Some descriptions/opinions about goalkeeper positioning

"Angle play is three-dimensional. Keeper must be concerned with their left and right sides, the near post and far post. They also must be concerned with balls kicked above their heads. So positioning is three dimensional, left, right and above the head. Factors that influence how far the goalkeeper should come off the goal-line include the following: their physical dimensions, the speed that the attacker is coming toward the goal, the likely speed of the shot, the likely direction of the ball, the likely flight path of the ball, driven, rising, falling, or looping, and the condition of the field. First priority is to protect the near post. The ball has a shorter distance to travel and its speed will be greater. Remember, two hands to the near post, one hand to the far post. Experience will help g goalkeeper constantly evaluate all the factors mentioned above. Have the keeper create an imaginary line from the belly button to the ball. This is known as the ball line. When the ball is in motion, the goalkeeper is in motion. When the ball is stationary, the goalkeeper is stationary. The motion of the goalkeeper should be harmonious and in synch with the movements of the ball. The further the ball is from the goal, the further the keeper is form the goal line. The closer the ball to the goal, the closer the keeper is to his/her line. One of the best aids in helping the keeper visualize correct angle play is the rope. Tie each end of the rope to each of the posts and then stretch it out to the point where the ball lies. You move the ball and the rope and evaluate the keeper’s movements. The goal is, of course stationary and fixed in its dimensions. However, simply as a result of a goalkeepers accurate positioning, the goal can be made to appear to a shooter to be much smaller. It’s magical! When goalkeepers are in the right place at the right time, it’s not luck. It’s because they have mastered angle play."
Dan Gaspar
keeperstop.com
"Goalkeepers need to understand when to close down an attacker and their shooting angle and when to stay in goal and protect their position. In addition, good body posture and positioning, dependent on the striker’s angle/distance from goal, are also important."
fifatrainingcentre.com
"Goalkeepers should take up the line between the ball and the middle of the goal and position themselves at a place off their goal line to act as a sweeper - keeper. Younger keepers, youth coaches, or keepers without footskills will not be terribly comfortable with this but it is a critical part of team defending."
keeperstop.com
"Your position should also put you in a location to easily get to flighted balls and get a jump on through-balls /breakaways. This requires you to read and understand what is happening in the game. Who has possession, how close are they to goal, do they have time and space, are they looking at one of their teammates for a run, are they looking at you to see where you are standing? All of these indicators may dictate minor adjustments in your position and stance to give you an edge at getting to a ball in the penalty area. This is beginning element of “controlling the box”. If you can shut down a play before it becomes dangerous you will make your job that much easier."
keeperstop.com
"Keeper should always try to position themselves on the imanginary line that runs from the ball to the center of the goal. this way, they can cover either post equally well"
totalsoccer.us
"Be towards the midline of a triangle formed by lines joining the position of the ball and the two goal-posts (see diagram)."
soccercoachweekly.net
"If an an attack is taking place in your third, you must constantly adjust your position to reduce how much of the goal the opposition has to aim at. This is what we refer to as “narrowing the angle” — which is the primary focus in goalkeepers’ positional training. Goalkeepers usually stand anywhere from the goal line to half way up the penalty area, depending on how close and imminent the threat is. Later in this post I take a closer look at how Keepers can practice calibrating their position during dangerous attacks."
topgoalkeeping.com