, see example:\n```javascript\nlet s = segment(point(10,30), point(150, 40));\nlet c = circle(point(75,75),10);\nlet [dist,shortest_segment] = s.distanceTo(c);\n```\n\n### Intersection model (DE-9IM) \n\nThe Dimensionally Extended nine-Intersection Model\n ([DE-9IM](https://en.wikipedia.org/wiki/DE-9IM)) is a topological model and a standard\n used to describe the spatial relations of two geometries in 2-dimensional plane.\n \n First, for every shape we define:\n * An interior\n * A boundary\n * An exterior\n \n For polygons, the interior, boundary and exterior are obvious, other types have some exclusions:\n * Point has no interior\n * Line has no boundary\n \n The DE-9IM model based on a 3×3 intersection matrix with the form:\n ```\n          [ I(a) ^ I(b)   B(a) ^ I(b)   E(a) ^ I(b)\n de9im =    I(a) ^ B(b)   B(a) ^ B(b)   E(a) ^ B(b)\n            I(a) ^ E(b)   B(a) ^ E(b)   E(a) ^ E(b)  ]\n```\n\nwhere ```a```and  ```b``` are two shapes (geometries), \n\n```I(), B(), E()``` denotes interior, boundary and exterior operator and\n\n```^``` denotes operation of intersection. \nDimension of intersection result depends on the dimension of shapes, for example,\n* intersection between an interior of the line and an interior of the polygon is an\n array of segments\n* intersection between an interior of the line and boundary polygon is \nan array of points (may include segments in case of touching)\n* intersection between interiors of two polygons (if exists) will be\na polygon. \n\nDE-9IM matrix describes any possible relationships between two shapes on the plane.\n\nDE-9IM matrix is available via method ```relate``` under namespace ```Relations```.\n\nEach element of DE-9IM matrix is an array of the objects representing corresponding intersection.\nEmpty array represents case of no intersection.\nIf intersection is not applicable (i.e. intersection with a boundary for a line which has no boundary),\ncorrespondent cell left undefined.\n\nIntersection between two exteriors not calculated because usually it is meaningless.\n\n```javascript\nlet {relate} = Flatten.Relations;\n// \n// define two shapes: polygon1, polygon2\n//\nlet de9im = relate(polygon1, polygon2);\n//\n// explore 8 of 9 fields of the de9im matrix:\n// de9im.I2I  de9im.B2I  de9im.E2I\n// de9im.I2B  de9im.B2B  de9im.E2B\n// de9im.I2E  de9im.B2E     N/A\n```\n\nAnother common way to represent DE-9IM matrix is a string where \n* ```T``` represent intersection where array is not impty\n* ```F``` represent intersection where array is empty\n* ```.``` means not relevant or not applicable\n\nString may be obtained with ```de9im.toString()``` method.\n\n### Relationship predicates\n\nThe spatial relationships between two shapes exposed via namespace `Relations`.\nThe spatial predicates return `true` if relationship match and `false` otherwise.\n```javascript\nlet {intersect, disjoint, equal, touch, inside, contain, covered, cover} = Flatten.Relations;\n// define shape a and shape b\nlet p = intersect(a, b);\nconsole.log(p)             // true / false\n```\n* ```intersect``` - shapes a and b have at least one common point\n* ```disjoint``` -  opposite to ```intersect```\n* `equal` - shapes a and b are topologically equal\n* `touch` - shapes a and b have at least one point in common but their interiors not intersect\n* `inside` - shape a lies in the interior of shape b\n* `contain` - shape b lies in the interior of shape a\n* `covered` - every point of a lies or in the interior or on the boundary of shape b\n* `covered` - every point of b lies or in the interior or on the boundary of shape a\n\n### Boolean operations\n\nBoolean operations on polygons available via namespace **BooleanOperations**.\nPolygons in boolean operation should be valid: both operands should have same meaning of face orientation,\nfaces should not overlap each other and should not have self-intersections.\n\nUser is responsible to provide valid polygons, boolean operation methods do not check validity.\n\n```javascript\nlet {unify, subtract, intersect, innerClip, outerClip} = BooleanOperations;\n```\n* `unify` - unify two polygons and return resulted polygon\n* `subtract` - subtract second polygon from the first and return resulted polygon\n* `intersect` - intersect two polygons and return resulted polygon\n* `innerClip` - intersect two polygons and return boundary of intersection as 2 arrays.\n The first aray contains edges of the first polygon, the second - the edges of the second\n* `outerClip` - clip boundary of the first polygon with the interior of the second polygon\n\nImplementation based on Weiler-Atherton clipping algorithm,\ndescribed in the article [Hidden Surface Removal Using Polygon Area Sorting](https://www.cs.drexel.edu/~david/Classes/CS430/HWs/p214-weiler.pdf)\n\n### Serialization\n\nAll **flatten-js** shape objects may be serialized using `JSON.stringify()` method.\n`JSON.stringify` transforms object to string using `.toJSON()` formatter implemented in the class. \n`JSON.parse` restore object from a string, and then constructor can use this object to create Flatten object.\n \n```javascript\nlet {lint, point} = Flatten;\nlet l = line(point(4, 0), point(0, 4));\n// Serialize\nlet str = JSON.stringify(l);  \n// Parse and reconstruct\nlet l_json = JSON.parse(str);\nlet l_parsed = line(l_json);\n```\n\n### Visualization\n\nAll classes provide `svg()` method, that create svg string that may be inserted into svg container element\nin a very straightforward way:\n\n```html\n<body>\n    <svg id=\"stage\" width=\"500\" height=\"500\"></svg>\n<script>\n    const Flatten = window[\"@flatten-js/core\"];\n    const {point, circle, segment} = Flatten;\n\n    // make some construction\n    let s1 = segment(10,10,200,200);\n    let s2 = segment(10,160,200,30);\n    let c = circle(point(200, 110), 50);\n    let ip = s1.intersect(s2);\n\n    document.getElementById(\"stage\").innerHTML = s1.svg() + s2.svg() + c.svg() + ip[0].svg();\n</script>\n</body>\n```\n\nMethod `svg()` may accept as a parameter an object that enables to define\nseveral basic attributes of svg element:\n `stroke`, `strokeWidth`, `fill`, `fillRule`, `fillOpacity`, `id` and `className`.\n If attributes not provided, method `svg()` use default values.\n \n\n### Other packages\n\nOther packages, published under scope **@flatten-js/**:\n\n| Name                                                                                    |                                  Description                                  |\n|-----------------------------------------------------------------------------------------|:-----------------------------------------------------------------------------:|\n| [@flatten-js/interval-tree](https://www.npmjs.com/package/@flatten-js/interval-tree)    |                          Interval binary search tree                          |\n| [@flatten-js/boolean-op](https://www.npmjs.com/package/@flatten-js/boolean-op)          | Boolean operations (deprecated, use this functionality from the core package) |\n|  [@flatten-js/polygon-offset](https://www.npmjs.com/package/@flatten-js/polygon-offset) |                                Polygon offset                                 |\n\n## Support\n\n<a href=\"https://www.buymeacoffee.com/alexbol99\" target=\"_blank\"><img src=\"https://cdn.buymeacoffee.com/buttons/default-orange.png\" alt=\"Buy Me A Coffee\" height=\"41\" width=\"174\"></a>","users":{}}