In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory.
Vector graphics are a form of computer graphics in which visual images are created directly from geometric shapes defined on a Cartesian plane, such as points, lines, curves and polygons. The associated mechanisms may include vector display and printing hardware, vector data models and file formats, as well as the software based on these data models. Vector graphics is an alternative to raster or bitmap graphics, with each having advantages and disadvantages in specific situations.
Computer-aided design (CAD) is the use of computers to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. Designs made through CAD software help protect products and inventions when used in patent applications. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations. The terms computer-aided drafting (CAD) and computer-aided design and drafting (CADD) are also used.
A pattern is a regularity in the world, in human-made design, or in abstract ideas. As such, the elements of a pattern repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes and typically repeated like a wallpaper design.
CAD data exchange is a method of drawing data exchange used to translate between different computer-aided design (CAD) authoring systems or between CAD and other downstream CAx systems.
Software visualization or software visualisation refers to the visualization of information of and related to software systems—either the architecture of its source code or metrics of their runtime behavior—and their development process by means of static, interactive or animated 2-D or 3-D visual representations of their structure, execution, behavior, and evolution.
Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-dimensional, although many of its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications. Two-dimensional models are important in computer typography and technical drawing. Three-dimensional models are central to computer-aided design and manufacturing (CAD/CAM), and widely used in many applied technical fields such as civil and mechanical engineering, architecture, geology and medical image processing.
Algorithmic art or algorithm art is art, mostly visual art, in which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists.
Virtual engineering (VE) is defined as integrating geometric models and related engineering tools such as analysis, simulation, optimization, and decision making tools, etc., within a computer-generated environment that facilitates multidisciplinary collaborative product development. Virtual engineering shares many characteristics with software engineering, such as the ability to obtain many different results through different implementations.
GenerativeComponents is parametric CAD software developed by Bentley Systems, was first introduced in 2003, became increasingly used in practice by early 2005, and was commercially released in November 2007. GenerativeComponents has a strong traditional base of users in academia and at technologically advanced design firms. GenerativeComponents is often referred to by the nickname of 'GC'. GC epitomizes the quest to bring parametric modeling capabilities of 3D solid modeling into architectural design, seeking to provide greater fluidity and fluency than mechanical 3D solid modeling.
A 3D city model is digital model of urban areas that represent terrain surfaces, sites, buildings, vegetation, infrastructure and landscape elements in three-dimensional scale as well as related objects belonging to urban areas. Their components are described and represented by corresponding two- and three-dimensional spatial data and geo-referenced data. 3D city models support presentation, exploration, analysis, and management tasks in a large number of different application domains. In particular, 3D city models allow "for visually integrating heterogeneous geoinformation within a single framework and, therefore, create and manage complex urban information spaces."
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.
SmartGeometry (SG) is a non-profit organization focusing on the use of the computer as an intelligent design aid in architecture, engineering and construction (AEC). It encourages collaboration between practicing AEC professionals, academics and students using computational and parametric software tools.
Geometrical design (GD) is a branch of computational geometry. It deals with the construction and representation of free-form curves, surfaces, or volumes and is closely related to geometric modeling. Core problems are curve and surface modelling and representation. GD studies especially the construction and manipulation of curves and surfaces given by a set of points using polynomial, rational, piecewise polynomial, or piecewise rational methods. The most important instruments here are parametric curves and parametric surfaces, such as Bézier curves, spline curves and surfaces. An important non-parametric approach is the level-set method.
Digital morphogenesis is a type of generative art in which complex shape development, or morphogenesis, is enabled by computation. This concept is applicable in many areas of design, art, architecture, and modeling. The concept was originally developed in the field of biology, later in geology, geomorphology, and architecture.
Generative design is an iterative design process that generates outputs that meet specified constraints to varying degrees. In a second phase, designers can then provide feedback to the generator that explores the feasible region by selecting preferred outputs or changing input parameters for future iterations. Either or both phases can be done by humans or software. One method is to use a generative adversarial network, which is a pair of neural networks. The first generates a trial output. The second provides feedback for the next iteration.
In 3D computer graphics, 3D modeling is the process of developing a mathematical coordinate-based representation of a surface of an object in three dimensions via specialized software by manipulating edges, vertices, and polygons in a simulated 3D space.
Computer-generated imagery (CGI) is a specific-technology or application of computer graphics for creating or improving images in art, printed media, simulators, videos and video games. These images are either static or dynamic. CGI both refers to 2D computer graphics and 3D computer graphics with the purpose of designing characters, virtual worlds, or scenes and special effects. The application of CGI for creating/improving animations is called computer animation, or CGI animation.
C3D Toolkit is a proprietary cross-platform geometric modeling kit software developed by Russian by C3D Labs. It's written in C++. It can be licensed by other companies for use in their 3D computer graphics software products. The most widely known software in which C3D Toolkit is typically used are computer aided design (CAD), computer-aided manufacturing (CAM), and computer-aided engineering (CAE) systems.
