"Animation can explain whatever the mind of man can conceive.
This facility makes it the most versatile and explicit means of communication yet
devised for quick mass appreciation."
1.1 Computer animation
Animated images are almost magical in their ability to capture our imagi- nation. By telling a whole story through the special effects, animation can bring into life a sequence of inert images with the illusion of motion.
Computer animation is the art of creating moving images using comput- ers. It is a subset of computer graphics and animation. Nowadays computer graphics mostly mean 3D computer graphics, though 2D computer graphics are still widely used for low bandwidth and faster real-time rendering needs.
It is also referred to as CGI (Computer-generated imagery or computer- generated imaging), especially when used in films. To create the illusion of movement, an image is displayed on the computer screen then quickly replaced by a new image that is similar to the previous image, but little bit shifted.
Definition 1 ISO animation definition
Animation is displaying a sequence of pictures sorted in time. This in-
cludes all possible changes causing visual effects (position, shape, color, trans-
parency, object structure and its texture, light, camera parameters, and even
But computer animators are still artists. It doesn’t matter if they use computers or pencils, nothing replaces their creative vision. Over the past two decades, computers have opened up unimaginable possibilities for ani- mators.
The applications of computer animation extend far beyond film and tele- vision. 3-D animators help design and model industrial machines, reconstruct cultural heritage, simulate some physical situations etc. In fields like medicine and engineering, 3-D animation can help simplify and visualize complex in- ternal processes. And computer animators are in high demand for marketing and advertising campaigns.
1.2 2D and 3D animation
1.2.1 2D animation
Commonly the 2D animation is regarded as the ancestor of 3D animation.
However 2D animation is more than that. As long as animators had to create all in 2D for long time, they had to learn techniques to help the animation live. These techniques  contribute a great deal to computer animation by providing the tools used for blending or morphing between images, embedding graphical objects in video footage, or creating abstract patterns from mathematical equations.
Figure 1.1: Keyframes of 2D animation are similar in the computer or on paper .
Morphing refers to animations where an image or model of one object is metamorphosed into another. Unfortunately, morphing is labor intensive because the key elements of each image must be specified by hand.
Objects can also be removed from a scene. Both the processes of embed-
ding and of removing objects are made more difficult if the camera is moving
because the alteration must be consistent with the changing viewpoint.
To create abstract motion sequences are often used mathematical equa- tions. When the values of the mathematical functions are mapped to color values and varied with time, the motion of the underlying structures can be quite beautiful. Fractals, such as the one shown in Figure1.2, are a well- known example of functions that create attractive patterns.
Figure 1.2: Julia set - fractal.
1.2.2 3D animation
For our research will be more important the 3D animation and its techniques.
By using 3D techniques , the animator constructs whole virtual world in which characters and objects move and interact. Using a virtual 3D world to generate an animation involves three steps: modeling, animating, and rendering.
Modeling involves setting up the elements in a scene and describing each of those elements. Rendering converts the description of the objects and their motion into images. Techniques for modeling and rendering are, for the most part, independent of their role in the animation process. Some modifications, however, must be made to the modeling or rendering procedures if they are to be used for animation.
1.3 Online and offline animation
The camera parameters, which include the position and orientation of the
3D window and the relative location of the camera, are given in the global
coordinate system thus defining the viewing transformation which takes us
from the world to the screen coordinate system. Both transformations can
be characterized by 4x4 homogeneous matrices. Let the time-varying mod-
elling transformation of object o be T
(t) and the viewing transformation
(t). A simplistic algorithm of the generation of an animation sequence,
assuming a built-in timer, is:
Result: Algorithm of generation of animation sequences Initialize Timer(t
T = Read Timer;
while t < t
do foreach object o do
Set modelling transformation T
(t) ; Set viewing transformation: T
In order to provide the effect of continuous motion, a new static image
should be generated at least every 60 msec. If the computer is capable of
producing the sequence at such a speed, we call this real-time animation ,
since now the timer can provide real time values. With less powerful com-
puters we are still able to generate continuous looking sequences by storing
the computed image sequence on mass storage, such as a video recorder,
and replaying them later. This technique, called non-real-time animation,
requires the calculation of subsequent images in uniformly distributed time
samples. The time gap between the samples has to exceed the load time
of the image from the mass storage, and should meet the requirements of
continuous motion as well. The general sequence of this type of animation
Result: The general sequence of real-time animation t = t
while t < t
do foreach object o do
Set modelling transformation T
(t) ; Set viewing transformation: T
t+ = δt;
while t < t
Initialize Timer( t
t = Read Timer;
Load next image; t+ = t;
while t>Read Timer do Wait
; end end end
1.4 Animating methods
1.4.1 Keyframe animation
Figure 1.3: Example of a key-frame animation of ball.
Traditionally , animation has been created by drawing images at certain
key points in the action. These images, known as key-frames, outline the motion for the sequence. Later, the images between the key-frames were filled in to complete the sequence, in a process called in-betweening mostly by another animator.
In computer animation the interpolation is made by computer. The sim- plest form of interpolation is linear interpolation, but it often results in mo- tion that appears jerky because the velocities of the moving objects are dis- continuous. To correct this problem, better interpolation techniques, such as splines, are used to produce smoothly interpolated curves.
1.4.2 Stop-motion animation
Also known as frame-by-frame animation. The punch line is to build the scene (physically or virtually in computer) and taking picture of this scene.
Then the scene is rebuild to another picture and the process repeat until the whole animation is done. The results are then the changing pictures in time.
The illusion of movement is made when the series of frames is played as a continuous sequence. Clay figures or toys with movable limbs are often used for their ease of repositioning. Stop motion animation using clay or plasticine is called clay animation or "clay-mation". Not every stop motion animation requires figures or models; many stop motion films can involve using humans or real environment around us, to make time-lapses for instance. With stop- motion technique one of the best animated movies were made - Coraline, Journey to the Beginning of Time or famous bed-time story Pat and Mat.
Figure 1.4: Example of producing the stop motion animation.
1.4.3 Motion capture
A motion capture  employs special sensors, called trackers, to record the
motion of a real performer (human, animal). The recorded data is then
used to generate the motion for a modelled object animation. Alternatively,
special puppets with joint angle sensors can be used in place of a human
performer. Motion capture belongs to very popular techniques because of the relative ease with which many human motions can be recorded.
However, it is not an ideal solution for all applications because of a num- ber of problems. First, accurately measuring the motion of the human body is tricky because trackers attached to skin or clothing shift as the performer moves, creating errors in the recorded data. Furthermore, it is good if the ac- tor has approximately the same dimension as the modelled object, elsewhere the animation may have noticeable flaws.
Figure 1.5: Illustration of how the motion capture works - The Polar Express.
The technology used for motion capture makes it difficult to capture some motions. One class of sensors are magnetic, so it creates noise in the data.
Another class of sensors requires that the actor should be connected to the computer by a cable and that’s restricting the actor’s motion. And finally all sensing technologies have a relatively small field of view nowadays, which limits the kinds of actions that can be captured. In spite of these difficulties, motion capture is widely used. Much of the motion found in commercial animation is generated by using captured data and “tweaking” the results by hand.
1.4.4 Procedural methods
These techniques are called procedural methods because a computer proce- durally follows the steps in an algorithm to generate the motion.
Procedural methods have two main advantages over keyframing tech- niques:
• they make it easy to generate a family of similar motions,
• and they can be used for systems that would be too complex to animate
by hand, such as particle systems or flexible surfaces.
Physically based simulation refers to a class of procedural methods that makes use of the laws of physics, or an approximation to those laws, to generate motion. Simulated motion is inherently realistic and for many ap- plications that is an advantage. Unfortunately, building a new simulation is sometimes a difficult process requiring an in-depth understanding of the relevant physical laws. Once a simulation has been designed, however, an animator may use it without knowing how the internals of the simulation function.
Figure 1.6: Procedural modelled and animated minions in Despicable me.
Procedural methods can also be used to generate motion for groups of objects that move together. Flocks of birds, schools of fish, herds of animals, or crowds of people are all situations where algorithms for group behaviours can be used. In Walt Disney’s animated version of The Hunchback of Notre Dame most of the crowd scenes, or in the Despicable me movie whole crowd of minions were animated using procedural animation. This animated film is particularly impressive because computer and hand animation are seamlessly combined to create very detailed scenes.
1.5 Animation Production
Computer animation production  has borrowed most of the ideas from conventional animation production.
The terms used in the animation production comes from film production in general. This refers to the entire piece under production. The major parts of the animations are the acts. An act is an episode within the animation and is usually identified by an associated inscenation. An animation usually has not more than a dozen acts. An act is divided into several scenes. A scene describes one venue of continuous action. A scene is broken down in one or more shots. A shot is a continuous camera recording. A shot consists of the individual frames of film.
The production of animation follows this pattern. First, a preliminary
story is decided on and then a storyboard is developed, which means to
sketch the most representative frame of every scene (keyframe) and write an explanation to it.
Figure 1.7: Trial of the storyboard of Last witch
Then the detailed story is worked out which identifies the actions in- volved in more detail. Then the keyframes are identified and produced by master animators. In computer animation there is usually a strict distinc- tion between the creation of the models, the specification of motion, and the rendering process. In conventional animation, the model building, motion specification, and rendering are really all the same thing.
Now a test shot comes. It is a short sequence rendered in full color to further test the rendering and motion techniques. A test shot in computer animation is usually a high quality rendering of a highly detailed model to see a single frame of the final product. Place-holder cubes can be rendered in wire frame to present the gross motion of rigid bodies in space and to see spacial and termporal relationships among objects.
Solids of revolution objects lend themselves quite well to allowing for
three, four or five levels of detail for a given model. Also, smooth shading,
texture mapping, specular reflection and solid texturing can all be options
presented to the animator for a given run. To simplify motion control, for
example, simple interpolation between poses may be used instead of inverse
 J. K. HODGINS and J. F. O’BRIAN. Computer Animation. part of Encyclopedia of computer graphics, 2008.
 R. PARENT. Computer Animation: Algorithms and Techniques. Else- vier, 2002. ISBN 13-978-1-55860-579-4.