I don't want to keep writing the same code over and over.

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// REQUIRES: Drawable.pde

/**
 * This class implements the basic layer,
 * but you still need to implement the draw()
 * and over() methods in subclasses.
 */
abstract class Movable extends Drawable {

  // very simple constructor
  Movable() { super(0,0); }
  
  // very simple constructor
  Movable(float x, float y) { super(x,y); }

  // coordinate getter overrides
  float getX() { return super.getX() + ox; }
  float getY() { return super.getY() + oy; }

  float getOX() { return ox; }
  float getOY() { return oy; }
  
  // still abstract
  abstract void draw();
  
  // still abstract
  abstract boolean over(float x, float y);
  
  // internal variables for movement administration
  private float mx=-1, my=-1, ox=0, oy=0;

  // mark mouse location when pressed
  boolean mousePressed(float mouseX, float mouseY, int mouseButton) {
    mx=mouseX;
    my=mouseY;
    return true;
  }

  // update the offsets to use as long as the mouse is being dragged
  boolean mouseDragged(float mouseX, float mouseY, int mouseButton) {
    if(mx!=-1 && my!=-1) {
      ox = mouseX-mx;
      oy = mouseY-my;
      for(Point p: points) { p.setOffsets(ox,oy); }
      return true;
    }
    return false;
  }

  // commit offsets on mouse release
  boolean mouseReleased(float mouseX, float mouseY, int mouseButton) {
    for(Point p: points) { p.commitOffsets(); }
    mx=-1; my=-1; ox=0; oy=0;
    return true;
  }
}