Video Time Stretch Calculator

Retiming a shot is fundamentally a resampling problem: the source holds a fixed number of samples in time (duration times source frame rate) and the delivery format demands a different number (target duration times output frame rate). The speed factor is simply original duration divided by target duration, so a 60-second clip stretched to 90 seconds runs at 0.667x and a clip compressed to 40 seconds runs at 1.5x. Because output frames must land at even intervals of the delivery frame rate, any factor below 1.0 leaves temporal gaps that no original frame occupies, and those gaps must be synthesised. Motion-compensated interpolation estimates a dense optical flow field between adjacent frames and warps pixels along those vectors to the requested sub-frame instant. The audio side follows a separate law. Naive resampling changes pitch by 12 times log base 2 of the speed factor, so 2.0x is exactly plus 12 semitones and 0.5x is minus 12 semitones, while 1.5x gives plus 7.02 semitones - close enough to a perfect fifth to detune a music bed. Practitioners treat stretch factors within roughly 10 percent of unity as visually transparent, 10 to 30 percent as showing edge warping on fast motion, and beyond 50 percent as prone to visible tearing, ghosting and swimming textures. Optical flow fails predictably at occlusion boundaries, on motion blur, on transparent or repeating detail such as water, foliage and hair, and on heavily compressed sources where block artifacts are mistaken for real motion.

Slow motion predates digital retiming by a century. The Austrian priest and physicist August Musger patented a mirror-drum apparatus in 1904 that recorded at an elevated frame rate and replayed at normal speed, and the German term he inspired, Zeitlupe, is still the standard word for slow motion. High-speed cinematography grew out of the chronophotographic work of Etienne-Jules Marey in the 1880s and was industrialised through rotating-prism cameras in the mid twentieth century. Because the film image rate and the projection rate were mechanically fixed, speed changes were achieved in the camera, not in post. Television forced the arithmetic into the open. The 24 frames per second sound-film standard, settled around 1927 to 1929, did not divide evenly into the 29.97 frames per second that NTSC adopted when colour subcarrier requirements shifted the rate off 30 in 1953, and the 3:2 pulldown field-repeat pattern became the industry workaround. Genuine frame synthesis arrived with computer vision: the differential optical flow formulations published independently by Berthold Horn and Brian Schunck and by Bruce Lucas and Takeo Kanade in 1981 supplied the motion-estimation mathematics. RE:Vision Effects commercialised that research as Twixtor in the late 1990s, and comparable engines are now built into DaVinci Resolve, Premiere Pro and Nuke. On the audio side, the phase vocoder described by James Flanagan and Roger Golden at Bell Labs in 1966 made pitch-independent time scaling practical.