Exact Stereo Vision from a Pair of Figures Tsukasa Sakai Research Institute for Polymers and Textiles. Agency of industrial Science and Technology. Higasi 1-1-4, Tsukuba 305, Japan Have you tried t o get fused stereo images from pairs of figures projected plainly onto a remote screen? Usually, we wear a pair of polarizingglasses and look at figures projected side by side through each polarizer on (two) regular screen(s) or projected confocally on a specially designed refractive screen. Without the use of such devices, the present method t o observe exact stereo images, in particular of molecular models, will work with figures directly projected (or with printed drawings as well). In what follows,
"Can the Fused Image ol the Right-Handed Hellx Be Right?" figure set
cross-eyed
I I
yes
Yes yeslno
[
A-B
a-A A-6-A
viewing habitude' uncross-eyed
11 I
yeslno
swltcher
yes Yyeslno
'[ I: yes by using flsld stop. [ I [ I: yes through slit I [between tw0~0ver9.lno:If OVBT-lUSBd
M over-CIOSSBd.
'A', 'B', A-B, B-A, and A-B-A represent figures projected or printed, while AorB is the 2-dimensional, flat image, and ( A 3 1 or (BA) symbolizes the 3-dimensional, stereo image, respectively. We can find examples of A-B-A-type stereo triplets of right-handed helices for molecular models in wire (1, 2), solid (31, or ball-and-stick (4) displays. Frequently, those who have used the cross-eyed viewing method, complain that, for the conventional parallel A-Btype pair of drawings, they obtain stereo images of reversed depth and handedness from the image assigned initially. They thus prefer A-B-A-type stereo triplets, from which images emerge as A @,A) (A,B)A
and recommend switching to either of the exact stereo images, symbolized here as (A,B) or (B,A), of prescribed orientation (1-3). However, for such stereo triplets, some uncrossed direct viewers actually fuse (A,B) and (B,A) and as a result, see only a series of flat images ABABA where the center image A is due to over-fusion of both the left and right figure 'A' (5). Similarly, some crossed direct viewers, by excessively cross-separating the triplet, have the series of images ABAABA none of which are in stereo (6). By covering one drawing like A-B-(-1 or [-1-B-A with a sheet of paper [-I, they restore the proper stereo image (A,B) or (B,A). The above four types of images viewed directly from the triplet A-B-A can be summarized as follows:
where images noted as A or B are not in stereo and the stereo image in symbol (B,A) has the reversed handedness or surfaceorientation to the image (A,B). Moreover, for stereo drawings of molecules, particularly of the rather popular ball-and-stick models, one of the stereo images, (A,B) or (B,A), has a strange surface orientation at the contact portion of the atomic ball and bonding stick (4). One possible approach, to avoid such problems in the
triplet figures, is to teach ourselves t o perceive exact stereo images from ordinary pair of figures. With the use of only a tiny piece of card, those who have the cross-eyed viewing habit mav consciouslv correct their habit. and the conventional stereo pairs can recoup their inherent context. I t apDears natural to look at the rieht - figure - with one's right - eve . and the left with the left. Acquiring the skill is very simple, i.e., not to separate but to avoid overlap of right and left visual fields. For the customary pair of A-B type stereofigures, afieldstop [ 1, as in A[ ]B, where it covers the figure 'A' from one's right eye or 'B' from the left, can restrict overlay of bothviewing fields in the cross-eyed method. Downward from above one's head, it lookslike V-V, where Vrepresents each visual field, the tip point of which corresponds to the left or right eye, and -is the field stop. A piece of business card, of suitable width either folded or cut, just held in front of one's nose ridge will suffice. Blinking alternately helps its appropriate positioning. Another trick is to align horizons of the figures and of one's eyes in parallel. In contrast, separation of viewing fields, by a partition 1 like VIV from the above, is effective if the partition bas enough length to reach almost to the page or even to the screen. Complementarily, those who use the uncrossed viewing method may obtain an exact image from crossed B-A type drawings by using an appropriate slit to cross visual fields like [ I[ 1, where figure 'B'is covered from the left eye and 'A' from the right, and looking at 'A' with the left eye and 'B' with the right, both through the slit ] [. This is a clumsy method and is not recommended hut offered as an alternative for those who use the uncrossed method to look a t B-A type stereo pairs. A question, "Can the fused image of the right-handed helix be rieht?" for molecular models (1-4). is answered for three types of direct viewers in the table. The oresent semi-direct method is simole but general and works ih with stereo pairs either printed on pagesor projected onto a remote screen. The princi~leunderlying the present method may be also instructive-for some beginners to overcome their first psychological barrier in getting direct stereo pairs. and exact stereo vision-fr&m From scenes in everyday life, without the use of any viewers, you have complete and natural stereo vision very easily. Why not from stereo figures? Literature CRed R.;Olson, W . K . J . Chsm. Edue. Edue, 1. Srinivassn,A, Srinivassn.A. R.:Olson, % Tuekcr, V. Nature 1985,337,605.
1969,66,664.
3. Wilson, J. H . Nature 1989,339,433. 4. Chapuis. G. Nature 1989,333,670. 5. S a k s i , T.. U, be published. 6. s u g ~ e s t e dby an anonymous rsferee rsferee.
Volume 68 Number 5 May 1991
375
