In the context of

live-action Live action (or live-action) is a form of cinematography or videography that uses photography instead of animation. Some works combine live-action with animation to create a live-action animated film. Live-action is used to define film, video ga ...

and

computer animation Computer animation is the process used for digitally generating animations. The more general term computer-generated imagery (CGI) encompasses both static scenes (still images) and dynamic images (moving images), while computer animation refe ...

, interpolation is

inbetweening Inbetweening, also known as tweening, is a process in animation that involves creating intermediate Film frame, frames, called inbetweens, between two key frame, keyframes. The intended result is to create the illusion of movement by smoothly trans ...

,{{Cite web, url=https://www.freecodecamp.org/news/understanding-linear-interpolation-in-ui-animations-74701eb9957c/, title=Understanding Linear Interpolation in UI Animation, date=2017-05-14, website=Developer News, language=en, access-date=2019-08-26 or filling in frames between the key frames. It typically calculates the in-between frames through use of (usually) piecewise

polynomial interpolation In numerical analysis, polynomial interpolation is the interpolation of a given data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of data points (x_0,y_0), \ldots, (x_n,y_n), with no ...

to draw images semi-automatically. For all applications of this type, a set of "key points" is defined by the graphic artist. These are values that are rather widely separated in space or time, and represent the desired result, but only in very coarse steps. The computed interpolation process is then used to insert many new values in between these key points to give a "smoother" result. In its simplest form, this is the drawing of two-dimensional curves. The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points. For a typical example of 2-D interpolation through key points see

cardinal spline In numerical analysis, a cubic Hermite spline or cubic Hermite interpolator is a spline where each piece is a third-degree polynomial specified in Hermite form, that is, by its values and first derivatives at the end points of the corresponding ...

. For examples which go near key points see

nonuniform rational B-spline Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analyt ...

, or

Bézier curve A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape t ...

. This is extended to the forming of three-dimensional curves, shapes and complex, dynamic artistic patterns such as used in laser light shows. The process can be extended to motions. The path of an object can be interpolated by providing some key locations, then calculating many in between locations for a smooth motion. In addition to position, the speed or velocity, as well as accelerations along a path, can be calculated to mimic real-life motion dynamics. Where the subjects are too large or complex to move, the camera position and orientation can be moved by this process. This last is commonly called

motion control Motion control is a sub-field of automation, encompassing the systems or sub-systems involved in moving parts of machines in a controlled manner. Motion control systems are extensively used in a variety of fields for automation purposes, includi ...

. Going further, orientations (rotations) of objects and parts of objects can be interpolated as well as parts of complete characters. This process mimics that used in early cartoon films. Master animators would draw key frames of the film, then, junior animators would draw the in-between frames. This is called

or tweening and the overall process is called "

key frame In animation and filmmaking, a key frame (or keyframe) is a drawing or shot that defines the starting and ending points of a smooth transition. These are called ''frames'' because their position in time is measured in frames on a strip of film ...

animation". To make these motions appear realistic, interpolation algorithms have been sought which follow, or approximate real life motion dynamics. This applies to things such as the motion of arms and legs from frame to frame, or the motion of all parts of a face, given the motion of the important, key points of the face. Defining the motion of key strands of hair, spread around an animal, can be made into full fur. Using custom algorithms, motions with unique, unnatural and entertaining visual characteristics can be formed. The color of an object can be defined by key color-locations or frames allowing the computation of smooth color gradients around an object or varying in time. Algorithms such as the

Kochanek–Bartels spline In mathematics, a Kochanek–Bartels spline or Kochanek–Bartels curve is a cubic Hermite spline with tension, bias, and continuity parameters defined to change the behavior of the tangents. Given ''n'' + 1 knots, :p0, ..., p''n'', to be inte ...

provide additional adjustment parameters which allow customizing the in-between behavior to suit a wide variety of situations. Another important area of this subject is the computational burden of these algorithms. Algorithms with faster execution times are sought to produce more of these results in less time in order to complete these projects quicker. As the resolution increases to produce animated feature films, the amount of processing can increase greatly.

References

Splines (mathematics) Interpolation

See also

References