Answer:

Unfortunately, the proposal leads to a never-terminating recursion: addStar() calls addStar() calls addStar() calls addStar() calls ...

Complete Flake

To end the recursion, when the star to draw is small, just draw it (add it to the graph) without going further.

If star is small, draw three lines.
If star is large then:
- Draw three lines with stars on their end.

Here is the code that does that:


import javafx.application.*;  
import javafx.stage.*;        
import javafx.scene.*;  
import javafx.scene.shape.*; 
import javafx.scene.paint.*;  
 
public class SnowFlake extends Application
{ 
  final double SIZELIMIT = 10;
  
  void addStar( Group root, Color color, double centerX, double centerY, double size )
  { 
    double startX, endX, startY, endY;
    
    // horizontal line
    startX = centerX - size/2;
    endX = centerX + size/2;
    Line line = new Line( startX, centerY, endX, centerY );
    line.setStrokeWidth( 2.0 );
    line.setStroke( color );
    Group grp = new Group( line );
    if ( size>SIZELIMIT )
    {
      addStar( grp, color, centerX-size/2, centerY, size*0.3);
      addStar( grp, color, centerX+size/2, centerY, size*0.3);
    }
    root.getChildren().add( grp );  
    
    // upward slanting line
    line = new Line( startX, centerY, endX, centerY );
    line.setStrokeWidth( 2.0 );
    line.setStroke( color );
    grp = new Group( line );
    if ( size>SIZELIMIT )
    {
      addStar( grp, color, centerX-size/2, centerY, size*0.3);
      addStar( grp, color, centerX+size/2, centerY, size*0.3);
    }
    grp.setRotate( +60.0 );
    root.getChildren().add( grp );  
    
    // downward slanting line
    line = new Line( startX, centerY, endX, centerY );
    line.setStrokeWidth( 2.0 );
    line.setStroke( color );
    grp = new Group( line );
    if ( size>SIZELIMIT )
    {
      addStar( grp, color, centerX-size/2, centerY, size*0.3);
      addStar( grp, color, centerX+size/2, centerY, size*0.3);
    }
    grp.setRotate( -60.0 );
    root.getChildren().add( grp );   
  }
  
  public void start(Stage stage) 
  { 
    double sceneWidth=400, sceneHeight= 300;  
    Group  root = new Group( );   
  
    addStar( root, Color.BLUE, sceneWidth/2, sceneHeight/2, sceneWidth*0.6 );
    
    Scene scene = new Scene(root, sceneWidth, sceneHeight, Color.SNOW ); 
    stage.setTitle("Snowflake"); 
    stage.setScene(scene); 
    stage.show(); 
  }      

}

Answer:

Complete Flake

QUESTION 20: