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Boolean Operations On Polygons
Boolean operations on polygons are a set of Boolean operations (AND, OR, NOT, XOR, ...) operating on one or more sets of polygons in computer graphics. These sets of operations are widely used in computer graphics, CAD, and in EDA (in integrated circuit physical design and verification software). These are also used for activities like rapid prototyping in product design, medical device development, or even the creation of elaborate artworks. Algorithms * Greiner–Hormann clipping algorithm * Vatti clipping algorithm * Sutherland–Hodgman algorithm (special case algorithm) * Weiler–Atherton clipping algorithm (special case algorithm) Uses in software Early algorithms for Boolean operations on polygons were based on the use of bitmaps. Using bitmaps in modeling polygon shapes has many drawbacks. One of the drawbacks is that the memory usage can be very large, since the resolution of polygons is proportional to the number of bits used to represent polygons. The hig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Operation (Boolean Algebra)
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to Huntington, the term ''Boolean algebra'' wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a simple polygon (not self-intersecting). Equivalently, a polygon is convex if every line that does not contain any edge intersects the polygon in at most two points. Strictly convex polygon A convex polygon is ''strictly'' convex if no line contains more than two vertices of the polygon. In a convex polygon, all interior angles are less than ''or equal'' to 180 degrees, while in a strictly convex polygon all interior angles are strictly less than 180 degrees. Properties The following properties of a simple polygon are all equivalent to convexity: *Every internal angle is less than or equal to 180 degrees. *Every point on every line segment between two points inside or on the boundary of the polygon remains inside or on the bou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Derick Wood
Derick Wood (1940–2010) was an English computer scientist who worked for many years as a professor of computer science in Canada and Hong Kong. He was known for his research in automata theory and formal languages, much of which he published in collaboration with Hermann Maurer and Arto Salomaa, and also for his work in computational geometry. Wood was born in 1940 in Lancashire, and educated at the University of Leeds. He earned his PhD from Leeds in 1968 under the supervision of Mike Wells. After postdoctoral studies at the Courant Institute of Mathematical Sciences of New York University, he took his first faculty position at McMaster University in Ontario, Canada. Before joining the Hong Kong University of Science and Technology (HKUST) in 1995, Wood also taught at the University of Waterloo and the University of Western Ontario The University of Western Ontario (UWO; branded as Western University) is a Public university, public research university in London, Ontario ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jon Louis Bentley
Jon Louis Bentley (born February 20, 1953) is an American computer scientist who is known for his contributions to computer programming, algorithms and data structure research. __NOTOC__ Education Bentley received a Bachelor of Science, B.S. in mathematical sciences from Stanford University in 1974. At this time he developed his most cited work, the heuristic-based partitioning algorithm k-d tree, published in 1975.See thJon Louis BentleyGoogle Scholar profile, last accessed on 14 February 2024. He received a Master of Science, M.S. and PhD in 1976 from the University of North Carolina at Chapel Hill. While a student, he also held internships at the Xerox Palo Alto Research Center and Stanford Linear Accelerator Center. Career After receiving his Ph.D., he taught programming and computer architecture for six years as member of the faculty at Carnegie Mellon University as an assistant professor of computer science and mathematics. At CMU, his students included Brian Reid (compu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Overmars
Markus Hendrik "Mark" Overmars (; born 29 September 1958) is a Dutch computer scientist and teacher of game programming known for his game development application GameMaker. GameMaker allows users to create computer games using a drag-and-drop interface. He is the former head of the ''Center for Geometry, Imaging, and Virtual Environments'' at Utrecht University in the Netherlands. This research center focuses on computational geometry and its applications in areas such as computer graphics, robotics, geographic information systems, imaging, multimedia, virtual environments, and games. Overmars received his Ph.D. in 1983 from Utrecht University under the supervision of Jan van Leeuwen, and remained a faculty member at the same university until September 2013. Overmars has published over 100 journal papers, largely on computational geometry, and is a co-author of several widely used textbooks on the subject. Overmars has also worked in robotics. He was the first to develop t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
General Polygon Clipper
The General Polygon Clipper (GPC) is a software library providing for computing the results of clipping operations on sets of polygons. It generalises the computer graphics clipping problem of intersecting polygons with polygons. The first release of GPC was designed and implemented in 1997 by Alan Murta. the final GPC release was version 2.32. The core GPC library is written in the C programming language but the library has also been ported to work with several other languages. Availability Since August 2020, GPC is no longer officially distributed by the author. In December 2021 a copy of the GPC code (v2.32) was placed on GitHub under the MIT License by Paint.NET author Rick Brewster. Licensing Developers may use GPC for any purpose without paid licensing restrictions. Features of GPC The following summarises the features and operations on polygons supported by GPC. GPC can compute the following clip operations: difference, intersection, exclusive-or and union. Po ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometry Processing
Geometry processing is an area of research that uses concepts from applied mathematics, computer science and engineering to design efficient algorithms for the acquisition, 3D reconstruction, 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, Laplacian smoothing, geometric smoothing might be achieved by convolving a Surface (mathematics), surface geometry with a blur kernel formed using the Laplace-Beltrami operator. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Geometry processing is a common research topi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory And Applications
A theory is a systematic and rational form of abstract thinking about a phenomenon, or the conclusions derived from such thinking. It involves contemplative and logical reasoning, often supported by processes such as observation, experimentation, and research. Theories can be scientific, falling within the realm of empirical and testable knowledge, or they may belong to non-scientific disciplines, such as philosophy, art, or sociology. In some cases, theories may exist independently of any formal discipline. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and comprehensive form of scientific kno ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
