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I think there's a scene in The Matrix where Neo does a bullet dodge in slow-motion and you also see the camera rotate around Neo, what do you call this effect?

For example:

The ____ when Neo dodges bullets in slow-mo was cool.

It's known by various terms, though the one I've heard used most often is bullet time. There are other names listed there - frozen moment, dead time, flow motion. It's even used in adverts on TV, these days.

The camera rotation part of the effect is known as an "arc shot." The first five results on on this search results page will give you information on "arc" shots. SamBC has already given you a link for the bullet slowdown effect.

It's generically referred to as MoCo, or motion control photography.

Pioneer and inexpensive solutions are realized using multiple cameras, an exception being Intel's FreeD or True Vue which uses two cameras at each spot to create 3D volumetric pixels, modern and professionally priced systems use a single high speed camera on a robotic arm.

Regardless of the hardware, post processing, and software used the motion being recorded is controlled by getting the shot in real time from the desired position.

This can be used when it's expensive to recreate the shot or to recreate the same shot with different actors and objects, allowing them to be combined in post and appear as though the shot was made normally by one camera (and an agile camera operator). Occasionally the same actor will appear multiple times in order to be their own twin or past/future self.

Sony calls their version "Multiple Camera Control".

• Sony YouTube Video: "Sony | Cyber-shot | RX0 - Fly into Ørbit".




• Sony YouTube BTS Video: "Sony | Cyber-shot | RX0 - Behind the scenes of 'Fly into Ørbit' ".

Intel's True Vue technology uses two cameras at each spot and a ring of 30-50 pairs around the area being captured, often a stadium, to produce 3D voxels. This allows them to smoothly interpolate between the pairs, even to take the field for a player's eye view. Intel uses JAI industrial cameras.

Intel True Vue videos:

• YouTube: "Intel FreeD Technology + NFL"




• YouTube: "360-degree replay at MLB All-Star Game" (360° Replay is the old name)

Robotics

The slowdown is created by filming at high speed but the camera tracking is called "motion control". The term "bullet time" was popularized due to the use of the effect in the movie The Matrix, most uses of motion control (MoCo) don't involve firing bullets or CGI and multiple cameras. Modern MoCo uses one high speed camera mounted on a robotic arm.

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  MrMoco Rentals

  
  
  

  • TV Commercial: "Citroën Cactus Milo Commercial".

  
  

  • Demo on Vimeo: "Bolt Stiller Show Reel Behind the Scenes".

  
  

  • Demo on YouTube: "Bolt On Track Showreel at Stiller Studios".

  
  


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  Production Company: Digital Air

  
  
  

  • Chanel Commercial: Chance (.MOV)

  
  

  • Intel Commercial: Core2 Duo (.MOV)

  
  

  • Ruffles Commercial: Hockey (.MOV)

  
  

It's more about being able to move the camera precisely along a predetermined course at a predetermined speed in a repeatable manner, than it is about bullets.

Frozen moment

Motion control can be used to match camera array shots. Camera Array shots are also known as frozen moment or time-slicing or bullet-time (made famous in The Matrix). Because the camera array represents a moving camera path the same path can be defined in a motion control move. This allows all of the other effects that are possible with motion control to be combined with frozen moments. For example, a live action pass filmed with motion control allows for the insertion of a moving person into a frozen scene.

Motion control can also be used to get into and out of frozen moment shots seamlessly. A camera move can begin with a motion control move and switch at some point to the camera array. The motion control system moves the motion picture camera's position from a start position to the first position of the camera array, at which point the camera array is triggered. In post production a straight cut joins the two shots.

Using one take, one bottle, they were able to obtain three shots and refocus the depth of field for each one. This clip was extracted from the Mr. MoCo "Bolt Stiller Show Reel" and was cropped and trimmed to fit within the upload parameters.

See also: Mark Roberts Motion Control: "The Seven Uses of Motion Control":

• Repeat Moves – Making elements appear and disappear, crowd replication, changing backgrounds and foregrounds, filming action at different speeds, putting elements together.




• Scaled Moves – Shooting miniatures, rotating camera moves, matching scales.




• Controlled Moves – For controlled filming and lighting on products.




• CGI Export – Combining live-action to CGI.




• CGI Import – Complex moves, unusual shapes, impossible moves, Pre-visualisation.




• Frozen Moment Integration – For mixing live-action and time-slicing or “bullet-time”.




• Specific Music Video Effects – Audio timecode triggering.