On a Given Line Placed at an Angle to the Base Draw a Square in Angular Perspective, the Point of Sight, and Distance, being given.
Let AB be the given line, S the point of sight, and D the distance (Fig. 151, 1). Through A draw SC from point of sight to base (Fig. 151, 2 and 3). From C draw CD to point of distance. Draw Ao parallel to base till it cuts CD at o, through o draw SP, from B mark off BE equal to CP. From E draw ES intersecting CD at K, from K draw KM, thus completing the outer parallel square. Through F, where PS intersects MK, draw AV till it cuts the horizon in V, its vanishing point. From V draw VB cutting side KE of outer square in G, and we have the four points
AFGB, which are the four angles of the square required. Join FG, and the figure is complete.
Fig. 151.
Any other side of the square might be given, such as AF. First through A and F draw SC, SP, then draw Ao, then through o draw CD. From C draw base of parallel square CE, and at M through F draw MK cutting diagonal at K, which gives top of square. Now through K draw SE, giving KE the remaining side thereof, produce AF to V, from V draw VB. Join FG, GB, and BA, and the square required is complete.
The student can try the remaining two sides, and he will find they work out in a similar way.