Boolean operations on polygons
Polygon is actually a multi-polygon which may be comprised from a number of faces. The orientation of faces (clockwise or counterclockwise) is matter, because algorithm implemented in the way that it never changes an original direction of the edge. For the boolean operation to be performed correctly, faces have to fit the following rules:
- Each face is a non-degenerated simple closed polygon. In another words, face should not have self-intersections and its orientation may be strictly defined.
- If one face is totally inside another face, its orientation should be opposite to the orientation of external face. Then we will call external faces islands and internal faces holes. So the rule is "no island inside island and no hole inside hole".
- Faces of the polygon should not overlap each other
Bollean operation algorithm does not check that polygon fits these rules, this is on the responsibility of the caller.
The result of boolean operation is also a polygon. Note, that the resulted polygon may be empty, for example as the result of the intersection between two disjoint polygons.
Follow me on Twitter @alex_bol_
Flatten-boolean-op depends on the flatten-js 2d geometry library.
This library provides Polygon class model together with the methods to treat faces and edges.
Explore this library at https://github.com/alexbol99/flatten-js and see more useful classes and methods.
Your can choose either to install package in your project or to consume algorithm as a serice.
Install in your project
Install this package together with flatten-js library in your project using npm:
npm install flatten-js flatten-boolean-op --save
Then require package in your module, create two polygons using flatten-js library and call one of the methods:
// require flatten-boolean-op packagelet BooleanOp = ;let unify intersect subtract = BooleanOp;// require flatten-js library that provides polygon model and other geometrical primitiveslet Flatten = ;let Polygon point = Flatten;// create first polygonlet poly1 = ;poly1;// create second polygonlet poly2 = ;poly2;// apply boolean operation "unify"let poly = ;console; // expected 1console; // expected 8
Consume as a service
Instead of installing the package in your project you may choose to consume it as a service from https://algorithmia.com
Define your account in Algorithmia platform and get your API key
Install Algorithmia client
npm install --save algorithmia
Instantiate an Algorithmia client using your API key:
var algorithmia = ;var client = ;
- Submit new call to boolean operation algorithm using Algorithmia API
Algorithm accepts input as an array of 3 elements: two polygon operands and boolean operation identifier.
Boolean operation identifier is one of
Flatten.BOOLEAN_UNION, Flatten.BOOLEAN_SUBTRACT, Flatten.BOOLEAN_INTERSECT constants.
Polygon operand is JSON object, which is array of faces, where each face represented as an array of edges.
Polygon JSON object may be obtained using build-in
.toJSON() method of
Algorithmia client calls JSON.serialize(), submits query to the Algorithmia server and returns promise. When promise resolved, it returns the result as a polygon JSON object - array of faces
Each face may be added to polygon using
// require Algorithmia client and instantiate it using your API keylet algorithmia = ;let client = ;// require flatten-js library that provides polygon model and other geometrical primitiveslet Flatten = ;let Polygon point = Flatten;// create first polygonlet poly1 = ;poly1;// create second polygonlet poly2 = ;poly2;// prepare input array for calling algorithm on cloudlet input = poly1 poly2 FlattenBOOLEAN_UNION;// submit query;
See https://algorithmia.com/algorithms/alexbol99/PolygonBooleanOp algorithm page for more details
Algorithm implements the version of Kevin Weiler and Peter Atherton clipping algorithm, described in the article Hidden Surface Removal Using Polygon Area Sorting see https://www.cs.drexel.edu/~david/Classes/CS430/HWs/p214-weiler.pdf
In pseudocode, it may be described as below:
- The borders of the two polygons are compared for intersections. Detected intersection points marked by references to the face they were taken, and by arc length - the arc distance from the start of the first edge in face. Then intersection points are sorted by arc length.
- At each intersection point a new vertex is added into the contour chain of each of the polygons.
- Faces that have no intersections are processing for detection inclusion flag
- List of intersection points are processed for both polygons. For each chain of edges defined by pair of intersection points, detected its inclusion flag. It may be INSIDE, OUTSIDE or BOUNDARY. For BOUNDARY chains we will defined addition overlapping flag: OVERLAPPING_SAME or OVERLAPPING_OPPOSITE, which will tell us how to treat boundary chains.
- Depending on performing boolean operation, not relevant chains are removing from both polygons
- UNION: remove inner chains
- SUBTRACT: remove inner chains from the first polygon and outers chains from the second polygon
- INTERSECT: remove outer chains from the second polygon Boundary chains with flag OVERLAPPING_OPPOSITE are always removed
- Restore faces connecting interrupted chains from the first polygon to the correspondent chains from the second polygon
Remember that algorithm relies on the direction of the edges. It can find continuation of the interrupted chain only if edge from the second polygon is an precise continuation of the edge from the first one. That is why faces that have same meaning (island or hole) should have same orientation is both polygons.
Documentation may be found here https://alexbol99.github.io/flatten-boolean-op/index.html