Gouraud shading, named after Henri Gouraud, is an interpolation method used in computer graphics to produce continuous shading of surfaces represented by polygon meshes. In practice, Gouraud shading is most often used to achieve continuous lighting on triangle meshes by computing the lighting at the corners of each triangle and linearly interpolating the resulting colours for each pixel covered by the triangle. Gouraud first published the technique in 1971. However, enhanced hardware support for superior shading models has yielded Gouraud shading largely obsolete in modern rendering.
Texture mapping is a method for mapping a texture on a computer-generated graphic. Texture here can be high frequency detail, surface texture, or color.
Edwin Earl Catmull is an American computer scientist and animator who served as the co-founder of Pixar and the President of Walt Disney Animation Studios. He has been honored for his contributions to 3D computer graphics, including the 2019 ACM Turing Award.
In 3D computer graphics and solid modeling, a polygon mesh is a collection of vertices, edges and faces that defines the shape of a polyhedral object. The faces usually consist of triangles, quadrilaterals (quads), or other simple convex polygons (n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes.
In the field of 3D computer graphics, a subdivision surface is a curved surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, the underlying inner mesh, can be calculated from the coarse mesh, known as the control cage or outer mesh, as the functional limit of an iterative process of subdividing each polygonal face into smaller faces that better approximate the final underlying curved surface. Less commonly, a simple algorithm is used to add geometry to a mesh by subdividing the faces into smaller ones without changing the overall shape or volume.
In computer graphics, level of detail (LOD) refers to the complexity of a 3D model representation. LOD can be decreased as the model moves away from the viewer or according to other metrics such as object importance, viewpoint-relative speed or position. LOD techniques increase the efficiency of rendering by decreasing the workload on graphics pipeline stages, usually vertex transformations. The reduced visual quality of the model is often unnoticed because of the small effect on object appearance when distant or moving fast.
The Catmull–Clark algorithm is a technique used in 3D computer graphics to create curved surfaces by using subdivision surface modeling. It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology.
In 3D computer graphics, polygonal modeling is an approach for modeling objects by representing or approximating their surfaces using polygon meshes. Polygonal modeling is well suited to scanline rendering and is therefore the method of choice for real-time computer graphics. Alternate methods of representing 3D objects include NURBS surfaces, subdivision surfaces, and equation-based representations used in ray tracers.
Geometry processing is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation and transmission of complex 3D models. As the name implies, many of the concepts, data structures, and algorithms are directly analogous to signal processing and image processing. For example, where image smoothing might convolve an intensity signal with a blur kernel formed using the Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami operator.
Mesh generation is the practice of creating a mesh, a subdivision of a continuous geometric space into discrete geometric and topological cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations of the larger domain. Meshes are created by computer algorithms, often with human guidance through a GUI, depending on the complexity of the domain and the type of mesh desired. A typical goal is to create a mesh that accurately captures the input domain geometry, with high-quality (well-shaped) cells, and without so many cells as to make subsequent calculations intractable. The mesh should also be fine in areas that are important for the subsequent calculations.
In 3D computer graphics, a Doo–Sabin subdivision surface is a type of subdivision surface based on a generalization of bi-quadratic uniform B-splines, whereas Catmull-Clark was based on generalized bi-cubic uniform B-splines. The subdivision refinement algorithm was developed in 1978 by Daniel Doo and Malcolm Sabin.
A geodesic grid is a spatial grid based on a geodesic polyhedron or Goldberg polyhedron.
In 3D computer graphics and modeling, volumetric meshes are a polygonal representation of the interior volume of an object. Unlike polygon meshes, which represent only the surface as polygons, volumetric meshes also discretize the interior structure of the object.
Computer graphics is a sub-field of computer science which studies methods for digitally synthesizing and manipulating visual content. Although the term often refers to the study of three-dimensional computer graphics, it also encompasses two-dimensional graphics and image processing.
A vertex in computer graphics is a data structure that describes certain attributes, like the position of a point in 2D or 3D space, or multiple points on a surface.
In computer graphics, tessellation is the dividing of datasets of polygons presenting objects in a scene into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11.
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra with mostly hexagonal faces.
The Goldberg–Coxeter construction or Goldberg–Coxeter operation is a graph operation defined on regular polyhedral graphs with degree 3 or 4. It also applies to the dual graph of these graphs, i.e. graphs with triangular or quadrilateral "faces". The GC construction can be thought of as subdividing the faces of a polyhedron with a lattice of triangular, square, or hexagonal polygons, possibly skewed with regards to the original face: it is an extension of concepts introduced by the Goldberg polyhedra and geodesic polyhedra. The GC construction is primarily studied in organic chemistry for its application to fullerenes, but it has been applied to nanoparticles, computer-aided design, basket weaving, and the general study of graph theory and polyhedra.
Hierarchical Triangular Mesh (HTM) is a kind of quad tree based on subdivision of a distorted octahedron, used for mesh generation in 3-D computer graphics and geometric data structures.
