Step 1: Rotate the line AB to make it parallel to VP.
Rotate the line AB about the end A, keeping θ, the inclination of AB with HP constant till it becomes parallel to VP. This rotation of the line will bring the end B to the new position B1. AB1 is the new position of the line AB when it is inclined at q to HP and parallel to VP. Project AB1 on VP and HP. Since AB1 is parallel to VP, a΄b1΄, the projection of AB1 on VP is in true length inclined at q to the XY line, and ab1, the projection of AB1 on HP is parallel to the XY line. Now the line is rotated back to its original position AB.
Figure 2. Illustrates the locus of end B of the line AB when the line is rotated about end A
Step 2: Rotate the line AB to make it parallel to HP.
Rotate the line AB about the end A keeping φ the inclination of AB with VP constant, till it becomes parallel to HP as shown in figure 2. This rotation of the line will bring the end B to the second new Position B2. AB2 is the new position of the line AB, when it is inclined at f to VP and parallel to HP.
Project AB2 on HP and VP. Since AB2 is parallel to HP, ab2, the projection of AB2 on HP is in true length inclined at f to XY line, and a΄b2΄ the projection of AB2 on VP is parallel to XY line. Now the line is rotated back to its original position AB.
Step 3: Locus of end B in the front view
Referring to figure 2, when the line AB is swept around about the end A by one complete rotation, while keeping θ the inclination of the line with the HP constant, the end B will always be at the same vertical height above HP, and the locus of the end B will be a circle which appears in the front view as a horizontal line passing through b'.
As long as the line is inclined at θ to HP, whatever may be the position of the line (i.e., whatever may be the inclination of the line with VP) the length of the top view will always be equal to ab1 and in the front view the projection of the end B lies on the locus line passing through b1’.
Thus ab1, the top view of the line when it is inclined at θ to HP and parallel to VP will be equal to ab and b΄, the projection of the end B in the front view will lie on the locus line passing through b1΄.