ALGORITHM

The larger is the shooting basis, the greater is the angular disparity, and the more effective are binocular factors within the distant areas of the frame's composition. So, in shots of distant landscape-like scenes without foreground objects the shooting basis should be increased.

The shooting basis is a major factor affecting the display of a stereoscopic image. It is not recommended to change it during the shooting of a single shot and even the whole single sequence.

The Algorithm for Parameter Selection in 3d Shooting

In 3D shooting we have the following parameter set: Вview = 65 mm

Р∞screen = 1% of the image width

Wscreen = 6500 mm – the average screen width Bshooting = 25 mm – the average shooting basis

While building the image composition the DP makes a number of consecutive decisions:

•Selecting the scale of the object within the ramp plane

•Selecting the lens with necessary angle and focal distance;

•Determining the size of the shooting basis;

•Determining the location of and distance to the ramp;

•Determining the depth boundaries of the comfortably viewed space.

Photo 2. An example of a foreground composition with the background at infinity

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Having selected the lenses (based on the view angle) and the shooting basis the DP chooses the shooting mode: proportional or hypertrophied. If the shot depth extends to infinity, the shooting should be made with the main ramp distance which is the derivative of the ratio between the selected focal distance and the shooting basis, and is calculated according to the equation [5]. It means that the distance to the objects cropped by the frame edges should not be less than the ramp distance. The shooting with these parameters will allow to render the image with the maximum depth of the comfortably viewed space when the parallaxes of the objects at infinity do not exceed 1% of the screen width (Photo 2).

In defining the ramp’s position in the 3D composition, the psychological perception of the foreground objects should be correlated with the effect of "the stereoscopic window paradox". The ramp may lie behind the foreground object which usually shouldn't be cut off by the frame edges. For example, in the medium shot of an actor with an outstretched arm, the foreground object is the arm and the ramp is behind the arm of the character cropped by the frame edges (Photo 3). In this case the close distance is the distance to the outstretched arm and it shouldn't be less than half of the ramp distance. Then the horizontal parallax values of the objects extending into the screen hall will not exceed the infinite parallax values (1% of the image width) taken with an opposite sign.

In the absence of objects "intruding" into the space in front of the screen, the object cropped by the frame edges becomes the foreground object, and it must lie within the ramp. (Photo 4).

Photo 3. "Intrusion" of the foreground object into the screen hall

Photo 4. Foreground object within the ramp

The ramp is a virtual plane of zero parallaxes going through a 3D object. So, in medium shots and close-ups the position of the zero parallax plane within the cross-section of this object will determine the intensity of the object’s 3D relief (the extension into the screen hall space). Fixing the ramp at the back of the character’s head is preferred to setting the zero parallax by the actor’s pupils.

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On the basis of the equations describing the relationships of 3D shooting parameters, cinematographer I. Pomorin compiled an interactive Microsoft Excel spreadsheet which helps the DP to efficiently define the limits of the comfortably viewed space with a given combination of the focal distance and the shooting basis, set in accordance with the artistic goals, or to select such combination using given space limits.

The reference parameters include:

the lens focal distance, F;

the 3D shooting basis, Bshooting

the infinity parallax on the sensor or the film, P∞film.

After entering the reference parameters the chart shows:

the ramp distance, Lramp;

the ramp index, H, equal to the space hypertrophy factor

the maximum allowable distance from the camera to the farthest object, Lbackground, calculated from the equation [7].

the minimum allowable distance from the camera to the nearest object, Lforeground, calculated from the equation [9].

			Lforeground		LrampH					[9]
					H 1
			Calculating parameters
	F mm		B shoot	Screen		Frame			Kpr		P∞screen	P∞film
			mm	mm		mm					mm	mm
	50		26,00	6500		25			260		65	0,25
	H		Lfground m	Lramp m		Lbground
	1		2,60	5,20		∞
	1,25		2,31	4,16		20,80
	2		1,73	2,60		5,20
	3		1,30	1,73		2,60
	4		1,04	1,30		1,73
	5		0,87	1,04		1,30
	H		Lfground m	Lramp m		Lbground
	5,2		084	1		1,24

The cells highlighted in blue contain the data unchangeable over the entire filmmaking span. Here, these values include the allowed infinity parallax on the screen (65 mm), the image width on the 3D camera sensor or film (25 mm) and the average screen width (6500 mm).

Having selected the appropriate lens, the DP enters its focal distance and the shooting basis. The chart then shows, line by line, the ranges of the comfortably

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viewed space shot with different hypertrophy indexes (the purple vertical row). The cyan and green vertical rows provide the variants of 3D composition ranges dependent on the hypertrophy index. The bottom horizontal row provides the limits of the comfortably viewed space based on the arbitrary ramp distance.

We installed a specialized electronic calculator into the lens’s remote control, and this calculator, like the above chart, shows the limits of the comfortably viewed space according to the initial 3D shooting parameters. (Photo 5)

. Photo 5

If we analyze the values of the ranges of the comfortably viewed space at different focal distances, we may notice a peculiar pattern within the Russian “Stereo-70” system, stemming from an apt combination of the shooting basis value of 26 mm and the frame width on the matrix of 24,8 mm. Such combination of values makes it possible to define the shooting parameters by a simple arithmetic calculation without any chart and with acceptable accuracy:

The main ramp distance in meters is determined by the first digit in the lens’s focal distance;

The farthest limit of the comfortably viewed space is equal to the main ramp distance with the previous hypertrophy index;

The nearest limit of the comfortably viewed space is equal to half of the ramp distance in use.

Thus, for example, in the “Stereo-70” lens array the main ramp distance values can be approximated as follows:

F, мм	Lforeground, м	Lramp, м	Lbackground, м
23	1,15	2,30	∞
28	1,40	2,80	∞
35	1,75	3,50	∞
40	2,00	4,00	∞
50	2,50	5,00	∞
75	3,75	7,50	∞
100	5,00	10,00	∞

With these values the farthest limit of the comfortably viewed space is always at infinity

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When shooting with the ramp distance equal to a half of the basic ramp distance (hypertrophy index H=2), the background distance values are set to values of the main ramp distances for given lenses

F, мм	L foreground, m	Lramp, m	Lbackground, m
23	0,58	1,15	2,30
28	0,70	1,40	2,80
35	0,88	1,75	3,50
40	1,00	2,00	4,00
50	1,25	2,50	5,00
75	1,88	3,75	7,50
100	2,50	5,00	10,00

With each change of the ramp distance by a multiplier the value of the previous ramp distance becomes the foreground distance.

Conclusion:

The above methodology allows the DP to use complex mathematical calculations in his daily work on the set, and now, the image creator can have an action algorithm independent from a 3D expert. Technical aspects of film making are important, but they should not stand in a way of the creative approach to selection of 3D shooting parameters in accordance with the artistic goals, and methods offered here help remove this obstacle.

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