Platformer programming theory

Generally, game physics defy real world physics. Consider the fact that in most games you are able to alter your direction of motion while being in mid-air! The easiest way I've found is to apply a downwards force and nothing else (maybe a movement restrictor like a 0.5 multiplier on horizontal movement speed). Then perform collision detection as normal.

For a platformer, you can get good jump results using m0nkfish's suggestion of simply applying a constant velocity modifier to bring the character back down to earth more naturally (in that they will decelerate to a stop going upwards and the accelerate back down to the ground).

To get the player off the ground in the first place simply apply a instantaneous velocity upwards to the player.

When you look at a game like Mario though there are several other components to a jump though. One has to do with tapping versus holding the jump button. The way you can simulate this is to continuously force the player's upwards velocity to the instantaneous jump velocity as long as the button is held (up to a certain height).

Another thing to consider in mario is the horizontal movement while in the air. You'll probably want to know the horizontal velocity at time of jump and come up with different rules for affecting the player's horizontal movement while in midair. This isn't really a physics issue though as people really can't adjust their movement while in air (outside of factors outside of our control such as wind that is).

I use a vector of forces with the first being gravity in the down direction. the rest of the vector could be wind forces or other forces based in your game world. Just remember the game shouldn't be real world physics but instead modeled after them.

I usually have a state based character for things like jumping.. standing.. sliding.. running.. Each of these states could have different types of physics applied. IE: if your standing and hit jump you just apply a upward velocity to your character once and while your not colliding with the 'ground' you apply gravity.

I see, and what about handling collisions to avoid characters falling through platforms?

my current idea is to be always incrementing its y value (like a gravity force)
and then check for collisions for the underlying area of each entity, but this sounds a little costly isnt?

directx comes with a math library that has something like check RECT collision that will return if two rectangles collides.

you could do 2d vector math after finding the collision.

project the closest point onto the rectangle and get the penetration depth. then negate it and add to current position, this will put you exactly at the point you collided with it.