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Bézier Patch
Bézier can refer to: *Pierre Bézier, French engineer and creator of Bézier curves *Bézier curve *Bézier triangle *Bézier spline (other) *Bézier surface * The town of Béziers in France * AS Béziers Hérault, a French rugby union team *Bézier Games, an American board game publisher {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre Bézier
Pierre Étienne Bézier (1 September 1910 – 25 November 1999; ) was a French engineer and one of the founders of the fields of solid, geometric and physical modelling as well as in the field of representing curves, especially in computer-aided design and manufacturing systems. As an engineer at Renault, he became a leader in the transformation of design and manufacturing, through mathematics and computing tools, into computer-aided design and three-dimensional modeling. Bézier patented and popularized the Bézier curves and Bézier surfaces that are now used in most computer-aided design and computer graphics systems. Background Born in Paris, Bézier was the son and grandson of engineers. He obtained a degree in mechanical engineering from the École nationale supérieure d'arts et métiers in 1930. He earned a second degree in electrical engineering in 1931 at the École supérieure d'électricité, and a doctorate in 1977 in mathematics from the Pierre-and-Marie-Cur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bézier Curve
A Bézier curve ( ) is a parametric curve used in computer graphics and related fields. A set of discrete "control points" defines a smooth, continuous curve by means of a formula. Usually the curve is intended to approximate a real-world shape that otherwise has no mathematical representation or whose representation is unknown or too complicated. The Bézier curve is named after French engineer Pierre Bézier (1910–1999), who used it in the 1960s for designing curves for the bodywork of Renault cars. Other uses include the design of computer fonts and animation. Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier surfaces. The Bézier triangle is a special case of the latter. In vector graphics, Bézier curves are used to model smooth curves that can be scaled indefinitely. "Paths", as they are commonly referred to in image manipulation programs, are combinations of linked Bézier curves. Paths are not bound by the limi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bézier Triangle
A Bézier triangle is a special type of Bézier surface that is created by (linear, quadratic, cubic or higher degree) interpolation of control points. ''n''th-order Bézier triangle A general ''n''th-order Bézier triangle has (''n'' +1)(''n'' + 2)/2 control points ''α''''i''''β''''j''''γ''''k'' where ''i'', ''j'', ''k'' are non-negative integers such that ''i'' + ''j'' + ''k'' = ''n''. The surface is then defined as : (\alpha s + \beta t + \gamma u)^n = \sum_ s^i t^j u^k \alpha^i \beta^j \gamma^k = \sum_ \frac s^i t^j u^k \alpha^i \beta^j \gamma^k for all non-negative real numbers ''s'' + ''t'' + ''u'' = 1. With linear order (n=1), the resulting Bézier triangle is actually a regular flat triangle, with the triangle vertices equaling the three control points. A quadratic (n=2) Bézier triangle features 6 control points which are all located on the edges. The cubic (n=3) Bézier triang ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bézier Spline (other)
Depending on the author, Bézier spline may refer to: * a Bézier curve or * a composite Bézier curve In geometric modelling and in computer graphics, a composite Bézier curve or Bézier spline is a spline made out of Bézier curves that is at least C^0 continuous. In other words, a composite Bézier curve is a series of Bézier curves joined ... {{DEFAULTSORT:Bezier spline Mathematics disambiguation pages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bézier Surface
Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central control points; rather, it is "stretched" toward them as though each were an attractive force. They are visually intuitive, and for many applications, mathematically convenient. History Bézier surfaces were first described in 1962 by the French engineer Pierre Bézier who used them to design automobile bodies. Bézier surfaces can be of any degree, but bicubic Bézier surfaces generally provide enough degrees of freedom for most applications. Equation A given Bézier surface of degree (''n'', ''m'') is defined by a set of (''n'' + 1)(''m'' + 1) control points k''i'',''j'' where ''i'' = 0, ..., ''n'' and ''j'' = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Béziers
Béziers (; oc, Besièrs) is a Subprefectures in France, subprefecture of the Hérault Departments of France, department in the Occitania (administrative region), Occitanie Regions of France, region of Southern France. Every August Béziers hosts the famous ''Feria de Béziers'', which is centred on bullfighting. A million visitors are attracted to the five-day event. The town is located on a small Cliff, bluff above the river Orb (river), Orb, about from the Mediterranean Sea, Mediterranean coast and southwest of Montpellier. At Béziers, the Canal du Midi passes over the river Orb by means of the ''Orb Aqueduct, Pont-canal de l'Orb'', an Navigable aqueduct, aqueduct claimed to be the first of its kind. History Béziers is one of the oldest cities in France. Research published in March 2013 shows that Béziers dates from 575 BC, making it older than Agde (Greek Agathe Tyche, founded in 525 BC) and a bit younger than Marseille (Greek Massalia, founded in 600 BC ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AS Béziers Hérault
Association Sportive Béziers Hérault ( oc, Associacion Esportiva de Besièrs Erau), often referred to by rugby media simply by its location of Béziers, is a French rugby union club currently playing in the second level of the country's professional rugby system, Pro D2. They earned their most recent promotion as 2011 Fédérale 1 champions, but the club also won 11 Top 14 titles since its establishment in 1911. Béziers was a major force in French rugby throughout the 1970s and 1980s; however, at the end of 2004–05 season they were relegated to Pro D2. After some years playing in French second division, they finished bottom of the table in 2008–09 and were relegated to amateur Fédérale 1, before returning to Pro D2 after their 2011 title. They are based in Béziers in Occitania, and play at Stade Raoul-Barrière (capacity 18,555). The club colors are red and blue. History The club was established in 1911. Their first notable honour was being runners-up in the Coupe de F ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
