Paper read to the Japan Graphic Science Society in Tokyo,  May 1981 and published in the meetings proceedings in the original English:

THREE DIMENSIONAL DRAWING INSTRUMENTS

by Vladimir Tamari

 

Vladimir Tamari is the president of Tamari 3DD Co. Ltd. He is a Palestinian artist and inventor bom in Jerusalem in 1942 and lives in Japan.

The space we live in is 3 dimensional XYZ space.  Drawing paper is a 2-dimensional XY flat surface.   This essential, problem has faced artists, architects, scientists and children when they tried to draw things on paper.  Drawing is an 'artificial' activity, and in many cultures, even some advanced civilizations drawing is hardly practiced: for example in the Gothic period cathedrals were probably built without a master plan drawn on paper.  The discovery of single-eye perspective in the Renaissance seemingly solved the problem of representing solid objects on flat paper.  However flattening everything on the picture plane gradually made us 'space blind':  since childhood we see flat photographs, paintings, diagrams and movies-  making our conception of the real three dimensional world very unreal.

In this paper I will describe two different types of drawing instruments that I have invented.  Both are three dimensional in the sense that they are mechanisms which operate in a 3-dimensional mode to create graphic projections.  Usually drafting instruments such as rulers, triangles and compasses operate in 2 dimensions, because paper is flat,  but it is quite useful to utilize mechanisms that function in space , since they are 'models' of an actual graphic situation.  (Fig. 1) shows a device invented by Dürer for making perspective projection drawings of actual objects. This is an example of an instrument which operates in 3D  mode.

The pivot on the wall represents the eye viewpoint while the picture frame represents the picture plane.  The line-of-sight is the string which is made in contact with the object.  Thus Dürer's instrument is a 1:1 scale model  of the actual perspective situation.  This concept of the model is basic to the two instruments I will describe.

Fig. 1 A 1525 woodcut by Dürer showing a device for tracing perspective projection. The artist holds a pencil at the point where the string meets the picture frame and transfers the point to the drawing when the 'window' is closed.

Imagine that you have a magical pen which can draw just like any other pen, but in addition it can move through a three dimensional paper space creating lines suspended as if they were made of wires. Such a pen would be very useful because any complicated shape or idea can be drawn as it is with no need to flatten the lines to fit on a 2 dimensional surface.  The instrument that I have invented in 1963 in Palestine is just such a 'space pen ­(1).  Using this instrument we can draw in space (Fig. 2) and it can be called a stereoscopic

pen because it uses the principle of binocular vision(2) - or seeing depth with two eyes. (Fig.3) shows this stereoscopic relationship projected on a picture plane seen with the two lenses of a stereoscope. (Fig.4) is a diagram explaining the functions of a 3 Dimensional Drawing Instrument.  Operating the instrument is quite  simple:  One hand holds the drawing handle which can be moved in three dimensional 'model space'. Looking through the 2 lenses of the instrument's stereoscope, the draftsman sees one pen floating in a 'paper space'.  This 'space pen' is guided in XYZ space by the spatial movements of the drawing handle, and it creates a solid line suspended in space.  Actually each eye is seeing a different pen and drawing, but they are both fused together in one image.   The left and right pens draw a flat projection of the handle's movement in space.  In addition, for each position of the handle in the Z direction (depth) a small parrallax adjustment is created by changing the distance between the two pens. This can be very small but the eyes are extremely sensitive to this parallax shift, so the instruments have to have extremely precise and smooth movements.  (Fig. 5-10) are examples of stereoscopic drawings made by using the 3DD instrument.  Of course a stereoscope is needed for comfortable fusing of the left and right flat images into one spatial image.

HISTORICAL BACKGROUND

The first simple stereoscopic drawings were made around 1836 by Charles Wheatestone, the inventor of the stereoscope.  They were simple geometrical figures (3). Wheatestone noted the extreme difficulty of making the precise parrallax shift by hand drawing, and soon the invention of photography made stereoscopic drawing an almost forgotten art. J.,C. Maxwell the scientist made his own 3D drawings, as did the artist Marcel Duchamp in 1917.  Picasso created a 'light pen' by waving a torchlight in space in front of an open camera shutter in a darkened room.  Several books of manually drafted stereoscopic drawings have been published, and computers can make excellent stereoscopic pairs.  However it is difficalt to call this 'drawing' as the computer must be fed mathematical information, completely neg-ating the physical action of drawing (4).

 

Fig.  2  The author with the 3DD he built in 1977. Photo by Wolter Witholt

Fig. 3  Stereoscopic Projection
   

Fig. 4 3DD parts and functions.  A stereoscope (1) fuses theimages of the two pens (2) to see one 'space pen'  making one 3D drawing.  A drawing handle (3) moves in space guiding the pens. A move in the Z direction causes a parallax shift (D). A tracing point (5) moves in model space XYZ (6) where it can trace small solid objects or 3D drawing accessories.

Stereoscopic drawing instruments have been independently invented on four separate occasions. The first is probably Prof. J.T. Rule of MIT who patented a 3D Drawing instrument in 1939 (5) but in correspondence with the author Rule mentioned that only one instrument was built which did not achieve the necessary precision. A. Cook's patent of 1958 shows an impractically complicated design of frames and wires (6). The work of Prof. R.L. Gregory in this field is described in his book, but again the ideas suggested are difficult to put into actual use (7).  The author did not know of these developments until after making his invention, so his instruments developed on quite different lines.  Many models and accessories have been built with continuous improvement in order to achieve Practical results.

3DD:  DRAWING METHOD OF THE FUTURE

The 3DD instruments I have described are not a mere method to produce stereoscopic drawings.  It is a new way of drawing - a practical method to conceptualize 3 dimensional images and ideas.  Holography, stereoscopic computer graphics and making stereoscopic drawings manually are all methods to make 3D images of preconceived ideas.  Only by using a 3DD instrument can one experience a real-time sense of creating a line in space. Among the several types of accessories made for the 3DD are a spherical compass, universally orientable plane, an axonometric perspective 3D template system and an optical method to visually project 3D drawings over real space.  This last device is fascinating to use, because it enables the user of the 3DD to see his drawings suspended in actual visual space in a 1:1 scale relationship to objects seen over vast distances. As an example, imagine an architect seated before the 3DD with the special superimposing attachment, and looking through it at an empty field where he is planning his building.  Superposed over the field he sees the 'space pen' of the 3DD and he can move it in XYZ space to sketch his building in actual size in its actual location.  He is moving the handle in XYZ model space of the 3DD, but the fused 3D image is located much further away in real space. This is the big difference between single eye perspective and stereoscopic perspective:  by using the 3DD we are making two drawings on the picture plane , but what we actually see  is a drawing identical in size, position, shape and orientation to the original 'object' in real space.  Drawing Space= Real Visual Space.

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(1)        - "3DD" The Architectural Forum p. 10. May 1965.

- “Opening of New Sense” by Itsuo Sakane. The Kagaku Asahi No.3,   1975 (in Japanese)

-"Drawing In Space" by V, Tamari. Graphic Design No. 57 (1975).

 

- "Making 3D drawings" by Itsuo Sakane Asobi Hakubuts-shi – Asahi Shimbun 1977.

            - Japanese Patent No. 762196 . 50.3.24.

(2)        Binocular Vision, by Solomon. Heinemann Medical Books.

(3)        "Looking back at Stereo" by B. Newhall. Stereo Realist Manual.

Morgan and Lester.

(4)        Solid Geometry in 3-D for Technical Drawing by A. Davies. Chatto

and Windus.

-Image Perspective and Design by T. Nagata. Bijitsu Shuppan-

-Stereogram Book of Contours by H. MacMahan, Jr, Hubbard Books.

(5)        U.S. Patent No. 2,171,894.  1939.

(6)        U.S. Patent No. 2,859,521.  1958.

(7)        The Intelligent Eye by R. L. Gregory. (1970). London: Weidenfeld and Nicolson

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THE SKIOMETER:

DRAWING THE SUN'S SHADOW LINE

 

This is an example of a 3 dimensional mechanism used as a model of an actual situation in order to create a graphic projection. The idea for this instrument occurred to the author when an architect friend told him about the difficulties of drawing the shadow map of a newly designed building still in the drawing stage.  Existing methods using graphs or photographic methods or computer programs are quite tedious and difficult (l). After a study of the actual physical situation (Earth’s rotation around its axis, and around the sun) a 3 Dimensional geometrical model was made showing the different parameters affecting the position and direction of a shadow of a point (Fig. A).

 

Using this geometrical model I designed a mechanical system as a 'model' of the rays the sun would make when falling at an object during a particular time of day, and year, and at a particular location on the earth's surface. This instrument, called Skiometer (in Greek Skio means shadow) enables a shadow map to be drawn quickly and accurately (Fig.B), (2). Please compare (Fig. A) with (Fig.B) to see the correlation between the mathematical model and the actual instrument. Plane (I) is both the Earth's ground plane and the drawing paper Point (0) is the corner of a roof or top of a pole whose shadow is to be determined. It is at a height (OP) from (I). In the instrument (OP) is a reduced distance according to the scale of the drawing. Plane (II) is at an angle (Φ) to (OP), passing through (0). (Φ) is the latitude angle of the location. (For example in Tokyo (Φ) is 35°). Plane (III) rotates around an axis perpendicular to (II) at (0). (h) is an angle corresponding to the time of day. Each hour advances (h) by 15°.  At 6:00 a.m.  (h) is zero. Strictly speaking this is so only at the time meridian. Small adjustments are needed for different longitudes. (d) is the inclination of the earth's axis to the sun. It varies from + 23° 26' (summer solstice) to 0°(spring and autumn equinox) to -23°26’ (winter solstice). (x) is the shadow point cast by (0) at height (OP) from (I) .  The locus of all point (X) for a fixed (OP) and (Φ) and (d), but for variable (h) is a hyperbola. To use the instrument, place point P on the ground plan of a building at point (0) whose shadow is needed.The arrow must point North ( for buildings in the Southern Hemisphere the arrow points South). The knobs for (Φ) and (d) and height to scale (OP) are locked at the correct values. For each (h) the pencil point (X) is made to slide until it draws a point on (I) - the paper. All points on the building's roof are similarly drawn for each (h) – points are connected to obtain the required map.

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(1)   Nippon Kenchiku Gakki Sekkei Keikaku  Pamphlet 24.   52.2.19.

(2)   Japanese patent application.