Looking at the shape of a haircut design, lets you see the lines of the cut. Where the lines change direction lets you see the angles of the haircut. Measuring the angle tells you how strong the change in direction is.
The lines of the cut are either horizontal, vertical, or diagonal which is between horizontal and vertical. Horizontal lines would be seen in a one length haircut where the hair is cut parallel to the floor. This kind of line is seen as creating the most weight of the different types of lines.
If you want to create the least amount of weight in a cut you would take vertical sections and cut vertical lines instead of the horizontal lines in the one length haircut. Vertical lines are seen frequently in hair cuts for men where a leaner or closer cut is desired.
For something between the most weight and the least weight, use a diagonal line to define your cutting line. A diagonal line is seen in a graduated haircut where the diagonal line moves the weight off the bottom of the hair cut up the diagonal line of the graduation.
These kinds of line encourage the eye to follow them. A vertical line makes the up and down view of the haircut more noticeable. It makes the eye move up and down the shape and gives the shape the appearance of being vertically longer. This could used to balance a head shape that is seen as too round.
A horizontal line encourages the eye to look from side to side. This is makes the haircut look wider along the horizontal lines. This might be used when the creation of width is desired to compensate for an area that seems too narrow.
Diagonal lines encourage the eye to follow lines that are curved. These kinds of lines are frequently used to direct the vision to a facial asset of the client like an attractive chin, symmetrical cheeks, or well shaped lips. They can be used to direct the hair to the side or back of the face to open the face or they can direct the hair to the front of the face. A narrow face might want the hair directed back to open the face. A wide face might want hair directed to the front to give it a narrower look.
When lines change direction they create an angle. The angle is an important part of the hair design. For example, men frequently want sharp angles in their hair between the top of the hair design and the sides of the design. This gives a square look to the shape that is sometimes seen as masculine. To make this sharp angle, cut the hair on top to a flat line parallel to the ceiling and the hair on the sides to a flat line parallel to the walls. This will give a corner to the design which runs along the top of the parietal ridge.
Sharp corners are not usually wanted along the top of the parietal ridge for a woman's haircut. These corners can be rounded by cutting a rounded or diagonal line connecting the top and sides of the haircut.
When designing a haircut, decide where the lines should go and where they should change direction. For example a one length hair cut would have a line along the bottom of the haircut. For a square one length haircut the line is parallel to the floor all around the perimeter. For a circular cut the length would shorter in the front and longer in the back. For a triangular cut the length is shorter in the back and longer in the front. The lines in the circular and triangular are both slightly diagonal. Round has a diagonal back line and triangular has a diagonal forward line.
If you now wanted to add graduation to these one length haircuts, you would add diagonal lines defining the graduated part. These lines would give you other points of interest where the lines of graduation meet the ungraduated hair. What you do to the ungraduated hair will create another line. These two areas (graduated and ungraduated hair) will meet at an angle which can be changed to give the style the best shape for the client.
In analyzing a picture of a haircut the same methods are used. Look at the lines in the haircut and determine where the lines change direction. See the angle between the lines and use this information for plan for the lines and how sharply they change direction.