Is topology used in computer graphics?

A broad classification of major subfields in computer graphics might be:

The subfield of geometry studies the representation of three-dimensional objects in a discrete digital setting. Because the appearance of an object depends largely on its exterior, boundary representations are most commonly used. Two dimensional surfaces are a good representation for most objects, though they may be non-manifold. Since surfaces are not finite, discrete digital approximations are used. Polygonal meshes (and to a lesser extent subdivision surfaces) are by far the most common representation, although point-based representations have become more popular recently (see for instance the Symposium on Point-Based Graphics).[8] These representations are Lagrangian, meaning the spatial locations of the samples are independent. Recently, Eulerian surface descriptions (i.e., where spatial samples are fixed) such as level sets have been developed into a useful representation for deforming surfaces which undergo many topological changes (with fluids being the most notable example).[9]

Geometry subfields include:

• Implicit surface modeling an older subfield which examines the use of algebraic surfaces, constructive solid geometry, etc., for surface representation.
• Digital geometry processing surface reconstruction, simplification, fairing, mesh repair, parameterization, remeshing, mesh generation, surface compression, and surface editing all fall under this heading.[10][11][12]
• Discrete differential geometry a nascent field which defines geometric quantities for the discrete surfaces used in computer graphics.[13]
• Point-based graphics a recent field which focuses on points as the fundamental representation of surfaces.
• Subdivision surfaces
• Out-of-core mesh processing another recent field which focuses on mesh datasets that do not fit in main memory.

AnimationEdit

The subfield of animation studies descriptions for surfaces (and other phenomena) that move or deform over time. Historically, most work in this field has focused on parametric and data-driven models, but recently physical simulation has become more popular as computers have become more powerful computationally.

Animation subfields include:

RenderingEdit

Rendering generates images from a model. Rendering may simulate light transport to create realistic images or it may create images that have a particular artistic style in non-photorealistic rendering. The two basic operations in realistic rendering are transport (how much light passes from one place to another) and scattering (how surfaces interact with light). See Rendering (computer graphics) for more information.

Rendering subfields include:

• Transport describes how illumination in a scene gets from one place to another. Visibility is a major component of light transport.
• Scattering: Models of scattering (how light interacts with the surface at a given point) and shading (how material properties vary across the surface) are used to describe the appearance of a surface. In graphics these problems are often studied within the context of rendering since they can substantially affect the design of rendering algorithms. Descriptions of scattering are usually given in terms of a bidirectional scattering distribution function (BSDF). The latter issue addresses how different types of scattering are distributed across the surface (i.e., which scattering function applies where). Descriptions of this kind are typically expressed with a program called a shader. (Note that there is some confusion since the word "shader" is sometimes used for programs that describe local geometric variation.)
• Non-photorealistic rendering
• Physically based rendering concerned with generating images according to the laws of geometric optics
• Real-time rendering focuses on rendering for interactive applications, typically using specialized hardware like GPUs
• Relighting recent area concerned with quickly re-rendering scenes