Supervised learning (SL) is a paradigm in machine learning where input objects and a desired output value train a model. The training data is processed, building a function that maps new data to expected output values. An optimal scenario will allow for the algorithm to correctly determine output values for unseen instances. This requires the learning algorithm to generalize from the training data to unseen situations in a "reasonable" way. This statistical quality of an algorithm is measured through the so-called generalization error.
In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset.
Topography is the study of the forms and features of land surfaces. The topography of an area may refer to the land forms and features themselves, or a description or depiction in maps.
In mathematics, a system of linear equations is a collection of two or more linear equations involving the same variables. For example,
Collision detection is the computational problem of detecting an intersection of two or more spatial objects, commonly computer graphics objects. It has applications in various computing fields, primarily in computer graphics, computer games, computer simulations, robotics and computational physics. Collision detection is a classic problem of computational geometry. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects.
Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry. While modern computational geometry is a recent development, it is one of the oldest fields of computing with a history stretching back to antiquity.
Constructive solid geometry is a technique used in solid modeling. Constructive solid geometry allows a modeler to create a complex surface or object by using Boolean operators to combine simpler objects, potentially generating visually complex objects by combining a few primitive ones.
Ray casting is the methodological basis for 3D CAD/CAM solid modeling and image rendering. It is essentially the same as ray tracing for computer graphics where virtual light rays are "cast" or "traced" on their path from the focal point of a camera through each pixel in the camera sensor to determine what is visible along the ray in the 3D scene. The term "Ray Casting" was introduced by Scott Roth while at the General Motors Research Labs from 1978–1980. His paper, "Ray Casting for Modeling Solids", describes modeled solid objects by combining primitive solids, such as blocks and cylinders, using the set operators union (+), intersection (&), and difference (-). The general idea of using these binary operators for solid modeling is largely due to Voelcker and Requicha's geometric modelling group at the University of Rochester. See solid modeling for a broad overview of solid modeling methods. This figure on the right shows a U-Joint modeled from cylinders and blocks in a binary tree using Roth's ray casting system in 1979.
Solid modeling is a consistent set of principles for mathematical and computer modeling of three-dimensional shapes (solids). Solid modeling is distinguished within the broader related areas of geometric modeling and computer graphics, such as 3D modeling, by its emphasis on physical fidelity. Together, the principles of geometric and solid modeling form the foundation of 3D-computer-aided design, and in general, support the creation, exchange, visualization, animation, interrogation, and annotation of digital models of physical objects.
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group are more similar to each other than to those in other groups (clusters). It is a main task of exploratory data analysis, and a common technique for statistical data analysis, used in many fields, including pattern recognition, image analysis, information retrieval, bioinformatics, data compression, computer graphics and machine learning.
In manufacturing industry, nesting refers to the process of laying out cutting patterns to minimize the raw material waste. Examples include manufacturing parts from flat raw material such as sheet metal, glass sheets, cloth rolls, cutting parts from steel bars, etc.
In machine learning and pattern recognition, a feature is an individual measurable property or characteristic of a phenomenon. Choosing informative, discriminating, and independent features is crucial to produce effective algorithms for pattern recognition, classification, and regression tasks. Features are usually numeric, but other types such as strings and graphs are used in syntactic pattern recognition, after some pre-processing step such as one-hot encoding. The concept of "features" is related to that of explanatory variables used in statistical techniques such as linear regression.
In geometry, a triangulation is a subdivision of a planar object into triangles, and by extension the subdivision of a higher-dimension geometric object into simplices. Triangulations of a three-dimensional volume would involve subdividing it into tetrahedra packed together.
In visual effects, match moving is a technique that allows the insertion of 2D elements, other live action elements or CG computer graphics into live-action footage with correct position, scale, orientation, and motion relative to the photographed objects in the shot. It also allows for the removal of live action elements from the live action shot. The term is used loosely to describe several different methods of extracting camera motion information from a motion picture. Also referred to as motion tracking or camera solving, match moving is related to rotoscoping and photogrammetry. Match moving is sometimes confused with motion capture, which records the motion of objects, often human actors, rather than the camera. Typically, motion capture requires special cameras and sensors and a controlled environment. Match moving is also distinct from motion control photography, which uses mechanical hardware to execute multiple identical camera moves. Match moving, by contrast, is typically a software-based technology, applied after the fact to normal footage recorded in uncontrolled environments with an ordinary camera.
In computing, data validation or input validation is the process of ensuring data has undergone data cleansing to confirm they have data quality, that is, that they are both correct and useful. It uses routines, often called "validation rules", "validation constraints", or "check routines", that check for correctness, meaningfulness, and security of data that are input to the system. The rules may be implemented through the automated facilities of a data dictionary, or by the inclusion of explicit application program validation logic of the computer and its application.
A convex polytope is a special case of a polytope, having the additional property that it is also a convex set contained in the -dimensional Euclidean space . Most texts use the term "polytope" for a bounded convex polytope, and the word "polyhedron" for the more general, possibly unbounded object. Others allow polytopes to be unbounded. The terms "bounded/unbounded convex polytope" will be used below whenever the boundedness is critical to the discussed issue. Yet other texts identify a convex polytope with its boundary.
Data cleansing or data cleaning is the process of identifying and correcting corrupt, inaccurate, or irrelevant records from a dataset, table, or database. It involves detecting incomplete, incorrect, or inaccurate parts of the data and then replacing, modifying, or deleting the affected data. Data cleansing can be performed interactively using data wrangling tools, or through batch processing often via scripts or a data quality firewall.
A bounding volume hierarchy (BVH) is a tree structure on a set of geometric objects. All geometric objects, which form the leaf nodes of the tree, are wrapped in bounding volumes. These nodes are then grouped as small sets and enclosed within larger bounding volumes. These, in turn, are also grouped and enclosed within other larger bounding volumes in a recursive fashion, eventually resulting in a tree structure with a single bounding volume at the top of the tree. Bounding volume hierarchies are used to support several operations on sets of geometric objects efficiently, such as in collision detection and ray tracing.
The Skewb Ultimate, originally marketed as the Pyraminx Ball, is a twelve-sided puzzle derivation of the Skewb, produced by German toy-maker Uwe Mèffert. Most versions of this puzzle are sold with six different colors of stickers attached, with opposite sides of the puzzle having the same color; however, some early versions of the puzzle have a full set of 12 colors.
In re Schrader, 22 F.3d 290 is a 1994 decision of the United States Court of Appeals for the Federal Circuit in which the court summarized and synthesized its precedents under the Freeman-Walter-Abele Test of patent eligibility. Under this test a key element is that the claimed invention is implemented with some type of hardware—that is, a particular machine. This was one of the last Federal Circuit decisions using that test.
