openlayers/tests/Geometry/Polygon.html

   1 <html>
   2 <head>
   3   <script src="../../lib/OpenLayers.js"></script>
   4   <script type="text/javascript">
   5     var polygon;
   6     var components = [new OpenLayers.Geometry.Point(10,14), new OpenLayers.Geometry.Point(5,3)];
   7     var components2 = [new OpenLayers.Geometry.Point(12,15), new OpenLayers.Geometry.Point(2,3), new OpenLayers.Geometry.Point(10,0), new OpenLayers.Geometry.Point(10,10)];
   8     var linearRing = new OpenLayers.Geometry.LinearRing(components);
   9     var linearRing2 = new OpenLayers.Geometry.LinearRing(components2);
  10
  11     function test_Polygon_constructor (t) {
  12         t.plan( 3 );
  13         polygon = new OpenLayers.Geometry.Polygon();
  14         t.ok( polygon instanceof OpenLayers.Geometry.Polygon, "new OpenLayers.Geometry.Polygon returns polygon object" );
  15         t.eq( polygon.CLASS_NAME, "OpenLayers.Geometry.Polygon", "polygon.CLASS_NAME is set correctly");
  16         t.eq( polygon.components.length, 0, "polygon.components is set correctly");
  17     }
  18
  19     function test_Polygon_constructor (t) {
  20         t.plan( 3 );
  21         polygon = new OpenLayers.Geometry.Polygon([linearRing]);
  22         t.ok( polygon instanceof OpenLayers.Geometry.Polygon, "new OpenLayers.Geometry.Polygon returns polygon object" );
  23         t.eq( polygon.CLASS_NAME, "OpenLayers.Geometry.Polygon", "polygon.CLASS_NAME is set correctly");
  24         t.eq( polygon.components.length, 1, "polygon.components.length is set correctly");
  25     }
  26
  27     function test_Polygon_constructor (t) {
  28         t.plan( 3 );
  29         polygon = new OpenLayers.Geometry.Polygon([linearRing, linearRing2]);
  30         t.ok( polygon instanceof OpenLayers.Geometry.Polygon, "new OpenLayers.Geometry.Polygon returns polygon object" );
  31         t.eq( polygon.CLASS_NAME, "OpenLayers.Geometry.Polygon", "polygon.CLASS_NAME is set correctly");
  32         t.eq( polygon.components.length, 2, "polygon.components.length is set correctly");
  33     }
  34
  35     function test_Polygon_transform_getBounds (t) {
  36         t.plan(3);
  37
  38         var components = [new OpenLayers.Geometry.Point(10,14), new OpenLayers.Geometry.Point(5,3)];
  39         var linearRing = new OpenLayers.Geometry.LinearRing(components);
  40         polygon = new OpenLayers.Geometry.Polygon([linearRing.clone()]);
  41         polygon.calculateBounds();
  42         t.ok( polygon.bounds != null, "bounds calculated by calcBounds" );
  43         polygon.transform(new OpenLayers.Projection("EPSG:4326"),
  44                         new OpenLayers.Projection("EPSG:900913"));
  45         t.eq(polygon.bounds, null, "Point bounds cleared after transform");
  46         t.eq(polygon.getBounds().toBBOX(), "556597.453889,334111.171355,1113194.907778,1574216.547942", "Bounds are correct")
  47     }
  48
  49     function test_Polygon_getArea(t) {
  50         t.plan( 5 );
  51
  52       //no components
  53         var polygon = new OpenLayers.Geometry.Polygon();
  54         t.eq(polygon.getArea(), 0, "getArea empty polygon is 0");
  55
  56         var createSquareRing = function(area) {
  57             var points = [
  58                 new OpenLayers.Geometry.Point(0, 0),
  59                 new OpenLayers.Geometry.Point(0, area),
  60                 new OpenLayers.Geometry.Point(area, area),
  61                 new OpenLayers.Geometry.Point(area, 0)
  62             ];
  63             var ring = new OpenLayers.Geometry.LinearRing(points);
  64             return ring;
  65         };
  66
  67
  68       //simple polygon
  69         var comps = [ createSquareRing(2) ];
  70
  71         var polygon = new OpenLayers.Geometry.Polygon(comps);
  72         t.eq(polygon.getArea(), 4, "getArea simple polygon works lovely");
  73
  74       //polygon with holes
  75         comps = [ createSquareRing(10),
  76                            createSquareRing(2),
  77                            createSquareRing(3),
  78                            createSquareRing(4)
  79                          ];
  80
  81         var polygon = new OpenLayers.Geometry.Polygon(comps);
  82         t.eq(polygon.getArea(), 71, "getArea polygon with holes works lovely");
  83
  84       //simple polygon negative
  85         comps = [ createSquareRing(-2) ];
  86
  87         var polygon = new OpenLayers.Geometry.Polygon(comps);
  88         t.eq(polygon.getArea(), 4, "getArea simple polygon negative works lovely");
  89
  90       //polygon with holes negative
  91         comps = [ createSquareRing(-10),
  92                            createSquareRing(-2),
  93                            createSquareRing(-3),
  94                            createSquareRing(-4)
  95                          ];
  96
  97         var polygon = new OpenLayers.Geometry.Polygon(comps);
  98         t.eq(polygon.getArea(), 71, "getArea negative polygon with holes works lovely");
  99
 100     }
 101
 102     function test_Polygon_move(t) {
 103         t.plan(4);
 104
 105         polygon = new OpenLayers.Geometry.Polygon([linearRing, linearRing2]);
 106
 107         var x = linearRing.components[0].x;
 108         var y = linearRing.components[0].y;
 109         var x2 = linearRing2.components[0].x;
 110         var y2 = linearRing2.components[0].y;
 111
 112         var dx = 10 * Math.random();
 113         var dy = 10 * Math.random();
 114
 115         polygon.move(dx, dy);
 116
 117         t.eq(polygon.components[0].components[0].x, x + dx, "move() correctly modifies first x");
 118         t.eq(polygon.components[0].components[0].y, y + dy, "move() correctly modifies first y");
 119         t.eq(polygon.components[1].components[0].x, x2 + dx, "move() correctly modifies second x");
 120         t.eq(polygon.components[1].components[0].y, y2 + dy, "move() correctly modifies second y");
 121     }
 122
 123     function test_Polygon_rotate(t) {
 124         t.plan(6);
 125
 126         var geometry = new OpenLayers.Geometry.Polygon([linearRing, linearRing2]);
 127
 128         var originals = [];
 129         var comp;
 130         var angle = 2 * Math.PI * Math.random();
 131         var origin = new OpenLayers.Geometry.Point(10 * Math.random(),
 132                                                    10 * Math.random());
 133         for(var i=0; i<geometry.components.length; ++i) {
 134             comp = geometry.components[i];
 135             originals[i] = comp.rotate;
 136             comp.rotate = function(a, o) {
 137                 t.ok(true, "rotate called for component " + i);
 138                 t.ok(a == angle, "rotate called with correct angle");
 139                 t.ok(o == origin, "rotate called with correct origin");
 140             }
 141         }
 142         geometry.rotate(angle, origin);
 143
 144         // restore the original rotate defs
 145         for(var i=0; i<geometry.components.length; ++i) {
 146             comp.rotate = originals[i];
 147         }
 148     }
 149
 150     function test_Polygon_resize(t) {
 151         t.plan(8);
 152
 153         var tolerance = 1e-10;
 154         var geometry = new OpenLayers.Geometry.Polygon([linearRing, linearRing2]);
 155         var origin = new OpenLayers.Geometry.Point(10 * Math.random(),
 156                                                    10 * Math.random());
 157         var scale = 10 * Math.random();
 158
 159         var oldArea = geometry.getArea();
 160         var oldPerimeter = geometry.getLength();
 161         geometry.resize(scale, origin);
 162         var newArea = geometry.getArea();
 163         var newPerimeter = geometry.getLength();
 164
 165         t.ok((((newArea / oldArea) - (scale * scale)) / (scale * scale)) < tolerance,
 166              "resize correctly changes the area of a polygon")
 167         t.ok((((newPerimeter / oldPerimeter) - scale) / scale) < tolerance,
 168              "resize correctly changes the perimeter of a polygon")
 169
 170         var originals = [];
 171         var comp;
 172         for(var i=0; i<geometry.components.length; ++i) {
 173             comp = geometry.components[i];
 174             originals[i] = comp.resize;
 175             comp.resize = function(s, o) {
 176                 t.ok(true, "resize called for component " + i);
 177                 t.ok(s == scale, "resize called with correct scale");
 178                 t.ok(o == origin, "resize called with correct origin");
 179             }
 180         }
 181         geometry.resize(scale, origin);
 182
 183         // restore the original resize defs
 184         for(var i=0; i<geometry.components.length; ++i) {
 185             comp.resize = originals[i];
 186         }
 187
 188     }
 189
 190     function test_Polygon_createRegular(t) {
 191         t.plan(22);
 192         var sides = 40;
 193         var poly = OpenLayers.Geometry.Polygon.createRegularPolygon(new OpenLayers.Geometry.Point(5,0), 6, sides);
 194         var polyBounds = poly.getBounds();
 195         t.eq(polyBounds.toBBOX(), "-0.981504,-5.981504,10.981504,5.981504", sides + " sided figure generates correct bbox.");
 196         t.eq(poly.components.length, 1, "Poly has one linear ring");
 197         t.eq(poly.components[0].components.length, sides + 1, "ring has 41 components");
 198         t.eq(poly.components[0].components[0].id, poly.components[0].components[sides].id, "ring starts and ends with same geom");
 199         t.eq(Math.round(poly.getArea()), Math.round(Math.PI * 36), "area of "+sides+" sided poly rounds to same area as a circle.");
 200
 201         var sides = 3;
 202         var poly = OpenLayers.Geometry.Polygon.createRegularPolygon(new OpenLayers.Geometry.Point(5,0), 6, sides);
 203         var polyBounds = poly.getBounds();
 204         t.eq(polyBounds.toBBOX(), "-0.196152,-3,10.196152,6", sides + " sided figure generates correct bbox.");
 205         t.eq(poly.components.length, 1, "Poly has one linear ring");
 206         t.eq(poly.components[0].components.length, sides + 1, "ring has  correct count of  components");
 207         t.eq(poly.components[0].components[0].id, poly.components[0].components[sides].id, "ring starts and ends with same geom");
 208         t.eq(Math.round(poly.getArea()), 47, "area of 3 sided poly is correct");
 209
 210         var sides = 3;
 211         var poly3 = OpenLayers.Geometry.Polygon.createRegularPolygon(new OpenLayers.Geometry.Point(10,0), 15, sides);
 212         var polyBounds = poly3.getBounds();
 213         t.eq(polyBounds.toBBOX(), "-2.990381,-7.5,22.990381,15", sides + " sided figure generates correct bbox.");
 214         t.eq(Math.round(polyBounds.getCenterLonLat().lon), 10, "longitude of center of bounds is same as origin");
 215         t.eq(poly3.components.length, 1, "Poly has one linear ring");
 216         t.eq(poly3.components[0].components.length, sides + 1, "ring has  correct count of  components");
 217         t.eq(poly3.components[0].components[0].id, poly3.components[0].components[sides].id, "ring starts and ends with same geom");
 218         t.ok(poly3.getArea() > poly.getArea(), "area with radius 15 > poly with radius 6");
 219
 220         var sides = 4;
 221         var poly4 = OpenLayers.Geometry.Polygon.createRegularPolygon(new OpenLayers.Geometry.Point(10,0), 15, sides);
 222         var polyBounds = poly4.getBounds();
 223         t.eq(polyBounds.toBBOX(), "-0.606602,-10.606602,20.606602,10.606602", sides + " sided figure generates correct bbox.");
 224         t.eq(Math.round(polyBounds.getCenterLonLat().lon), 10, "longitude of center of bounds is same as origin");
 225         t.eq(poly4.components.length, 1, "Poly has one linear ring");
 226         t.eq(poly4.components[0].components.length, sides + 1, "ring has  correct count of  components");
 227         t.eq(poly4.components[0].components[0].id, poly4.components[0].components[sides].id, "ring starts and ends with same geom");
 228         t.ok(poly4.getArea() > poly3.getArea(), "square with radius 15 > triangle with radius 15");
 229     }
 230
 231     function test_Polygon_equals(t) {
 232         t.plan(3);
 233
 234         var x0 = Math.random() * 100;
 235         var y0 = Math.random() * 100;
 236         var x1 = Math.random() * 100;
 237         var y1 = Math.random() * 100;
 238         var x2 = Math.random() * 100;
 239         var y2 = Math.random() * 100;
 240         var point0 = new OpenLayers.Geometry.Point(x0, y0);
 241         var point1 = new OpenLayers.Geometry.Point(x1, y1);
 242         var point2 = new OpenLayers.Geometry.Point(x2, y2);
 243         var pointX = new OpenLayers.Geometry.Point(x0 + 1, y0);
 244         var pointY = new OpenLayers.Geometry.Point(x0, y0 + 1);
 245         var geometry = new OpenLayers.Geometry.Polygon([
 246                             new OpenLayers.Geometry.LinearRing([point0, point1, point2])]);
 247         var equal = new OpenLayers.Geometry.Polygon([
 248                             new OpenLayers.Geometry.LinearRing([point0, point1, point2])]);
 249         var offX = new OpenLayers.Geometry.Polygon([
 250                             new OpenLayers.Geometry.LinearRing([pointX, point1, point2])]);
 251         var offY = new OpenLayers.Geometry.Polygon([
 252                             new OpenLayers.Geometry.LinearRing([pointY, point1, point2])]);
 253         t.ok(geometry.equals(equal),
 254              "equals() returns true for a geometry with equivalent coordinates");
 255         t.ok(!geometry.equals(offX),
 256              "equals() returns false for a geometry with offset x");
 257         t.ok(!geometry.equals(offY),
 258              "equals() returns false for a geometry with offset y");
 259     }
 260
 261     function test_distanceTo(t) {
 262         var wkt = OpenLayers.Geometry.fromWKT;
 263         var geoms = [
 264             wkt("POLYGON((0 3, 1 4, 2 3, 1 2, 0 3))"),
 265             wkt("POINT(0 0)"),
 266             wkt("LINESTRING(-2 0, 0 -2, 2 -1, 2 0)"),
 267             wkt("LINESTRING(0 2, 1 3)"),
 268             wkt("POINT(1 3)")
 269         ];
 270
 271         var cases = [{
 272             got: geoms[0].distanceTo(geoms[1]),
 273             expected: Math.sqrt(5)
 274         }, {
 275             got: geoms[0].distanceTo(geoms[1], {details: true}),
 276             expected: {
 277                 distance: Math.sqrt(5),
 278                 x0: 1, y0: 2,
 279                 x1: 0, y1: 0
 280             }
 281         }, {
 282             got: geoms[0].distanceTo(geoms[2], {details: true}),
 283             expected: {
 284                 distance: Math.sqrt(5),
 285                 x0: 1, y0: 2,
 286                 x1: 2, y1: 0
 287             }
 288         }, {
 289             got: geoms[0].distanceTo(geoms[3], {details: true}),
 290             expected: {
 291                 distance: 0,
 292                 x0: 0.5, y0: 2.5,
 293                 x1: 0.5, y1: 2.5
 294             }
 295         }, {
 296             got: geoms[0].distanceTo(geoms[4]),
 297             expected: Math.sqrt(0.5)
 298         }, {
 299             got: geoms[0].distanceTo(geoms[4], {edge: false}),
 300             expected: 0
 301         }];
 302
 303         t.plan(cases.length);
 304         for(var i=0; i<cases.length; ++i) {
 305             t.eq(cases[i].got, cases[i].expected, "case " + i);
 306         }
 307
 308     }
 309
 310     function test_getVertices(t) {
 311         t.plan(6);
 312
 313         var points = [
 314             new OpenLayers.Geometry.Point(10, 20),
 315             new OpenLayers.Geometry.Point(20, 30),
 316             new OpenLayers.Geometry.Point(30, 40),
 317             new OpenLayers.Geometry.Point(40, 50)
 318         ];
 319         var polygon = new OpenLayers.Geometry.Polygon([
 320             new OpenLayers.Geometry.LinearRing(points)
 321         ]);
 322
 323         var verts = polygon.getVertices();
 324         t.ok(verts instanceof Array, "got back an array");
 325         t.eq(verts.length, points.length, "of correct length length");
 326         t.geom_eq(verts[0], points[0], "0: correct geometry");
 327         t.geom_eq(verts[1], points[1], "1: correct geometry");
 328         t.geom_eq(verts[2], points[2], "2: correct geometry");
 329         t.geom_eq(verts[3], points[3], "3: correct geometry");
 330
 331     }
 332
 333     function test_Polygon_clone(t) {
 334         t.plan(2);
 335
 336         var x0 = Math.random() * 100;
 337         var y0 = Math.random() * 100;
 338         var x1 = Math.random() * 100;
 339         var y1 = Math.random() * 100;
 340         var x2 = Math.random() * 100;
 341         var y2 = Math.random() * 100;
 342         var point0 = new OpenLayers.Geometry.Point(x0, y0);
 343         var point1 = new OpenLayers.Geometry.Point(x1, y1);
 344         var point2 = new OpenLayers.Geometry.Point(x2, y2);
 345         var geometry = new OpenLayers.Geometry.Polygon([
 346                             new OpenLayers.Geometry.LinearRing([point0, point1, point2])]);
 347         var clone = geometry.clone();
 348         t.ok(clone instanceof OpenLayers.Geometry.Polygon,
 349              "clone() creates an OpenLayers.Geometry.Polygon");
 350         t.ok(geometry.equals(clone), "clone has equivalent coordinates");
 351     }
 352
 353     function test_getGeodesicArea(t) {
 354
 355         t.plan(1);
 356
 357         // from the wfs-states.html example
 358         var illinois = OpenLayers.Geometry.fromWKT(
 359             "MULTIPOLYGON(((-88.071564 37.51099,-88.087883 37.476273,-88.311707 37.442852,-88.359177 37.409309,-88.419853 37.420292,-88.467644 37.400757,-88.511322 37.296852,-88.501427 37.257782,-88.450699 37.205669,-88.422516 37.15691,-88.45047 37.098671,-88.476799 37.072144,-88.4907 37.06818,-88.517273 37.06477,-88.559273 37.072815,-88.61422 37.109047,-88.68837 37.13541,-88.739113 37.141182,-88.746506 37.152107,-88.863289 37.202194,-88.932503 37.218407,-88.993172 37.220036,-89.065033 37.18586,-89.116821 37.112137,-89.146347 37.093185,-89.169548 37.064236,-89.174332 37.025711,-89.150246 36.99844,-89.12986 36.988113,-89.193512 36.986771,-89.210052 37.028973,-89.237679 37.041733,-89.264053 37.087124,-89.284233 37.091244,-89.303291 37.085384,-89.3097 37.060909,-89.264244 37.027733,-89.262001 37.008686,-89.282768 36.999207,-89.310982 37.009682,-89.38295 37.049213,-89.37999 37.099083,-89.423798 37.137203,-89.440521 37.165318,-89.468216 37.224266,-89.465309 37.253731,-89.489594 37.256001,-89.513885 37.276402,-89.513885 37.304962,-89.50058 37.329441,-89.468742 37.339409,-89.435738 37.355717,-89.427574 37.411018,-89.453621 37.453186,-89.494781 37.491726,-89.524971 37.571957,-89.513367 37.615929,-89.51918 37.650375,-89.513374 37.67984,-89.521523 37.694798,-89.581436 37.706104,-89.666458 37.745453,-89.675858 37.78397,-89.691055 37.804794,-89.728447 37.840992,-89.851715 37.905064,-89.861046 37.905487,-89.866814 37.891876,-89.900551 37.875904,-89.937874 37.878044,-89.978912 37.911884,-89.958229 37.963634,-90.010811 37.969318,-90.041924 37.993206,-90.119339 38.032272,-90.134712 38.053951,-90.207527 38.088905,-90.254059 38.122169,-90.289635 38.166817,-90.336716 38.188713,-90.364769 38.234299,-90.369347 38.323559,-90.358688 38.36533,-90.339607 38.390846,-90.301842 38.427357,-90.265785 38.518688,-90.26123 38.532768,-90.240944 38.562805,-90.183708 38.610271,-90.183578 38.658772,-90.20224 38.700363,-90.196571 38.723965,-90.163399 38.773098,-90.135178 38.785484,-90.121727 38.80051,-90.113121 38.830467,-90.132812 38.853031,-90.243927 38.914509,-90.278931 38.924717,-90.31974 38.924908,-90.413071 38.96233,-90.469841 38.959179,-90.530426 38.891609,-90.570328 38.871326,-90.627213 38.880795,-90.668877 38.935253,-90.70607 39.037792,-90.707588 39.058178,-90.690399 39.0937,-90.716736 39.144211,-90.718193 39.195873,-90.732338 39.224747,-90.738083 39.24781,-90.779343 39.296803,-90.850494 39.350452,-90.947891 39.400585,-91.036339 39.444412,-91.064384 39.473984,-91.093613 39.528927,-91.156189 39.552593,-91.203247 39.600021,-91.317665 39.685917,-91.367088 39.72464,-91.373421 39.761272,-91.381714 39.803772,-91.449188 39.863049,-91.450989 39.885242,-91.434052 39.901829,-91.430389 39.921837,-91.447243 39.946064,-91.487289 40.005753,-91.504005 40.066711,-91.516129 40.134544,-91.506546 40.200459,-91.498932 40.251377,-91.486694 40.309624,-91.448593 40.371902,-91.418816 40.386875,-91.385757 40.392361,-91.372757 40.402988,-91.385399 40.44725,-91.374794 40.503654,-91.382103 40.528496,-91.412872 40.547993,-91.411118 40.572971,-91.37561 40.603439,-91.262062 40.639545,-91.214912 40.643818,-91.162498 40.656311,-91.129158 40.682148,-91.119987 40.705402,-91.092751 40.761547,-91.088905 40.833729,-91.04921 40.879585,-90.983276 40.923927,-90.960709 40.950504,-90.954651 41.070362,-90.957787 41.104359,-90.990341 41.144371,-91.018257 41.165825,-91.05632 41.176258,-91.101524 41.231522,-91.102348 41.267818,-91.07328 41.334896,-91.055786 41.401379,-91.027489 41.423508,-91.000694 41.431084,-90.949654 41.421234,-90.844139 41.444622,-90.7799 41.449821,-90.708214 41.450062,-90.658791 41.462318,-90.6007 41.509586,-90.54084 41.52597,-90.454994 41.527546,-90.434967 41.543579,-90.423004 41.567272,-90.348366 41.586849,-90.339348 41.602798,-90.341133 41.64909,-90.326027 41.722736,-90.304886 41.756466,-90.25531 41.781738,-90.195839 41.806137,-90.154518 41.930775,-90.14267 41.983963,-90.150536 42.033428,-90.168098 42.061043,-90.166649 42.103745,-90.176086 42.120502,-90.191574 42.122688,-90.230934 42.159721,-90.323601 42.197319,-90.367729 42.210209,-90.407173 42.242645,-90.417984 42.263924,-90.427681 42.340633,-90.441597 42.360073,-90.491043 42.388783,-90.563583 42.421837,-90.605827 42.46056,-90.648346 42.475643,-90.651772 42.494698,-90.638329 42.509361,-90.419975 42.508362,-89.923569 42.504108,-89.834618 42.50346,-89.400497 42.49749,-89.359444 42.497906,-88.939079 42.490864,-88.764954 42.490906,-88.70652 42.489655,-88.297897 42.49197,-88.194702 42.489613,-87.79731 42.489132,-87.836945 42.314213,-87.760239 42.156456,-87.670547 42.059822,-87.612625 41.847332,-87.529861 41.723591,-87.532646 41.469715,-87.532448 41.301304,-87.531731 41.173756,-87.532021 41.00993,-87.532669 40.745411,-87.53717 40.49461,-87.535675 40.483246,-87.535339 40.166195,-87.535774 39.887302,-87.535576 39.609341,-87.538567 39.477448,-87.540215 39.350525,-87.597664 39.338268,-87.625237 39.307404,-87.610619 39.297661,-87.615799 39.281418,-87.606895 39.258163,-87.584564 39.248753,-87.588593 39.208466,-87.5942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 360         );
 361
 362         // two calculations of the area (in square meters)
 363         var planar = illinois.getArea() * Math.pow(OpenLayers.INCHES_PER_UNIT['dd'] / OpenLayers.INCHES_PER_UNIT['m'], 2);
 364         var geodesic = illinois.getGeodesicArea();
 365
 366         // from http://en.wikipedia.org/wiki/Illinois
 367         var expected = 1.40998e11; // square meters
 368
 369         var planarErr = Math.abs(planar - expected) / expected;
 370         var geodesicErr = Math.abs(geodesic - expected) / expected;
 371
 372         t.ok(geodesicErr < planarErr, "geodesic measure is better (" + geodesicErr.toFixed(3) + " vs. " + planarErr.toFixed(3) + ")");
 373
 374     }
 375
 376
 377   </script>
 378 </head>
 379 <body>
 380 </body>
 381 </html>