• CN: 11-2187/TH
  • ISSN: 0577-6686

›› 1957, Vol. 5 ›› Issue (1): 88-94.

• Article • Previous Articles     Next Articles

DIRECT METHOD FOR OBLIQUE VIEW

LEE CHUNG-CHING   

  1. Water Conservancy School of Canton
  • Published:1957-01-01

Abstract: 1.The oblique view is one of orthographic projection of which the planes of projection is not perpendicular to any one of the three principal planets of projection. Yet the projectors from the points of the object are running perpendicularly to the oblique plane. Therefore, the oblique view is quite different from an oblique projection of which the projectors (projecting lines) is oblique to the plane of projection. The isometric projection and dimetric projection may be considered as the special case of an oblique view with a definite inclined angles between the oblique plane and the principal planes. The cavalier and cabinet projections are the examples of oblique projectin. The isometric drawing for pictorial uses differs from the isometric projection in without reducing the scale along the isometric axes. 2. To obtain an oblique view; usually, .one of the following methods is used. A. To draw the projections of any plane figures in any oblique plane, we may use the revolving plane method, b. To draw. An oblique view of a solid figure or a part of it, the method of change of plane of projection is generally applied as in solving the problem of determining the intersection line of two surfaces or to find the true size of an area etc. C. The method of rotating the object. D. The method of inclined principal views. Using the above method, a same view should be drawn for twice times. Author suggest the "Direct method" to take any' oblique view of any object of any shape. Actually, it is a derivative of the revolving plane method but is much simplified. The nomanclatnre of "revolving trace axes" and "splitting trace axes" are suggested also to denote the edges of the triangle of oblique plane in order to facilitate the explanation of this process, 3. Principle and process of drafting: If we want to get the projection of a point in space in a oblique plane, we should consider a projector (line of projection) passing through the point and perpendicular to the oblique plane. Then the piercing point of the projector is the required projection. Moreover, we consider an auxiliary plane which is passing through' the projector and perpendicular to one of the principal planes of projection. Now the auxiliary plane is perpendicular to the oblique plane already for it contains the perpendicular line of the oblique plane. The piercing point must lie on the intersection line of the two planes, the auxiliary and the oblique planes. Therefore we can obtain the piercing point by two lines of intersection of two auxiliary planes cutting on the oblique plane. For example, if a plane ? is perpendicular to the oblique plane (P) and the horizontal plane (H), then, the plane ? must be perpendicular to the tracing line 'PH. Since three planes meet at one point, the line PH meet plane ? at the point, say (RPH), the PH must be perpendicular to all lines that are passing through the point (RPH) and on the plane ?. Therefore, we obtain the relation that the intersection lines of ? and (P), of ? and (H) must be perpendicular to the PH respectively. This relation is hold even when the oblique plane (P) is removed out from its original position, Lastly, we can obtain the oblique view by passing the points of the two principal views with lines perpendicular to the tracing lines of the oblique plane as shown in Fig. 2 and Fig. 3. The tracing lines of the oblique plane can he chosen arbitrary or obtained by "cone method" as in a given condition. It is shown in Fig. 1. If we have chosen a certain definite inclined angle between the tracing line and the axis VH, we might get the desirable projection as the isometric or dimetric etc. It is shown in Fig.4. If any two tracing lines were given, the can get the third easily. With one tracing line as the base line of a triangle and the other two as the other two edges we can construct a triangle. Now the oblique plane is coincided on the principal plane already because the triangle reveals its true size now and has one side on the principal plane. The base side of the triangle is denoted as “revolving trace axes”. The other two edges is denoted as "splitting trace axes": If any two principal views were given, we can obtain the: oblique view by passing through the point on the view; say, of'(V) plane; ,with lines perpendicular to the "revolving trace axes", and with lines passing through the points of another view on the H plane and perpendicular to the PH tracing line, “splitting trace axes”, then the intersecting points were removed on to the new position of the tracing line and perpendicular lines were set up there. Therefore, the points of intersection of any two equivalent lines are the points of the oblique view. We can check it by the third principal projection as shown in Fig.2, or by running any enclosed surface of the object with noting number as to avoid the erroneous connection. It is very interesting to note that the triangle of the oblique plane on its revolved position does not confine the region of drafting since a plane may be extended unlimitedly. In fact, we may consider the triangle as “coordinate oil drafting”. 4. Reversely, we can obtain any other view from the oblique view without using any counter revolving process. So the advantages of the "Direct method" apt to evolve a new series of drafting process for solving the problems of intersection of curve surfaces or to draw the pictorial projection etc.