How to Center a group of shapes on the slide?

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• How focus a JavaFX Group properly and set the pivot (reverse) by using translations in 3D space?

  Description:

  I m referring to the Oracle tutorial http://docs.Oracle.com/JavaFX/2/transformations/jfxpub-transformations.htm using the transformations.zip source code, which is available for download on this page. I Don t understand why they Center the xylophone in space 3D like this and why they calculate the pivot (reverse) using translations. So they are creating a large number of groups, including rectangles, representing the xylophone, in addition to finally to a group called "cam".    

  class Cam extends Group {     
       Translate t  = new Translate();     
       Translate p  = new Translate();     
       Translate ip = new Translate();     
       Rotate rx = new Rotate();     
       { rx.setAxis(Rotate.X_AXIS); }     
       Rotate ry = new Rotate();     
       { ry.setAxis(Rotate.Y_AXIS); }     
       Rotate rz = new Rotate();     
       { rz.setAxis(Rotate.Z_AXIS); }     
       Scale s = new Scale();     
       public Cam() { 
            super(); getTransforms().addAll(t, p, rx, rz, ry, s, ip); 
       }     
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  final Cam camOffset = new Cam();    
  final Cam cam = new Cam();    
  ...    
  camOffset.getChildren().add(cam);    
  ...    
  final Scene scene = new Scene(camOffset, 800, 600, true);    
  ... 
  

  The Group "cam" is added to another group called "camOffset", which is added to the 'scene' as root the node.

  Until there , everything is understandable to me, but there is a method, called "frameCam (.)" which calls 4 other methods: ""

  public void setCamOffset(final Cam camOffset, final Scene scene) {         
       double width = scene.getWidth();         
       double height = scene.getHeight();         
       camOffset.t.setX(width/2.0);         
       camOffset.t.setY(height/2.0);     
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  //=========================================================================    
  // setCamScale    
  //=========================================================================    
  
  public void setCamScale(final Cam cam, final Scene scene) {        
       final Bounds bounds = cam.getBoundsInLocal();         
       final double pivotX = bounds.getMinX() + bounds.getWidth()/2;         
       final double pivotY = bounds.getMinY() + bounds.getHeight()/2;         
       final double pivotZ = bounds.getMinZ() + bounds.getDepth()/2;         
       double width = scene.getWidth();         
       double height = scene.getHeight();         
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       double scaleFactorY = 1.0;         
       double scaleFactorX = 1.0;         
  if (bounds.getWidth() > 0.0001) {            
       scaleFactorX = width / bounds.getWidth(); // / 2.0;        
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  if (bounds.getHeight() > 0.0001) {            
       scaleFactorY = height / bounds.getHeight(); //  / 1.5;         
  }        
  if (scaleFactorX > scaleFactorY) {            
       scaleFactor = scaleFactorY;         
  } else {            
       scaleFactor = scaleFactorX;         
  }        
       cam.s.setX(scaleFactor);         
       cam.s.setY(scaleFactor);         
       cam.s.setZ(scaleFactor);     
  }    
  
  //=========================================================================    
  // setCamPivot    
  //=========================================================================    
  
  public void setCamPivot(final Cam cam) {        
       final Bounds bounds = cam.getBoundsInLocal();         
       final double pivotX = bounds.getMinX() + bounds.getWidth()/2;         
       final double pivotY = bounds.getMinY() + bounds.getHeight()/2;        
      final double pivotZ = bounds.getMinZ() + bounds.getDepth()/2;         
  
  //*1*        
       cam.p.setX(pivotX);         
       cam.p.setY(pivotY);         
       cam.p.setZ(pivotZ);         
  //*1*        
  
  //*2*        
       cam.ip.setX(-pivotX);         
       cam.ip.setY(-pivotY);         
       cam.ip.setZ(-pivotZ);         
  //*2*     }    
  
  //=========================================================================    
  // setCamTranslate    
  //=========================================================================    
  
  public void setCamTranslate(final Cam cam) {        
       final Bounds bounds = cam.getBoundsInLocal();         
       final double pivotX = bounds.getMinX() + bounds.getWidth()/2;         
       final double pivotY = bounds.getMinY() + bounds.getHeight()/2;         
       cam.t.setX(-pivotX);         
       cam.t.setY(-pivotY);     
  } 
  

  If the method ' setCamScale (...) 'is understandable,' setCamOffset (...) ' puts the root node ('camOffset') in the center of the screen, but I Don t understand the 2 following methods at all. Of course, the child ("cam") is not centered, by putting just the root node ('camOffset') in the center of the screen, but how they focus the xylophone / "cam" and set the pivot, using translations:

  Questions:

  1. Why they use 3 different translations (', 'ip', 'p')?
  2. Referring to ' setCamPivot (...) ': Why they are the first translation of 'cam.p' to "pivotX", 'pivotY' and 'pivotZ' and then 'cam.ip' to '-pivotX', '-pivotY' and '-pivotZ' (marked in the source code with * 1 * and * 2 *)? Should he not just put the Group at his position, where it has been positioned before, as if the method has never been called? That would be my guess, because I expect that an object is placed in the same position as before, if I first move with the values X, Y, Z and then return with the same values - X, - Y, - Z in the opposite direction.
  3. Even with the method ' setCamTranslate (...) ' ': Why use another translation "cam.t", moving the Group ("cam") with the same values "-pivotX', '-pivotY' (and not '-pivotZ'), which they used in the"setCamPivot (...) method `?

  Annotations:

  Of course it works, the xylophone is located in the center of the screen and could turn perfectly, without change of rotation point / pivot point, but I Don t understand how they did it. I read everything about layoutBound, boundsInLocal, boundsInParent, blogs about page layout and page layout goes into javaFX https://blogs.oracle.com/jfxprg/entry/the_peculiarities_of_javafx_layout and http://amyfowlersblog.wordpress.com/2011/06/02/javafx2-0-layout-a-class-tour/ and finally a large number of questions to stackoverflow, but I still Don t understand the meaning behind the methods stated.

  Before the call of ' frameCam (...) ', they ask:

  double halfSceneWidth = 375;  // scene.getWidth()/2.0;     
  double halfSceneHeight = 275;  // scene.getHeight()/2.0;    
  cam.p.setX(halfSceneWidth);    
  cam.ip.setX(-halfSceneWidth);    
  cam.p.setY(halfSceneHeight);    
  cam.ip.setY(-halfSceneHeight); 
  

  I deleted these lines, because it doesn't change anything.

  The base in place, is that there are three defined different rotations, one around each axis. Of course, these could be combined into a single rotation, but doing so would make the geometry in the mouse dragging very complex managers. As it is, the degree of rotation around each axis can be calculated and changed independently.

  In general, the rotations are defined by an angle, an axis and a (pivot) point. The axis is a 3D vector and goes through the pivot point; the rotation is around this axis through that point.

  In the configuration in the example, the pivot of each of the individual rotations is set to the default (0,0,0). Because we really want the rotation to be around the center of the group, not the original, the Group translates first point appropriate pivot (ip), the rotations are applied then (around (0,0,0) after translation by ip), then the group is reflected in its location of origin (p). These operations are not commutative, yes show ip, then the rotation, then p is not the same as when you run ip, then p, then the rotation (in the second, ip and p would cancel and rotation would be about (0,0,0) instead of around the Center).

  For good measure, there is a scale, that is also applied after ip (so that scaling occurs from the Center, not the original) and then a final translation.

  The final effect is that there is a lot of transformations that can be controlled independently. There is a scale (s), a rotation about each axis (rx, ry, rz), and a translation (t). The p in translations and its inverse ip are just "housekeeping" to ensure that rotation and scaling are done from the center of the screen, instead of (0,0,0).

  So:

  1. Why they use 3 different translations (', 'ip', 'p')?

  p and ip are translations for the rotation and scaling are done from the Center and not to the origin. t is a general translation, the user sees.

  Referring to ' setCamPivot (...) ': Why they are the first translation of 'cam.p' to "pivotX", 'pivotY' and 'pivotZ' and then 'cam.ip' to '-pivotX', '-pivotY' and '-pivotZ' (marked in the source code with * 1 * and * 2 *)? Should he not just put the Group at his position, where it has been positioned before, as if the method has never been called?

  He puts the group to its original position, but other changes are between p and ip. These transformations behave differently (in a planned way) because the group is translated when they are applied.

  Even with the method ' setCamTranslate (...) ' ': Why use another translation "cam.t", moving the Group ("cam") with the same values "-pivotX', '-pivotY' (and not '-pivotZ'), which they used in the"setCamPivot (...) method `?

  The t values are changed in the mouse Manager (with alt-middle mouse button-drag, which I can't test actually using my trackpad...). As you have noted, the effect of p and IP translation cancel out, so we end up with t, which can be changed by the user. They could have combined t and p a single transformation, but updated since the mouse Manager would have been more delicate, and the intent of the code would be less clear.

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  Adobe® Expert community: Dreamweaver
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