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Bézier curve

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Curve used in computer graphics and related fieldsCubic Bézier curve with four control pointsThe basis functions on the range t in [0,1] for cubic Bézier curves: blue: y = (1 − t), green: y = 3(1 − t)t, red: y = 3(1 − t)t, and cyan: y = t.A Bézier curve ( , French pronunciation:) is a parametric curve used in computer graphics and related fields. A sequence of discrete "control points" defines a smooth, continuous curve by means of a formula.

Composite Bézier curveComposite Bézier curveIn geometric modelling and in computer graphics, a composite Bézier curve or Bezier spline is a spline made out of Bézier curves that is at least C0{\displaystyle C^{0}}continuous. In other words, a composite Bézier curve is a series of Bézier curves joined end to end where the last point of one curve coincides with the starting point of the next curve.Bézier surfaceBézier surfaceBézier surfaces are a type 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.Bézier triangleBézier triangleA Bézier triangle is a special type of Bézier surface that is created by (linear, quadratic, cubic or higher degree) interpolation of control points.Parametric equationParametric equationIn mathematics, a parametric equation expresses several quantities, such as the coordinates of a point, as functions of one or more variables called parameters. In the case of a single parameter, parametric equations are commonly used to express the trajectory of a moving point. For this case, the parameter is often, but not necessarily, time, and the point describes a curve, called a parametric curve.Vector graphicsVector graphicsVector 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 (especially graphic design software, computer-aided design, and geographic information systems).Pierre BézierPierre Étienne Bézier (French pronunciation: [pjɛʁ etjɛn bezje]; 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.RenaultRenaultRenault S.A., commonly referred to as Groupe Renault (UK: REN-oh, US: rə-NOH; French: [ʁəno], also known as the Renault Group in English), is a French multinational corporation and automobile manufacturer established in 1899. The company produces a range of cars and vans; it has previously manufactured trucks, tractors, tanks, buses/coaches, aircraft and aircraft engines, as well as autorail vehicles.FontFontIn metaltypesetting, a font is a particular size, weight, and style of a typeface, a set of fonts that share an overall design. For instance, the typeface Bauer Bodoni (shown in the figure) includes fonts "Roman 12pt" (or "regular"), "bold 12pt" and "italic 12pt"; each of these styles is also available in a range of other common sizes. In traditional printing, fonts were physically created using metal or wood type, with a font for each size.FranceFranceCountry primarily in Western EuropeFrance, officially the French Republic, is a country primarily located in Western Europe. Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the North Atlantic, the French West Indies, and many islands in Oceania and the Indian Ocean.Raster graphicsRaster graphicsIn computer graphics and digital photography, a raster graphic, raster image, or simply raster is a digital image made up of a rectangular grid of tiny colored (usually square) so-called pixels. Unlike vector graphics which use mathematical formulas to describe shapes and lines, raster images store the exact color of each pixel, making them ideal for photographs and images with complex colors and details.Computer graphicsComputer graphicsComputer graphics (CG) deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science.SequenceSequenceIn mathematics, a sequence is a collection of objects possibly with repetition, that come in a specified order. Like a set, it contains members (also called elements, or terms). Unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter. The notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set.

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