lets you create this kind of line. (this is a great line!) 
Classically, you grip the hands 
and hold the grip when you come up. This is not anywhere near the line you are
looking for, 
These were from some of the highlights of the mat workshop hosted by Connie Vasey on February 1st, 2002 in Irving, Texas. Thanks to Connie and Therese Nix for being the talent.
First up, how to lift your head. Start with a relaxed back of neck.
Rotate
around your ears to make the back of your neck long. 
Continue to rotate till your chin lowers into your throat. 
Continue to lift the weight of your head by rotating around the axis that runs
through your ears. 
Crease at the sternum to complete the lift. 
From your head being down, 
feel the difference when you lift your face straight to the ceiling. 
See the strain in the neck? This is NOT the way to lift your head! 
This way, with a neutral spine, 
not this way where shoulders and hips are "over tucked." Hips in neutral,
good 
hips clenched in a tuck, bad.
Neutral 
over tucked.
Same with the arms, arms are back only to the point where the ribs stay in and
the back doens't arched. 
Here ares are too far back forcing the ribs to pop up and the back to arch. 
Here's the beginning of the swan, note the elbows and palms.
As you press down in your elbows lift your chest and keep the back of your neck
long. 
Press into your palms to come higher without losing the line through your head.
Finish maintaining the line holding good posture throughout the upper body.
Can you see how bad this is by comparison to the previous? 
Too much like Yoga and not at all like the Pilates ideal.
lets you create this kind of line. (this is a great line!)
Classically, you grip the hands
and hold the grip when you come up. This is not anywhere near the line you are
looking for, In the return from the pushup, 
curl the head around the ears 
then push through the shoulders rounding your back 
continue the rounding return
walking your hands back to your feet.
If the back of your neck is long 
and you lift from your hips first 
it's more like the downward dog in Yoga and not in the ideal of Pilates.
In Pilates, you are constantly trying to use contact points of tension to trigger
uniform usage. Be the magic circle in your body. 
In rolling like a ball, shoulders down, long neck like a proud turtle.
Never hunched in like this. 
Never letting your head break backwards as you rock.
In the swan weight stays equally on both hips 
not leaning like this. 
Another take, this is good, 
this is bad. 
Good saw, 
bad saw.
When creating a point of tension at the ankles keep the knees soft,
never lock the knees to press through the heels.
In the spine stretch, sit up straight like this.
Not like this where the shoulder blades are released and arms hunch forward.
In the open leg rocker, start with the whole hand, thumbs running with your
fingers to create a solid press of legs against hands
The traditional grip of the hands at the ankles usually ends up looking like
this, way out of posture at the shoulders. 
In side kicks, it is terribly important that you keep your hips square, so as
the leg comes forward pressing through your heel, the hip holds back in oppositional
tension. 
Here, the leg comes further forward, but at the cost of losing square hips.
When you swim, keep the line of your neck long and try to lift more from your
upper body. 
Here the line out the neck is lost.
In the shoulder bridge, keep a strong connection of ribs through the body to
the engagement of the gloots. 
Here, that connection is lost and your hips are higher at the expense of compression
in the lower back.
Finally, when rolling down in the shoulder bridge, keep reaching the back of
the neck long 
if you let the back of your neck shorten you lose a key point to the exercise,
decompressive enlongation between the axis through the ears and the axis through
the shoulders.
Want some homework? Learn about Alfred Cornu, (Cornu's Spiral), and be able to explain what is a point of inflection.
How does that relate to the true point of eccentricity in our bodies.
Remember to breathe!