International photographer (Jan-Dec 1934)

Eight The INTERNATIONAL PHOTOGRAPHER March, 1934 The Mathematics of Motion Picture Miniatures By Paul R. Harmer HE mathematics used to build and set miniatures is not generally known. Most of the layout and plans are privately made, the principles employed are closely guarded as secrets, although in reality the system is based on the mathematical invention called proportion. Many fine examples of the art of miniatures, full size and process photography have been accomplished. Some of the problems are very intricate and complex, others are less so, and easily understood with very little explanation necessary. It is almost impossible to give proper credit to the host of cameramen, artists, architects and mechanics who have made possible the gigantic spectacles which pass before your eyes as if they had actually taken place. Hardly a picture leaves Hollywood but some part of it has been helped by miniature and process. When the production office decides that the construction of a large building cannot be undertaken because of the budget and in the second place there isn't room to build it, and in the third place it isn't necessary to build all of it, because part of it can be built in miniature thereby saving money, time and space, the job is handed to the art department which immediately calls in the miniature chief and they both talk it over with the director. Between the three of them they decide how much of the full size building is necessary for the action, the rest of the building to be made in miniature and matched in. The first problem is selecting the proper lens which cause corresponding parts of similar triangles prove this. WXD Therefore F = . See Illustration No. I. W F = 1.6 inches, which is mighty close to a 40 mm. lens. Checking the height of the building which is 38 feet 2.4 inches, we find that this lens gets our height and gives us plenty of foreground for action. The director has already decided that 16 feet in height will give him plenty of room to take care of the usual street traffic such as busses, cars and pedestrians, so the miniature department knows they have only to supply the top 22 feet 4.8 inches. The scale, the miniature is built on, is the next step. First we must decide how far from the camera we should set the miniature for convenience to the cameraman. We find that 12 feet will give him the distance necessary to closely match in the lines and also give the electrician room to set and manipulate his lights. We will then decide that 12 feet is all right. Using Formula No. 3, N 12 1 S = — , the scale proves to be S = = S = — of a D 144 12 foot, which is one inch. Therefore, the 1-inch scale is correct and the miniature will be built 1/12 of the full size. The next condition to be considered is how high from the floor should the miniature be set. In the drawing (see Page 9) you will see that the full size structure PICTURE APERTURE .868 3*. 631 INCHES W. APERTURE WIDTH w w r field iviorrt H, = APERTUAe height H r FIELD HEIGHT F = FOCAL LEHCTH or LEH5 D = DtiTANCE FROM LEHS ^■i = i*^. <. FORMULA No. 1 f 0 H Hi 1L * FORMULA NO. Z F 0 .aie i 57J w 144 «IZ *33.<?' —nr~ W = 77-7? .(>3< _ H 1. 5 7S 1+4-XIZ . i\ 3 *ZI ___ — — W u -j — T -f* — 1 ~l — hi 1 1 1 1 1 % -C \. 4 ^F it V pi3 : === r < 2 U h — ' t r l"~H F ^ M— 1 r4 ■*-H H H — ! ' — * — ^-S H— * — 1 — V. m=H H" H Tl~H E= \V\ -H- *4ffe u/ 1 ; 1 M I ! _ x r= "n \f I1T 4 in ? i 'Ttt X JL 1! L JX L-IE L -»-. n FORE &«our>(o H = 626.8" 12 Fig. 1 H r 52 -4.8' will take in the required spread of the building. Most of these shots are made in the stage and 150 feet is about the average size allowed because of the crowded conditions prevailing in most studios, so to begin with we have a set with a front of 77 feet 9 inches. Now what lens can we use in 150 feet? Some room must be allowed around the camera and light platforms must be set behind the full size, so we have only 144 feet left. W1 w Formula No. 1 shows us — = — . This is true be F D is built to a point four feet above the center line of the camera lens. As we are working with the 1/12 foot scale, we will take 1/12 of 4 feet, which is 4 inches. The miniature is then set 4 inches above the center line. In this case the center line parallels the floor and we have in all 12 feet and 4 inches from the floor. The final test in setting of all miniatures is done by looking through the camera and aligning the adjoining parts, then running a short test through the camera. The print from this film is carefully watched in the projection room for errors in alignment, painting and lighting. The five formulas given here, with their various transitions, can be applied to many other cases. The next problem dealing with full size structure and miniature is when the miniature lies beyond the full Please mention The International Photographer when corresponding with advertisers.