Abstract

Drawings giving the impression of three dimensions are frequently needed in the analysis of optical components and systems. The normal methods for preparing such picture drawings from plan and elevation views are applicable for only limited viewing positions, require large paper and straightedges and very precise drafting, or are approximations which produce distorted pictures. From the basic characteristics of monocular vision, simple equations can be derived with which the three dimensional coordinates of object points can be converted to two dimensional coordinates on the drawing plane. By use of this transformation, perspective, general trimetric, and isometric drawings to scale can be prepared easily with paper and ruler no larger than the finished drawing. The scale of the drawing and the viewing point can be chosen without restriction. Stereoscopic pairs of drawings may be prepared readily when a more effective illusion of depth is desired.

© 1961 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Rex V. Cole, Perspective (Seeley, Service & Company, Ltd., London, 1927).
  2. Thomas E. French, A Manual of Engineering Drawing (McGraw-Hill Book Company, Inc., New York, 1941), 6th ed., pp. 430–440.
  3. Gilbert McPherson, Trans. Inst. Min. Met. 47, 347 (1938).

1938 (1)

Gilbert McPherson, Trans. Inst. Min. Met. 47, 347 (1938).

Cole, Rex V.

Rex V. Cole, Perspective (Seeley, Service & Company, Ltd., London, 1927).

French, Thomas E.

Thomas E. French, A Manual of Engineering Drawing (McGraw-Hill Book Company, Inc., New York, 1941), 6th ed., pp. 430–440.

McPherson, Gilbert

Gilbert McPherson, Trans. Inst. Min. Met. 47, 347 (1938).

Trans. Inst. Min. Met. (1)

Gilbert McPherson, Trans. Inst. Min. Met. 47, 347 (1938).

Other (2)

Rex V. Cole, Perspective (Seeley, Service & Company, Ltd., London, 1927).

Thomas E. French, A Manual of Engineering Drawing (McGraw-Hill Book Company, Inc., New York, 1941), 6th ed., pp. 430–440.

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Perspective and trimetric views of a cube from a general viewing point and from the isometric point. The numerical values are the actual lengths of the lines on a full scale drawing of a 1.5-in. cube.

Fig. 2
Fig. 2

Perspective view showing the position P′ on the drawing paper at which the eye E on the Z axis sees the object point P.

Fig. 3
Fig. 3

Perspective view showing the shift in the apparent position of P on the paper for a more general eye location. Transformation of the coordinates of P into the XYZ″ system restores simple expressions for x′ and y′.

Fig. 4
Fig. 4

Plan and elevation views of a simple roof prism, and perspective drawings of the prism from three viewing positions.

Fig. 5
Fig. 5

Amici prism. The three perspective views show the freedom of choice of viewing point.

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

x = S x / ( L - z ) ,
y = S y / ( L - z ) ,
tan A = x 0 / z 0 ,
tan B = - y 0 / ( x 0 2 + z 0 2 ) 1 2 .
x = x cos A - z sin A , y = x sin A sin B + y cos B + z cos A sin B , z = x sin A cos B - y sin B + z cos A cos B .
sin A = x 0 / ( x 0 2 + z 0 2 ) 1 2 cos A = z 0 / ( x 0 2 + z 0 2 ) 1 2 sin B = - y 0 / ( x 0 2 + y 0 2 + z 0 2 ) 1 2 = - y 0 / L cos B = ( x 0 2 + y 0 2 ) 1 2 / L .
x = S x / ( L - z ) , y = S y / ( L - z ) .
x = S x / L , y = S y / L .