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Taking the great-circle idea and applying Euclidean geometry techniques, we can actually arrive at a perfectly valid formula for calculating the length of a great-circle path. The steps to this solution are as follows: 1. Using trigonometry and the radius of earth, transform each latitude/longitude pair into three-dimensional Cartesian coordinates. 2. Determine the distance between the two points, by calculating x, y, and z displacements, and then applying the Pythagorean theorem. (In three dimensions, it s exactly the same; just add the square of the Z-dimension under the root sign.) 3. Picture that distance as a chord on a great circle around the earth, and then using basic two-dimensional geometry, calculate the arc-length bracketed by the known straight-line length. Although this method is accurate, unfortunately even in its simplified form, it s frighteningly complex:

Earlier, in Listing 9-2, we built a login screen that protected the password in Flex. To expand on that example, we need to use that component to authenticate the user with Spring Security. We will also use this opportunity to apply the granted user groups to authorize components in the Flex application based on whether the user is an administrator. This technique can be used to secure access rights for users of enterprise Flex applications. Listing 9-10 shows the Flex Spring Security application, and Listing 9-11 shows the user profile. Listing 9-10. The Flex SpringSecurity Application (SpringSecurity.mxml) < xml version="1.0" encoding="utf-8" > <mx:Application xmlns:mx="http://www.adobe.com/2006/mxml"> <mx:Script> <![CDATA[ import import import import

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As with many of the mathematical tools we ve used with the Google Maps API, the Haversine formula has a history with marine navigation. Although both work perfectly well, the Haversine formula has an elegant simplicity that makes it appealing. Indeed, as of version 2.0, the functionality you see here is provided in the Google Maps API, by the GLatLng::distanceFrom() method. Here is the Haversine formula:

Although we presented the extra information that we added to the $user object on the my account page, remember that because the $user object is global, any other module can access it. We leave it as a useful exercise for the reader to modify the preceding module to provide a nicely formatted list of past logins as a block in a sidebar for security purposes ( Hey! I didn t log in this morning at 3:00 a.m.! ).

com.af.security.vo.UserProfile; mx.rpc.events.ResultEvent; mx.rpc.events.FaultEvent; mx.controls.Alert;

You get surface distance by plugging in the two points latitudes and longitudes into 1, 1 and 2, 2, respectively, and then multiplying d by the radius of the earth, 6,378,137 meters. JavaScript exposes all of the mathematical functions required to implement an expression such as this, in the Math object.

private var userProfile:UserProfile = new UserProfile();

If you have an account on http://drupal.org, you can see the effects of providing categories of user information by logging in and clicking the my account link, and then selecting the edit tab. In addition to editing your account information, such as your password, you can provide information about yourself in several other categories. At the time of this writing, http:// drupal.org supported editing of CVS information, Drupal involvement, personal information, work information, and preferences for receiving newsletters. You can add information categories like these by using profile.module or by responding to the categories operation of the user hook; see the implementation in profile.module.

An excellent resource for the Math object can be found at W3Schools: http://www.w3schools.com/ Tip

private function doLogin():void { securityService.authenticateUser(txtUserName.text, txtPassword.text); } private function authorizationResultHandler (event:ResultEvent):void { userProfile.groups = event.result.groups as Array; userProfile.userIsAdmin(); } private function authorizationFaultHandler(event:FaultEvent):void { Alert.show(event.fault.toString()); } ]]> </mx:Script> <mx:RemoteObject id="securityService" destination="securityService" endpoint="http://localhost:8080/blazeds/messagebroker/amf" fault="authorizationFaultHandler(event)" result=" authorizationResultHandler (event)"> </mx:RemoteObject> <mx:Panel title="Spring Security Example" paddingLeft="10" paddingRight="10" paddingBottom="10" paddingTop="10" horizontalAlign="center" width="506" height="300" styleName="blackBackground" label="horizontal"> <mx:HBox width="100%" height="100%"> <mx:VBox id="loginBox" backgroundImage="assets/images/LoginScreen.png"> <mx:Canvas width="370" height="227" styleName="canvasFont"> <mx:VBox x="50" y="9" verticalGap="-1"> <mx:HBox horizontalGap="0" x="26" y="14"> <mx:Label text="APPFOUNDATION" styleName="labelFontOrange"/> <mx:Label text="LOG IN" styleName="labelFontWhite"/> </mx:HBox> <mx:TextArea backgroundAlpha="0" wordWrap="true" borderStyle="none" selectable="false" editable="false" text="Enter your username and password below." width="288" height="35"/> </mx:VBox>

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