Building a model and setting it in motion
Modelling is the forming of an object's shape. Two sources dominate. An artist or an engineer builds the model on a computer with a modelling tool. Or a real object is scanned, and the scan becomes the model. Polygonal modelling, patch modelling, and NURBS modelling are among the common toolsets. Models can also be produced procedurally, by a rule rather than by a hand, or by a physical simulation that is allowed to run and then frozen into geometry. A city of identical windows is a bad job for a sculptor and a reasonable job for a rule. A drape of cloth is often a better job for a simulation than for someone pushing vertices one at a time.
Vertices and the faces between them
A 3D model is formed from points called vertices. The vertices define the shape and they define polygons. A polygon is an area made from at least three vertices, a triangle. A polygon of n points is an n-gon. The integrity of the model, and whether it will survive animation, depends on how those polygons are structured. A mesh that looks right in a still frame can tear the moment a joint bends, because the vertices were never arranged for that bend. The still frame was a lucky camera angle. Animation removes the luck.
Before anything is rendered, objects have to be laid out in a scene. Layout defines spatial relationships: where something is, and how big it is relative to the rest. Animation is the temporal description of an object, how it moves and deforms over time. The popular methods include keyframing, inverse kinematics, and motion capture. They are often used together. A performance can be captured, cleaned up with inverse kinematics so the feet stay on the floor, and then adjusted with keys where the capture got the hands wrong. Physical simulation also specifies motion. It is animation whose author is a set of forces rather than a set of poses.
Underneath those methods, a virtual object carries attributes, among them transform values: location, orientation, and scale, stored in a transformation matrix. Animation, at the most basic, is the change of an attribute over time. The rudimentary form is keyframes, each storing a value at a given time for each attribute you mean to animate. The software builds a curve of that value against time. You edit the curve. Procedural methods bundle related attributes, which is how particle effects and crowd simulations stay manageable. Expression-based methods let a user-defined expression, with mathematics in it, return a value and drive the animation. That is a practical way to control a bone beyond what a simple hierarchy gives you in a skeleton. To the viewer it is still the old trick. An image is shown, then quickly replaced by a similar image, shifted a little. Film and television have always worked that way. The computer's contribution is where the next image comes from.
What the software is for
3D graphics software produces imagery through modelling and rendering, or it produces models for analysis, science, entertainment, and industry. A modeller is the class of program used to make the models. Modelling starts from three kinds of display: drawing points, drawing lines, and drawing triangles and other polygonal patches.
In a mesh modeller you add, subtract, stretch, and otherwise change the mesh. You can look at the model from several angles, often at the same time. You can rotate it and you can zoom. The model can be written to a file and read by another application, provided the metadata is compatible. Many modellers let importers and exporters be plugged in, so they can read and write the native formats of other programs. Most also contain a ray tracer or some other renderer, and some facility for texture mapping. Some support animation. Some can render a series of frames out to a moving picture.
Computer-aided design software may use the same underlying techniques and still be a different tool, because the goal is different. CAD is used in engineering, in manufacturing, in finite-element analysis, in the management of a product's life, in 3D printing, and in architectural design. A model that has to be machined is not allowed the casual geometry a film model is allowed. A gap that a renderer would hide will be a gap in the part. The file formats split along the same line. A format for a game and a format for a machined bracket are solving different problems, even when both of them contain triangles.
Once a picture sequence exists, studios edit and composite it. At the middle of the market that might be Premiere Pro or Final Cut Pro. At the high end it has meant tools such as Combustion, Digital Fusion, and Shake. Match-moving software lines a live camera up with a computer-generated camera, so the two stay in step as the real camera moves. If they drift, the audience sees a drawing laid on top of a photograph, which is sometimes the style and usually a mistake.
Using a real-time graphics engine to make a cinematic piece is called machinima. The pictures are rendered under the same constraints as a game, because they are a game, pointed at a film rather than at a player. That constraint is the method. It is also the look.