Question

It is so easy to write some code to achieve the bouncing ball based on the open source project cocos2d,here is the question.

So without cocos2d, how to implement this with the simplest code.

Answer 1

First you need to create a ball class. This class should have ivars for position, velocity, direction etc.
It should also have some methods for when the ball needs to change direction, like hitTop, hitBottom, hitLeft, hitRight. It should also have a method for updating the position, to move it one step forward.
I also have a BallView so that I can use a image or just a color as the ball.

To make it move you need to have a gameloop in you view controller, there are many methods for doing that but the one I find easiest is CADisplayLink.

Here are some code if you have problems implementing it:

Ball.h

#import <Foundation/Foundation.h>
#import "MovingObjectView.h"

@interface MovingObject : NSObject

@property(nonatomic, retain) MovingObjectView *ball;

@property CGRect bounds;
@property CGPoint position;
@property CGPoint direction;
@property float velocity;

-(id)initWithBounds:(CGRect)b andPosition:(CGPoint)p;

-(BOOL)positionIsInsideRect;
-(void)update;

-(void)hitLeft;
-(void)hitRight;
-(void)hitTop;
-(void)hitBottom;

@end

Ball.m

#import "MovingObject.h"

@implementation MovingObject

-(id)initWithBounds:(CGRect)b andPosition:(CGPoint)p
{
    if (self = [super init]) {
        self.bounds = b;
        self.position = p;
        self.direction = CGPointMake(1, 1);

        //Change the position to middle if position is outside bounds
        if (![self positionIsInsideRect]) {
            NSLog(@"Position changed to center");
            self.position = CGPointMake(self.bounds.size.width/2, self.bounds.size.height/2);
        }

        self.ball = [[[MovingObjectView alloc]initWithFrame:CGRectMake(self.position.x, self.position.y, 15, 15)]autorelease];
    }
    return self;
}

//checks if the balls position is correct
-(BOOL)positionIsInsideRect {
    if (self.position.x < self.bounds.origin.x || self.position.x > self.bounds.size.width || self.position.y < self.bounds.origin.y || self.position.y > self.bounds.size.height) {
        NSLog(@"Position is outside bounds");
        return NO;
    }else{
        return YES;
    }
}

//Call this method to move a ball
-(void)update {
    //Checks if the ball is outside bounds
    if (self.position.x-(self.ball.frame.size.width/2) <= self.bounds.origin.x) {
        [self hitLeft];
    }else if (self.position.x+(self.ball.frame.size.width/2) >= self.bounds.size.width){
        [self hitRight];
    }else if (self.position.y-(self.ball.frame.size.height/2) <= self.bounds.origin.y) {
        [self hitTop];
    }else if (self.position.y+(self.ball.frame.size.height/2) >= self.bounds.size.height){
        [self hitBottom];
    }

    //Updates the balls position
    CGPoint p = self.position;
    p.x += self.direction.x*self.velocity;
    p.y += self.direction.y*self.velocity;
    self.position = p;

    self.ball.center = self.position;
}

//Call this when the ball need to bounce
-(void)hitLeft
{
    NSLog(@"hitLeft");
    CGPoint d = self.direction;
    d.x = fabsf(self.direction.x);
    self.direction = d;
}

-(void)hitRight
{
    NSLog(@"hitRight");
    CGPoint d = self.direction;
    d.x = -fabsf(self.direction.x);
    self.direction = d;
}

-(void)hitTop
{
    NSLog(@"hitTop");
    CGPoint d = self.direction;
    d.y = fabsf(self.direction.y);
    self.direction = d;
}

-(void)hitBottom
{
    NSLog(@"hitBottom");
    CGPoint d = self.direction;
    d.y = -fabsf(self.direction.y);
    self.direction = d;
}

-(void)dealloc {
    [super dealloc];
}

@end

BallView.h

#import <UIKit/UIKit.h>

@interface MovingObjectView : UIView

@property (nonatomic, retain) UIImage *img;

@end

BallView.m

#import "MovingObjectView.h"

@implementation MovingObjectView

- (id)initWithFrame:(CGRect)frame
{
    self = [super initWithFrame:frame];
    if (self) {
        // Initialization code
    }
    return self;
}


// Only override drawRect: if you perform custom drawing.
// An empty implementation adversely affects performance during animation.
- (void)drawRect:(CGRect)rect
{
    if (self.img == nil) {
        CGRect bounds = [self bounds];
        [[UIColor blackColor]set];
        UIRectFill(bounds);
    }else {
        CGRect bounds = [self bounds];
        [[UIColor whiteColor]set];
        UIRectFill(bounds);
        [self.img drawInRect:rect];
    }
}

@end

Then finally in the viewcontroller you need this:

ViewController

In viewdidload:

self.displayLink = [CADisplayLink displayLinkWithTarget:self selector:@selector(gameLoop)];
[self.displayLink addToRunLoop:[NSRunLoop currentRunLoop] forMode:NSRunLoopCommonModes];

Then add this method:

-(void)gameLoop
{   
    //Updates the balls position
    [self.movingBall update];

    //Here you could add your collision detection code
}