CHARTS AND FORMULAS

Miniatures

(From The Photography of Miniature Effects—High-Speed Photography in Chapter 3.)

Formula to determine proper frame rate for scale being used:

(√m) × (r) = f

where

m = miniature’s scale

r = base frame rate

f = new frame rate.

Example: 1:4 scale at 24 fps = (√4) × (24) = (2) × (24) = 48 fps

Formula to determine proper actual speed of a scaled object at a scaled frame rate:

(rs/m) = (b)
(b) × (r) = (as)

where

rs = real object speed

m = miniature’s scale

b = base speed

r = frame rate factor

as = actual speed for filming.

Examples: 36 mph × 1:6 scale car = 8.8 feet per second 8.8 feet per second × 2.5 normal frame rate = 22 feet per second

Camera and Lens Chart

(From Digital Cinematography in Chapter 3.)

Pixel Resolution

(From 4K+ Systems Theory Basics for Motion Picture Imaging in Chapter 6.)

Mattes

(From 3D Compositing in Chapter 7.)

Result = Fg*(A) + Bg*(1 − A)

where Fg is the foreground, Bg is the background, and A is the alpha, or matte.

Premultiplied

Result = Fg + Bg*(1 − A)

This operation is often referred to as an over.

Camera and Lens Formulas

(From American Cinematographer Manual.¹)

For these variables:

O = object size

D = distance from object to camera lens

F = focal length

A = aperture size

35mm film full frame sound aperture: 0.866 inch × 0.630 inch

35mm film full frame aperture: 0.980 inch × 0.735 inch

(See the American Cinematographer Manual for other film formats.)

Lens Angle

Tangent ½ viewing angle =

where

A = aperture size (width or height)

F = focal length in same units.

For anamorphic:

Depth of Field

where

H = hyperfocal distance

F = focal length of lens

S = distance from camera to object,

Total depth = D_F − D_N

Hyperfocal Distance

where

H = hyperfocal distance

F = focal length of lens

f = f-stop

Cc = circle of confusion, where 35mm camera Cc = 0.002 inch (0.0508mm).

Right Triangles

Right triangles are useful for calculating sizes and distances and for laying out 2D objects.

Figure A.1 Right triangle formulas. (© Carr Lane Manufacturing Co. All rights reserved. Compliments of Carr Lane Mfg. Co., www.carrLane.com)

Compositing Blends Modes

(Based on http://dunnbypaul.net/blends. Used with permission from Paul Dunn.)

These are approximate formulas. Pixel values are considered to be 0−1 and results are scaled to this range. Use 255 for 8-bit and 65535 for 16-bit.

The values p1 and p2 represent two corresponding pixels, and pixel represents the final. Values are computed on red, green, and blue channels separately.

Multiply: pixel = p1 * p2

Screen: pixel = 1 − (1 − p1) * (1 − p2)

Darker: if (p1 < p2) pixel = p1

if (p2 < p1) pixel = p2

Lighter: if (p1 > p2) pixel = p1

 if (p2 > p1) pixel = p2

Difference: pixel = |p1 − p2|

Negation: pixel = 1 − |1 − p1 − p2|

Exclusion: pixel = ½ − 2 × (p1 − ½) × (p2 − ½)

Color Burn: pixel = 1 − (1 − p1)/p2

Linear Burn: pixel = p1 + p2 − 1

Color Dodge: pixel = p1/(1 − p2)

Linear Dodge: pixel = p1 + p2

Overlay: if (p1 > ½) pixel = 1 − (1 − 2 × (p1 − ½)) × (1 − p2)

   if (p1 < = ½) pixel = (2 × p1) × p2

Soft Light: if (p2 > ½) pixel = 1 − (1 − p1) × (1 − (p2 − ½))

      if (p2 < = ½) pixel = p1 × (p2 + ½)

Hard Light: if (p2 > ½) pixel = 1 − (1 − p1) × (1 − 2 × (p2 − ½))

       if (p2 < = ½) pixel = p1 × (2 × p2)

Vivid Light: if (p2 > ½) pixel = 1 − (1 − p1)/(2 × (p2 − ½))

        if (p2 < = ½) pixel = p1/(1 − 2 × p2)

Linear Light: if (p2 > ½) pixel = p1 + 2 × (p2 − ½)

         if (p2 < = ½) pixel = p1 + 2 × p2 − 1

Pin Light: if (p2 > ½) pixel = max (p1, 2 × (p2 − ½))

    if (p2 < = ½) pixel = min (p1, 2 × p2))

¹ Reproduced by permission of the American Society of Cinematographers.