The best way to make this work is to update your geometry and then set the geometry for your graphic. After a graphic's setGeometry method is called, the graphic will update.
If everything worked as it should, you would call insertPoint on your polyline and then pass your polyline to your graphic's setGeometry method. That being said, your use case uncovered a bug in insertPoint. The current implementation(version 2.6 of the API) won't let you insert a point on the end of a path. The best workaround is to use addPath. The code would look like this:
// add a polyline, line and lineGraphic are global
var p1 = esri.geometry.geographicToWebMercator(new esri.geometry.Point(-100, 40, map.spatialReference));
var p2 = esri.geometry.geographicToWebMercator(new esri.geometry.Point(-90, 40, map.spatialReference));
line = new esri.geometry.Polyline();
line.addPath([p1, p2]);
lineGraphic = map.graphics.add(new esri.Graphic(
line,
new esri.symbol.SimpleLineSymbol()
));
dojo.connect(map, "onClick", addPt);
And the body of the addPt function:
line.addPath([
line.paths[pathCount-1][line.paths[pathCount-1].length-1],
[e.mapPoint.x, e.mapPoint.y]
]);
lineGraphic.setGeometry(line);
Here's a working example: http://jsfiddle.net/swingley/SntsN/ Click the map to extend the line. We will (hopefully) fix this bug in the next release of the API, which is 2.7.
Best Answer
Unless your parcel polygons are unusually shaped, you get get the center point of the extent of the parcel polygon and use that to draw your center graphic.
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