@flatten-js/core

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width,initial-scale=1"> <title>Face - Documentation</title> <script src="scripts/prettify/prettify.js"></script> <script src="scripts/prettify/lang-css.js"></script>  <link type="text/css" rel="stylesheet" href="https://code.ionicframework.com/ionicons/2.0.1/css/ionicons.min.css"> <link type="text/css" rel="stylesheet" href="styles/prettify-tomorrow.css"> <link type="text/css" rel="stylesheet" href="styles/jsdoc-default.css"> </head> <body> <input type="checkbox" id="nav-trigger" class="nav-trigger" /> <label for="nav-trigger" class="navicon-button x"> <div class="navicon"></div> </label> <label for="nav-trigger" class="overlay"></label> <nav> <li class="nav-link nav-home-link"><a href="index.html">Home</a></li><li class="nav-heading">Classes</li><li class="nav-heading">C<a href="Arc.html">Arc</a></li><li class="nav-item">F<a href="Arc.html#clone">clone</a></li><li 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href="Circle.html#clone">clone</a></li><li class="nav-item">F<a href="Circle.html#contains">contains</a></li><li class="nav-item">F<a href="Circle.html#toArc">toArc</a></li><li class="nav-item">F<a href="Circle.html#intersect">intersect</a></li><li class="nav-item">F<a href="Circle.html#distanceTo">distanceTo</a></li><li class="nav-item">F<a href="Circle.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Circle.html#svg">svg</a></li><li class="nav-heading">C<a href="Edge.html">Edge</a></li><li class="nav-item">F<a href="Edge.html#middle">middle</a></li><li class="nav-item">F<a href="Edge.html#contains">contains</a></li><li class="nav-item">F<a href="Edge.html#setInclusion">setInclusion</a></li><li class="nav-item">F<a href="Edge.html#setOverlap">setOverlap</a></li><li class="nav-heading">C<a href="Face.html">Face</a></li><li class="nav-item">F<a href="Face.html#append">append</a></li><li class="nav-item">F<a href="Face.html#insert">insert</a></li><li class="nav-item">F<a href="Face.html#remove">remove</a></li><li class="nav-item">F<a href="Face.html#reverse">reverse</a></li><li class="nav-item">F<a href="Face.html#setArcLength">setArcLength</a></li><li class="nav-item">F<a href="Face.html#area">area</a></li><li class="nav-item">F<a href="Face.html#signedArea">signedArea</a></li><li class="nav-item">F<a href="Face.html#orientation">orientation</a></li><li class="nav-item">F<a href="Face.html#isSimple">isSimple</a></li><li class="nav-item">F<a href="Face.html#findEdgeByPoint">findEdgeByPoint</a></li><li class="nav-item">F<a href="Face.html#toPolygon">toPolygon</a></li><li class="nav-item">F<a href="Face.html#svg">svg</a></li><li class="nav-heading">C<a href="Line.html">Line</a></li><li class="nav-item">F<a href="Line.html#clone">clone</a></li><li class="nav-item">F<a href="Line.html#parallelTo">parallelTo</a></li><li class="nav-item">F<a href="Line.html#incidentTo">incidentTo</a></li><li class="nav-item">F<a href="Line.html#contains">contains</a></li><li class="nav-item">F<a href="Line.html#coord">coord</a></li><li class="nav-item">F<a href="Line.html#intersect">intersect</a></li><li class="nav-item">F<a href="Line.html#distanceTo">distanceTo</a></li><li class="nav-item">F<a href="Line.html#split">split</a></li><li class="nav-item">F<a href="Line.html#sortPoints">sortPoints</a></li><li class="nav-item">F<a href="Line.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Line.html#svg">svg</a></li><li class="nav-heading">C<a href="Matrix.html">Matrix</a></li><li class="nav-item">F<a href="Matrix.html#clone">clone</a></li><li class="nav-item">F<a href="Matrix.html#transform">transform</a></li><li class="nav-item">F<a href="Matrix.html#multiply">multiply</a></li><li class="nav-item">F<a href="Matrix.html#translate">translate</a></li><li class="nav-item">F<a href="Matrix.html#rotate">rotate</a></li><li class="nav-item">F<a href="Matrix.html#scale">scale</a></li><li class="nav-item">F<a href="Matrix.html#equalTo">equalTo</a></li><li class="nav-heading">C<a href="Multiline.html">Multiline</a></li><li class="nav-item">F<a href="Multiline.html#clone">clone</a></li><li class="nav-item">F<a href="Multiline.html#addVertex">addVertex</a></li><li class="nav-item">F<a href="Multiline.html#split">split</a></li><li class="nav-item">F<a href="Multiline.html#findEdgeByPoint">findEdgeByPoint</a></li><li class="nav-item">F<a href="Multiline.html#translate">translate</a></li><li class="nav-item">F<a href="Multiline.html#rotate">rotate</a></li><li class="nav-item">F<a href="Multiline.html#transform">transform</a></li><li class="nav-item">F<a href="Multiline.html#toShapes">toShapes</a></li><li class="nav-item">F<a href="Multiline.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Multiline.html#svg">svg</a></li><li class="nav-heading">C<a href="Point.html">Point</a></li><li class="nav-item">F<a href="Point.html#clone">clone</a></li><li class="nav-item">F<a href="Point.html#equalTo">equalTo</a></li><li class="nav-item">F<a href="Point.html#lessThan">lessThan</a></li><li class="nav-item">F<a href="Point.html#rotate">rotate</a></li><li class="nav-item">F<a href="Point.html#translate">translate</a></li><li class="nav-item">F<a href="Point.html#transform">transform</a></li><li class="nav-item">F<a href="Point.html#projectionOn">projectionOn</a></li><li class="nav-item">F<a href="Point.html#leftTo">leftTo</a></li><li class="nav-item">F<a href="Point.html#distanceTo">distanceTo</a></li><li class="nav-item">F<a href="Point.html#on">on</a></li><li class="nav-item">F<a href="Point.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Point.html#svg">svg</a></li><li class="nav-heading">C<a href="Polygon.html">Polygon</a></li><li class="nav-item">F<a href="Polygon.html#clone">clone</a></li><li class="nav-item">F<a href="Polygon.html#isEmpty">isEmpty</a></li><li class="nav-item">F<a href="Polygon.html#isValid">isValid</a></li><li class="nav-item">F<a href="Polygon.html#area">area</a></li><li class="nav-item">F<a href="Polygon.html#addFace">addFace</a></li><li class="nav-item">F<a href="Polygon.html#deleteFace">deleteFace</a></li><li class="nav-item">F<a href="Polygon.html#removeChain">removeChain</a></li><li class="nav-item">F<a href="Polygon.html#addVertex">addVertex</a></li><li class="nav-item">F<a href="Polygon.html#cut">cut</a></li><li class="nav-item">F<a href="Polygon.html#cutFace">cutFace</a></li><li class="nav-item">F<a href="Polygon.html#findEdgeByPoint">findEdgeByPoint</a></li><li class="nav-item">F<a href="Polygon.html#splitToIslands">splitToIslands</a></li><li class="nav-item">F<a href="Polygon.html#reverse">reverse</a></li><li class="nav-item">F<a href="Polygon.html#contains">contains</a></li><li class="nav-item">F<a href="Polygon.html#distanceTo">distanceTo</a></li><li class="nav-item">F<a href="Polygon.html#intersect">intersect</a></li><li class="nav-item">F<a href="Polygon.html#translate">translate</a></li><li class="nav-item">F<a href="Polygon.html#rotate">rotate</a></li><li class="nav-item">F<a href="Polygon.html#transform">transform</a></li><li class="nav-item">F<a href="Polygon.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Polygon.html#toArray">toArray</a></li><li class="nav-item">F<a href="Polygon.html#svg">svg</a></li><li class="nav-heading">C<a href="Ray.html">Ray</a></li><li class="nav-item">F<a href="Ray.html#clone">clone</a></li><li class="nav-item">F<a href="Ray.html#contains">contains</a></li><li class="nav-item">F<a href="Ray.html#split">split</a></li><li class="nav-item">F<a href="Ray.html#intersect">intersect</a></li><li class="nav-item">F<a href="Ray.html#svg">svg</a></li><li class="nav-heading">C<a href="Segment.html">Segment</a></li><li class="nav-item">F<a href="Segment.html#clone">clone</a></li><li class="nav-item">F<a href="Segment.html#equalTo">equalTo</a></li><li class="nav-item">F<a href="Segment.html#contains">contains</a></li><li class="nav-item">F<a href="Segment.html#intersect">intersect</a></li><li class="nav-item">F<a href="Segment.html#distanceTo">distanceTo</a></li><li class="nav-item">F<a href="Segment.html#tangentInStart">tangentInStart</a></li><li class="nav-item">F<a href="Segment.html#tangentInEnd">tangentInEnd</a></li><li class="nav-item">F<a href="Segment.html#reverse">reverse</a></li><li class="nav-item">F<a href="Segment.html#split">split</a></li><li class="nav-item">F<a href="Segment.html#middle">middle</a></li><li class="nav-item">F<a href="Segment.html#translate">translate</a></li><li class="nav-item">F<a href="Segment.html#rotate">rotate</a></li><li class="nav-item">F<a href="Segment.html#transform">transform</a></li><li class="nav-item">F<a href="Segment.html#isZeroLength">isZeroLength</a></li><li class="nav-item">F<a href="Segment.html#sortPoints">sortPoints</a></li><li class="nav-item">F<a href="Segment.html#toJSON">toJSON</a></li><li class="nav-item">F<a href="Segment.html#svg">svg</a></li><li class="nav-heading">C<a href="Vector.html">Vector</a></li><li class="nav-item">F<a href="Vector.html#clone">clone</a></li><li class="nav-item">F<a href="Vector.html#equalTo">equalTo</a></li><li class="nav-item">F<a href="Vector.html#multiply">multiply</a></li><li class="nav-item">F<a href="Vector.html#dot">dot</a></li><li class="nav-item">F<a href="Vector.html#cross">cross</a></li><li class="nav-item">F<a href="Vector.html#normalize">normalize</a></li><li class="nav-item">F<a href="Vector.html#rotate">rotate</a></li><li class="nav-item">F<a href="Vector.html#rotate90CCW">rotate90CCW</a></li><li class="nav-item">F<a href="Vector.html#rotate90CW">rotate90CW</a></li><li class="nav-item">F<a href="Vector.html#invert">invert</a></li><li class="nav-item">F<a href="Vector.html#add">add</a></li><li class="nav-item">F<a href="Vector.html#subtract">subtract</a></li><li class="nav-item">F<a href="Vector.html#angleTo">angleTo</a></li><li class="nav-item">F<a href="Vector.html#projectionOn">projectionOn</a></li><li class="nav-item">F<a href="Vector.html#toJSON">toJSON</a></li><li class="nav-heading">C<a href="CircularLinkedList.html">CircularLinkedList</a></li><li class="nav-item">F<a href="CircularLinkedList.html#append">append</a></li><li class="nav-item">F<a href="CircularLinkedList.html#insert">insert</a></li><li class="nav-item">F<a href="CircularLinkedList.html#remove">remove</a></li><li class="nav-heading">C<a href="DE9IM.html">DE9IM</a></li><li class="nav-item">F<a href="DE9IM.html#toString">toString</a></li><li class="nav-heading">C<a href="LinkedList.html">LinkedList</a></li><li class="nav-item">F<a href="LinkedList.html#toArray">toArray</a></li><li class="nav-item">F<a href="LinkedList.html#append">append</a></li><li class="nav-item">F<a href="LinkedList.html#insert">insert</a></li><li class="nav-item">F<a href="LinkedList.html#remove">remove</a></li><li class="nav-item">F<a href="LinkedList.html#isEmpty">isEmpty</a></li><li class="nav-item">F<a href="LinkedList.html#.testInfiniteLoop">testInfiniteLoop</a></li><li class="nav-heading">C<a href="PlanarSet.html">PlanarSet</a></li><li class="nav-item">F<a href="PlanarSet.html#add">add</a></li><li class="nav-item">F<a href="PlanarSet.html#delete">delete</a></li><li class="nav-item">F<a href="PlanarSet.html#clear">clear</a></li><li class="nav-item">F<a href="PlanarSet.html#search">search</a></li><li class="nav-item">F<a href="PlanarSet.html#hit">hit</a></li><li class="nav-item">F<a href="PlanarSet.html#svg">svg</a></li><li class="nav-heading">C<a href="Errors.html">Errors</a></li><li class="nav-heading">Modules</li><li class="nav-heading">M<a href="module-BooleanOperations.html">BooleanOperations</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.unify">unify</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.subtract">subtract</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.intersect">intersect</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.innerClip">innerClip</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.outerClip">outerClip</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.calculateIntersections">calculateIntersections</a></li><li class="nav-heading">M<a href="module-RayShoot.html">RayShoot</a></li><li class="nav-item">F<a href="module-RayShoot.html#.ray_shoot">ray_shoot</a></li><li class="nav-heading">M<a href="module-Relation.html">Relation</a></li><li class="nav-item">F<a href="module-Relation.html#.equal">equal</a></li><li class="nav-item">F<a href="module-Relation.html#.intersect">intersect</a></li><li class="nav-item">F<a href="module-Relation.html#.touch">touch</a></li><li class="nav-item">F<a href="module-Relation.html#.disjoint">disjoint</a></li><li class="nav-item">F<a href="module-Relation.html#.inside">inside</a></li><li class="nav-item">F<a href="module-Relation.html#.covered">covered</a></li><li class="nav-item">F<a href="module-Relation.html#.contain">contain</a></li><li class="nav-item">F<a href="module-Relation.html#.cover">cover</a></li><li class="nav-item">F<a href="module-Relation.html#.relate">relate</a></li><li class="nav-heading"><a href="global.html">Globals</a></li><li class="nav-item">F<a href="global.html#inverse">inverse</a></li><li class="nav-item">M<a href="global.html#arc">arc</a></li><li class="nav-item">M<a href="global.html#box">box</a></li><li class="nav-item">M<a href="global.html#circle">circle</a></li><li class="nav-item">M<a href="global.html#line">line</a></li><li class="nav-item">M<a href="global.html#matrix">matrix</a></li><li class="nav-item">M<a href="global.html#multiline">multiline</a></li><li class="nav-item">M<a href="global.html#point">point</a></li><li class="nav-item">M<a href="global.html#polygon">polygon</a></li><li class="nav-item">M<a href="global.html#segment">segment</a></li><li class="nav-item">M<a href="global.html#vector">vector</a></li><li class="nav-item">M<a href="global.html#CCW">CCW</a></li><li class="nav-item">M<a href="global.html#CW">CW</a></li><li class="nav-item">M<a href="global.html#ORIENTATION">ORIENTATION</a></li><li class="nav-item">M<a href="global.html#DP_TOL">DP_TOL</a></li><li class="nav-item">F<a href="global.html#setTolerance">setTolerance</a></li><li class="nav-item">F<a href="global.html#getTolerance">getTolerance</a></li><li class="nav-item">F<a href="global.html#EQ_0">EQ_0</a></li><li class="nav-item">F<a href="global.html#EQ">EQ</a></li><li class="nav-item">F<a href="global.html#GT">GT</a></li><li class="nav-item">F<a href="global.html#GE">GE</a></li><li class="nav-item">F<a href="global.html#LT">LT</a></li><li class="nav-item">F<a href="global.html#LE">LE</a></li> </nav> <div id="main"> <h1 class="page-title">Face</h1> <section> <header> <h2> Face </h2> <div class="class-description">Class representing a face (closed loop) in a <code>polygon</code> object. Face is a circular bidirectional linked list of <code>edges</code>. Face object cannot be instantiated with a constructor. Instead, use <code>polygon.addFace()</code> method. Note, that face only set entry point to the linked list of edges but does not contain edges by itself. Container of edges is a property of the polygon object. </div> </header> <article> <div class="container-overview"> <div class="section-method"> <h2>Constructor</h2> <h4 class="name" id="Face">new Face()</h4> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line33">line 33</a> </li></ul></dd> </dl> <div class="section-examples"> <h5>Example</h5> <pre class="prettyprint"><code>// Face implements "next" iterator which enables to iterate edges in for loop: for (let edge of face) { console.log(edge.shape.length) // do something } // Instead, it is possible to iterate edges as linked list, starting from face.first: let edge = face.first; do { console.log(edge.shape.length); // do something edge = edge.next; } while (edge != face.first)</code></pre> </div> </div> </div> <h3 class="subsection-title">Classes</h3> <dl> <dt><a href="Face.html">Face</a></dt> <dd></dd> </dl> <h3 class="subsection-title">Members</h3> <div class="section-members"> <h4 class="name" id="_box">_box</h4> <div class="description"> Reference to the last edge in face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line44">line 44</a> </li></ul></dd> </dl> </div> <div class="section-members"> <h4 class="name" id="edges">edges</h4> <div class="description"> Return array of edges from first to last </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line141">line 141</a> </li></ul></dd> </dl> </div> <div class="section-members"> <h4 class="name" id="shapes">shapes</h4> <div class="description"> Return array of shapes which comprise face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line149">line 149</a> </li></ul></dd> </dl> </div> <div class="section-members"> <h4 class="name" id="box">box</h4> <div class="description"> Return bounding box of the face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line157">line 157</a> </li></ul></dd> </dl> </div> <h3 class="subsection-title">Methods</h3> <div class="section-method"> <h4 class="name" id="append">append(edge) → {<a href="Face.html">Face</a>}</h4> <div class="description"> Append edge after the last edge of the face (and before the first edge). </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line194">line 194</a> </li></ul></dd> </dl> <h5>Parameters:</h5> <table class="params"> <thead> <tr> <th>Name</th> <th>Type</th> <th class="last">Description</th> </tr> </thead> <tbody> <tr> <td class="name"><code>edge</code></td> <td class="type"> <code><a href="Edge.html">Edge</a></code> </td> <td class="description last"> Edge to be appended to the linked list </td> </tr> </tbody> </table> <div class="section-returns"> <h5>Returns:</h5> <dl class="param-type"> <dt> Type: </dt> <dd> <code><a href="Face.html">Face</a></code> </dd> </dl> </div> </div> <div class="section-method"> <h4 class="name" id="insert">insert(newEdge, edgeBefore) → {<a href="Face.html">Face</a>}</h4> <div class="description"> Insert edge newEdge into the linked list after the edge edgeBefore </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line209">line 209</a> </li></ul></dd> </dl> <h5>Parameters:</h5> <table class="params"> <thead> <tr> <th>Name</th> <th>Type</th> <th class="last">Description</th> </tr> </thead> <tbody> <tr> <td class="name"><code>newEdge</code></td> <td class="type"> <code><a href="Edge.html">Edge</a></code> </td> <td class="description last"> Edge to be inserted into linked list </td> </tr> <tr> <td class="name"><code>edgeBefore</code></td> <td class="type"> <code><a href="Edge.html">Edge</a></code> </td> <td class="description last"> Edge to insert newEdge after it </td> </tr> </tbody> </table> <div class="section-returns"> <h5>Returns:</h5> <dl class="param-type"> <dt> Type: </dt> <dd> <code><a href="Face.html">Face</a></code> </dd> </dl> </div> </div> <div class="section-method"> <h4 class="name" id="remove">remove(edge) → {<a href="Face.html">Face</a>}</h4> <div class="description"> Remove the given edge from the linked list of the face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line222">line 222</a> </li></ul></dd> </dl> <h5>Parameters:</h5> <table class="params"> <thead> <tr> <th>Name</th> <th>Type</th> <th class="last">Description</th> </tr> </thead> <tbody> <tr> <td class="name"><code>edge</code></td> <td class="type"> <code><a href="Edge.html">Edge</a></code> </td> <td class="description last"> Edge to be removed </td> </tr> </tbody> </table> <div class="section-returns"> <h5>Returns:</h5> <dl class="param-type"> <dt> Type: </dt> <dd> <code><a href="Face.html">Face</a></code> </dd> </dl> </div> </div> <div class="section-method"> <h4 class="name" id="reverse">reverse()</h4> <div class="description"> Reverse orientation of the face: first edge become last and vice a verse, all edges starts and ends swapped, direction of arcs inverted. If face was oriented clockwise, it becomes counter clockwise and vice versa </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line234">line 234</a> </li></ul></dd> </dl> </div> <div class="section-method"> <h4 class="name" id="setArcLength">setArcLength()</h4> <div class="description"> Set arc_length property for each of the edges in the face. Arc_length of the edge it the arc length from the first edge of the face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line283">line 283</a> </li></ul></dd> </dl> </div> <div class="section-method"> <h4 class="name" id="area">area() → {number}</h4> <div class="description"> Returns the absolute value of the area of the face </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line302">line 302</a> </li></ul></dd> </dl> <div class="section-returns"> <h5>Returns:</h5> <dl class="param-type"> <dt> Type: </dt> <dd> <code>number</code> </dd> </dl> </div> </div> <div class="section-method"> <h4 class="name" id="signedArea">signedArea() → {number}</h4> <div class="description"> Returns signed area of the simple face. Face is simple if it has no self intersections that change its orientation. Then the area will be positive if the orientation of the face is clockwise, and negative if orientation is counterclockwise. It may be zero if polygon is degenerated. </div> <dl class="details"> <dt class="tag-source">Source:</dt> <dd class="tag-source"><ul class="dummy"><li> <a href="classes_face.js.html">classes/face.js</a>, <a href="classes_face.js.html#line314">line 314</a> </li></ul></dd> </dl> <div class="section-returns"> <h5>Returns:</h5> <dl class="param-type"> <dt> Type: </dt> <dd> <code>number</code> </dd> </dl> </div> </div> <div class="section-method"> <h4 class="name" id="orientation">orientation() → {number}</h4> <div class="description"> Return face orientation: one of Flatten.ORIENTATION.CCW, Flatten.ORIENTATION.CW, Flatten.ORIENTATION.NOT_ORIENTABLE According to Green theorem the area of a closed curve may be calculated as double integral, and the sign of the integral will be