An object is an angular perspective when neither side is parallel with the picture plane. In Fig. 9 we have a box in angular perspective.
Draw picture plane, horizon, point of sight, prime vertical and station point, also distance points the same as you did in parallel perspective. The measuring scale in the foreground may also be used but instead of using D and D' use M and M'.
You will note that this station is not 11/2 the diagonal of the picture plane.
Remember, when neither side of the object is parallel to the picture plane, both sides are on the slant.
To draw the cube, draw the height, and one vanishing line to the horizon; where it touches the horizon we call V or vanishing point. You may place this line on any slant. When drawing from a real cube, hold your pencil along the line and get the direction this way. Remember, if the near edge of the cube is on the prime vertical at an angle of 45°, you see as much of one side of the cube as you do of the other. Both sides will vanish at equal angles and the vanishing points will fall on D and D', but the minute you move the cube at another angle or change its position to the right or left, the vanishing points will change. So in a room, different objects have different vanishing points while objects in parallel perspective all vanish in the point of sight.
This cube is to the right PS. You see more of the one side than you do of the other, the vanishing line will fall elsewhere on the horizon. The greater the slant of one side the more gentle the slant of the other, the vanishing point on the side with
the greater slant will be nearer PS than the other vanishing point.
You know the angle of the object is really a right angle, so after finding one vanishing point V, draw the line from V to S (or station point), and at the station construct a right angle. Continue this line to the horizon, which will give V or the other vanishing point.
You know that parallel oblique lines vanish in the same point, so the parallel sides of the cube vanish in the same points. How much of the side is seen we determine by M and M' instead of D and D'.
Using a compass and with V as a center and VS as a radius, mark off the horizon M. With V as a center and V'S as a radius, mark off the horizon M'. These points are used as D and D' in parallel perspective.
Draw the auxiliary lines the same length as the height of the cube, then the dotted line to M and M'. The parallel sides of the cube vanish to the same points. Carry measuring lines forward to obtain the size on the scale.
Fig. 10 is an angular view of a room; it is like the inside of a large box.
Draw the picture plane, horizon, point