|
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). 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 higher the resolution is desired, the more the number of bits is required. Modern implementations for Boolean operations on polygons tend to use plane sweep ... [...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 variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses Logical connective, logical operators such as Logical conjunction, conjunction (''and'') denoted as ∧, Logical disjunction, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is 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 ''The Laws of Thought, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monotone Polygon
In geometry, a polygon ''P'' in the plane is called monotone with respect to a straight line ''L'', if every line orthogonal to ''L'' intersects the boundary of ''P'' at most twice. Similarly, a polygonal chain ''C'' is called monotone with respect to a straight line ''L'', if every line orthogonal to ''L'' intersects ''C'' at most once. For many practical purposes this definition may be extended to allow cases when some edges of ''P'' are orthogonal to ''L'', and a simple polygon may be called monotone if a line segment that connects two points in ''P'' and is orthogonal to ''L'' lies completely in ''P''. Following the terminology for monotone functions, the former definition describes polygons strictly monotone with respect to ''L''. Properties Assume that ''L'' coincides with the ''x''-axis. Then the leftmost and rightmost vertices of a monotone polygon decompose its boundary into two monotone polygonal chains such that when the vertices of any chain are being traversed in th ... [...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. He became a chair professor at HKUST in 2006. He died on 4 October 2010 iSunnyside Long-Term Care, Kitchener where he moved after his retirement. ... [...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 credited with the heuristic-based partitioning algorithm ''k''-d tree. Education and career Bentley received a B.S. in mathematical sciences from Stanford University in 1974, and 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. After receiving his Ph.D., he joined the faculty at Carnegie Mellon University as an assistant professor of computer science and mathematics. At CMU, his students included Brian Reid, John Ousterhout, Jeff Eppinger, Joshua Bloch, and James Gosling, and he was one of Charles Leiserson's advisors. Later, Bentley moved to Bell Laboratories, where he co-authored an optimized Quicksort algorithm with Doug McIlroy. He found an optimal solution for the two dimensional case of Klee's measure problem: given a set of ''n'' rectangles, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mark Overmars
Markus Hendrik Overmars (; born 29 September 1958 in Zeist, Netherlands) is a Dutch computer scientist and teacher of game programming known for his game development application GameMaker. GameMaker lets people 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 concentrates on computational geometry and its application in areas like 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 continued to be a member of the faculty of the same university until September 2013. Overmars has published over 100 journal papers, largely on computational geometry, and is the co-author of several books including a widely used computational geometry text. Overmars has also wo ... [...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. Pol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
