Removing duplicate code from basic collision detection implementation
It seems this is a job for a Parameter class.

public abstract class DeltaParameters{
  protected ? tileMap;
  protected int x, y;

  DeltaParameters(Point point, ? tileMap){
    this.x = point.x;
    this.y = point.y;
    this.tileMap = tileMap;
  }

  public int getX(){
    return x;
  }

  public int getY(){
    return y;
  }
  public abstract int getTileSideSize();
  public abstract int getMovingCoordinate();
  public abstract void offsetMovingCoordinate(int delta);
}

public class DeltaXParameters extends DeltaParameters{
  DeltaXParameters(Point point, ? tileMap){
    super(point, tileMap);
  }

  public int getTileSideSize(){
    return tileMap.getTileWidth();
  }
  public int getMovingCoordinate(){
    return x;
  }
  public void offsetMovingCoordinate(int delta){
    x += delta;
  }
}


I leave to you the job of guessing what would be DeltaYParameters :p 

public int getMaxDelta(DeltaParameters dparams, int delta){
    if(delta&gt;=dparams.getTileSideSize()) throw new IllegalArgumentException("This message is yet to be determined. It could be another method in DeltaParameters");
    if(delta==0) return delta;

    dparams.offsetMovingCoordinate(delta);
    if(isInsideTile(dparams.getX(), dparams.getY())){
        int map = dparams.getMovingCoordinate() /dparams.getTileSideSize() ;
        int offset = dparams.getMovingCoordinate() - (map * dparams.getTileSideSize() );
        int maxDelta = 0;

        if(delta &lt; 0){
            maxDelta = delta + (dparams.getTileSideSize() - offset);
        }
        else if(delta &gt; 0){
            maxDelta = delta - offset;
        }

        return maxDelta;
    }
    return delta;
}


Now you could call getMaxDelta just like this

getMaxDelta(new DeltaXParameters(new Point(0, 0), tileMap), 5);


What I have done here is to take the advantage of polymorphism over DeltaParameters class. Which could not be a so straigthforward method to refactor is now proven to be in a quite simple fashion imho.