For understanding angles in martial arts it is recommended that you read about martial arts mathematics. For understanding dimensional zones and the center-line in martial arts, it is recommended that you read How Not to Get Hit.
In terms of self defense, not only is it important to protect your center-line and keep a strong base (or stance), in addition to entering your attacker's center-line, and understanding distance and range to achieve this result, but it is equally important to understand how to open the opponent's center-line and take away his base. For him to defeat you, he must attack your center-line, where your vulnerable targets are, and disrupt your base; so the reverse is true: For you to defend yourself, you must unbalance the attacker, disrupt his dimensional zones, and enter and attack his center-line.
This can be achieved in various ways, which we will explore in this article.
Moving Yourself To His Center-line
One way to gain access to the attacker's center-line is by putting yourself in a position, at the correct angle to attack his center-line. This is done by moving at angles that render a straight line to his targets.
Jamie and Glenn demonstrate a Kenpo technique called Broken Gift, against an unfriendly handshake in which the intent of the handshake is to distract and control so the attacker can deliver a punch. | Source
Before Jamie can punch, Glenn applies an arm bar using his own arm as leverage to nullify Jamie's attack. | Source
Glenn then delivers a back-knuckle strike to the face. | Source
Moving into Jamie's center-line by stepping towards it with his right foot, Glenn strikes and grabs Jamie's head. | Source
Shifting into a good fighting stance with his left foot back, Glenn is now in Jamie's center-line... | Source
From there, he delivers a forearm strike to Jamie's jaw or most available target. | Source
Jamie and Glenn face off, Glenn armed with a club, to show you a Kenpo technique called Checking the Storm. | Source
As Glenn delivers an over-head club attack, Jamie maneuvers aside, positioned in Glenn's center-line. | Source
Being in Glenn's center-line, Jamie delivers a kick to the groin.
Jamie shifts to prepare for another kick and as he does so he strikes Glenn in a raking fashion with his right hand. | Source
Jamie then delivers a side kick to the knee. | Source
Move The Opponent To Open The Center-line
The other way to gain access to your opponent's targets is by moving him, through manipulation, blocks, or strikes.
Glenn and Jamie demonstrate a Kenpo technique called Buckling Branch, against a Left Front Thrust Kick | Source
Glenn blocks the kick. | Source
Glenn then has access to Jamie's center-line. | Source
Glenn delivers a front scoop kick to Jamie's groin while checking him at the shoulders. | Source
Glenn maintains the check at Jamie's shoulders and prepares to kick. | Source
Glenn delivers a side thrust kick to the back of Jamie's knee. | Source
Glenn claws Jamie's eyes and face. | Source
Being in Jamie's center-line where he has no bracing angle, Glenn drags Jamie to the ground and drops a knee on his head. | Source
Jamie and Glenn demonstrate a Kenpo technique called Calming the Storm. | Source
Jamie blocks the attack and strikes at the same time. | Source
To open Glenn's center-line, Jamie strikes or bumps his right shoulder. | Source
Jamie then delivers a series of strikes. | Source
Glenn and Jamie demonstrate a Kenpo technique called the Dance of Death, against a right step-through thrust punch. | Source
Glenn slips and blocks the punch. | Source
He then strikes Jamie in the groin. | Source
Glenn knees Jamie's thigh to open his center-line and to grab his leg. | Source
Glenn has Jamie's leg in his hand. | Source
He then delivers an elbow strike which takes Jamie down. | Source
Jamie and Glenn demonstrate a Kenpo technique called Gathering Clouds. | Source
Glenn slips and parries the punch. | Source
Glenn delivers a chop to Jamie's ribs. | Source
Glenn then drives an elbow into Jamie's ribs as he lands behind Jamie's right leg. | Source
Glenn buckles, or sweeps, Jamie's right leg with his right leg, to open the center-line. | Source
Glenn kicks to the groin. | Source
Glenn and Jamie demonstrate a Kenpo technique called Thrusting Salute. | Source
Glenn blocks the kick. | Source
Now in Jamie's center-line, Glenn delivers a front kick to the groin. | Source
Glenn delivers a heel-palm strike. | Source
Move To Where He Has No Base
In your opponent's center-line is also the place where he has no base; in Kenpo terminology, where he has no Bracing Angle. This is where if he is hit, you disturb his depth zone, disrupt his balance, and if pulled or pushed he can be taken down.
Jamie and Glenn demonstrate a Kenpo technique called the Back Breaker, against a surprise attack from the flank. | Source
Glenn parries the attack. | Source
Glenn then positions himself in back of Jamie in his center-line and where he has no bracing angle, by stepping with his left foot to the rear of Jamie and then sliding his right foot back to put him in an adequate stance. | Source
Glenn delivers a knee to the spine. | Source
Pulling Jamie off his base, Glenn puts him on his knee. | Source
Glenn wrenches Jamie's neck. | Source
Glenn delivers a hand-sword strike.
Glenn claws the eyes. | Source
Glenn strikes the clavicles and drops Jamie to the ground by taking his knee out from under him. | Source
Glenn then drops a knee to the head. | Source
Glenn and Jamie demonstrate a Kenpo technique called Circling Destruction. | Source
Glenn parries the punch. | Source
Glenn strikes the ribs. | Source
Glenn moves to position himself in Jamie's center-line and hooks Jamie's chin with his left hand. | Source
Glenn now in Jamie's center-line and controlling his head, strikes him in the neck. | Source
Glenn scoop kicks the groin. | Source
Glenn delivers an elbow strike to the kidneys. | Source
Bumping Jamie at the waist with his shoulder, Glenn grabs Jamie's ankles. | Source
Having no bracing angle, Jamie is easily taken off his base. | Source
Glenn delivers a kick to the groin. | Source
So, it is advantageous to understand at what angles you can enter your opponent's center-line, how to get there to do it, and how to disturb his base or balance.