APPLICATION TO PERSPECTIVE DRAWING The Picture five axioms just formulated apply to conditions which are apparent but which do not really exist. In a perspective drawing these apparent conditions in space must be represented by actual conditions on paper. The perspectives of parallel lines are represented by converging lines which actually meet at a point which is the perspective of their vanishing point. Fig. 8 illustrates this. An observer stands before an object. Be tween him and the object is a plane called the picture plane. The object becomes visible to him by rays of light known as visual rays reflected into his eye from each point on its surface.
Each point is projected upon the picture plane by its visual ray and the result is a perspective view.
Rule C. The perspective of any point is where the visual ray from the point intersects the picture plane.
A perspective is really a conical projection of the object on the picture plane, the projecting cone being made up of visual rays. In order to locate the imaginary vanishing point of the roof lines ab and the observer looks in a direction parallel to ab and al b1 (Rule B). The direction in which he is looking becomes the visual ray passing between the imaginary vanishing point and his eye. The point in which this visual ray intersects the picture plane is the perspective of the vanishing point (Rule C), and to this perspective vanishing point the perspectives of the roof lines ab and actually converge.
Rule D. To find the perspective of the vanishing point of any system of lines, pass a line parallel to the system through the observer's eye and find where the line pierces the picture plane.
equals the height of a man (to the scale of the drawing) the view obtained will be as though seen by an observer standing on the ground plane. Increasing this distance is equivalent to rais ing the observer's eye, and if the distance is great the result is a bird's eye view. The ground plane may be taken above the horizon plane and the result ing view will show the object as though the observer were looking up at it. The picture plane and the horizon plane are known as the co-ordinate planes of projection and on them is per formed all the work of construct ing the perspective view.
Orthographic Projection.— As already stated the perspective view is a conical projection on the picture plane. This conical projection is in practice not found from the actual object in space, but from a plan and an elevation of the object. The plan is essentially a top view and the elevation a front view or sometimes a side view.
A plan is constructed by projecting each point in the object to a horizontal reference plane by lines or projectors which are perpendicular to the horizontal plane. An elevation is constructed by projectors perpendicular to the vertical plane. Such views are known as orthographic or right-line projections in contrast to the conical or perspective projection, and are the ordinary means of representing objects on paper (see DRAWING, ENGINEERING). Fig.
io shows a conical and an orthographic projection. Fig. i i illus trates the construction of a plan and an elevation. Fig. 12 shows the two views as they are represented on paper. Each point in the object, has two projections, both being necessary to locate accurately the relations of the point to the two planes. Thus the point a is above the horizontal reference plane, a distance equal to am as indicated in elevation, and in front of the vertical reference plane a distance equal to an as shown in plan. The eleva tion shows vertical distances, the plan shows horizontal distances. The object in space may be above the horizontal plane as in figs. II and 12, or it may be below the horizontal plane as in fig.