How familiar are you with Newtonian physics? (Specifically the nature of force and inertia.)

Apart from basic physics it's just a matter of good collision detection.

Someone linked to this recently:

http://www.gamedev.net/page/resources/_/technical/game-programming/the-guide-to-implementing-2d-platformers-r2936

I found it to be a good article.

Instead of looking for a tutorial that matches your exact requirements, you can gain a lot more by solving this yourself.

1. When pressing the jump button, do not jump to the maximum height immediately. Instead, you have to hold the jump button to jump higher(and respect a limit). This feature would allow short-jumps and give you more control over your character.

How do you think this could be achieved? If you know the maximum jump height and specify a jump speed, you can increment the characters height by the speed until they've reached the height limit - whilst the jump button is pressed. And when the jump button is released, the player falls. Once you've done this, you could improve the "feel" of the jump, by changing the characters jump height to increase by smaller and smaller amounts over time - rather than a constant speed. This will create a slightly floaty/hovery jump depending on the curve/falloff.

2. Activate gravity if you walked down from a cliff for example(i e, you are in the air without have jumped).

(Detecting whether or not I am in air is not a problem, but where to put the code is).

So you know the solution to the problem, but don't know where to put the code? You could place this code just after the input if you'd like.

(Though I'd suggest you place the physics code in the same area)

3. After you released your jump button, you can not jump again until you hit the ground.

You know when the jump button has been released, so you'll need to know when you've hit the ground. If you're using tiles/grid, check the tile below you is a floor/ground tile. If you're touching this tile, you've hit the ground. Reset the jump ability here.

None of these are not really hard to implement, but combining all these function is hard.

At this stage, solve the problems one at a time.

Additionally, I'd like to add that it took a long time for them to get the movement mechanics right, with lots of tweaking. You would probably benefit from making a simpler jump system first, and then improving that once it's complete.

I will show it tomorrow, but until then, I hope to get some ideas.

Looking forward to it

Vector2 position(0.0, 0.0);
Vector2 velocity(0.0, 0.0);
Vector2 force(0.0, 0.0);
float mass = 1.0;
float gravity = -9.8;
float damping = 0.001f;

while(true)
{
    float dt = 0.016;//time elapse per frame in seconds

    //Do game logic here

    position = position + velocity * dt;

    //adds fake friction
    velocity *= 1.0 - (damping * dt);

    //adds gravity based on mass
    force.y += mass * gravity;

    velocity = velocity + (force / mass) * dt;
    force = 0;
}

1. When pressing the jump button, do not jump to the maximum height immediately. Instead, you have to hold the jump button to jump higher(and respect a limit). This feature would allow short-jumps and give you more control over your character.

To the algorithm above, add some value to force.y once. If you hold down a key then continue to add a force over multiple frames.

2. Activate gravity if you walked down from a cliff for example(i e, you are in the air without have jumped)

The algorithm above with handle this automatically with gravity. Change the gravity value to increase the acceleration.

3. After you released your jump button, you can not jump again until you hit the ground.

For this you'll need to add collision detection and response, and may get tricky.

I wasn't joking about physics. Gravity and jumping force can very easily be handled as classical Newtonian forces.

If you understand the terms 'force', 'acceleration', 'velocity', 'terminal velocity', 'speed' and 'momentum' in the sense that they are used in physics then this should be very easy to implement.

If you don't know them in the scientific sense then spend a few hours getting to understand those concepts well, especially the relationship between force, acceleration and speed. Once you understand those concepts you can apply them directly to this kind of physics.

The only queer thing about jumping force is that the application of the force is dependent on whether the button is still pressed. When I did platformers I would have a 'jump_potential' variable that specified the amount of jumping force available. When the jump button was pressed then each frame I'd apply a set fraction of the jump_potential to the character as an upward force. (You can avoid asymptotic behavior in this case by simply using integer division.) If the button was released then the jump_potential would be emptied. If the character was standing on something (and the button was not pressed) then the jump_potential would be reset to its start value.

Since you're using a char array it shouldn't take too much to detect if a slope is coming:

int tilePositionX, tilePositionY;
char tileArray[mapSizeX][mapSizeY];

int nextXTile = tilePositionX+1;//+1 assuming you are moving forward
int yTileBelow = tilePositionY+1;

if ((nextXTile < mapSizeX) && (yTileBelow < mapSizeY))
{
    //where 0 is solid and 1 is hollow
    if (tileArray[nextXTile][yTileBelow]) == 1)
    {
        //the next tile is on a slope or there is a hole
    }
}