final collision detection

public void update(float delta) {
    // apply gravity
    velocity.y -= gravity * delta;

    // clamp velocity
    if(velocity.y > speed)
        velocity.y = speed;
    else if(velocity.y < -speed)
        velocity.y = -speed;

    // save old position
    float oldX = getX(), oldY = getY();
    boolean collisionX = false, collisionY = false;

    // move on x
    setX(getX() + velocity.x * delta);

    // calculate the increment for step in #collidesLeft() and #collidesRight()
    increment = collisionLayer.getTileWidth();
    increment = getWidth() < increment ? getWidth() / 2 : increment / 2;

    if(velocity.x < 0) // going left
        collisionX = collidesLeft();
    else if(velocity.x > 0) // going right
        collisionX = collidesRight();

    // react to x collision
    if(collisionX) {
        setX(oldX);
        velocity.x = 0;
    }

    // move on y
    setY(getY() + velocity.y * delta * 5f);

    // calculate the increment for step in #collidesBottom() and #collidesTop()
    increment = collisionLayer.getTileHeight();
    increment = getHeight() < increment ? getHeight() / 2 : increment / 2;

    if(velocity.y < 0) // going down
        canJump = collisionY = collidesBottom();
    else if(velocity.y > 0) // going up
        collisionY = collidesTop();

    // react to y collision
    if(collisionY) {
        setY(oldY);
        velocity.y = 0;
    }

    // update animation
    animationTime += delta;
    setRegion(velocity.x < 0 ? left.getKeyFrame(animationTime) : velocity.x > 0 ? right.getKeyFrame(animationTime) : still.getKeyFrame(animationTime));
}

private boolean isCellBlocked(float x, float y) {
    Cell cell = collisionLayer.getCell((int) (x / collisionLayer.getTileWidth()), (int) (y / collisionLayer.getTileHeight()));
    return cell != null && cell.getTile() != null && cell.getTile().getProperties().containsKey(blockedKey);
}

public boolean collidesRight() {
    for(float step = 0; step <= getHeight(); step += increment)
        if(isCellBlocked(getX() + getWidth(), getY() + step))
            return true;
    return false;
}

public boolean collidesLeft() {
    for(float step = 0; step <= getHeight(); step += increment)
        if(isCellBlocked(getX(), getY() + step))
            return true;
    return false;
}

public boolean collidesTop() {
    for(float step = 0; step <= getWidth(); step += increment)
        if(isCellBlocked(getX() + step, getY() + getHeight()))
            return true;
    return false;
}

public boolean collidesBottom() {
    for(float step = 0; step <= getWidth(); step += increment)
        if(isCellBlocked(getX() + step, getY()))
            return true;
    return false;
}