Bezier curve - definição. O que é Bezier curve. Significado, conceito
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O que (quem) é Bezier curve - definição

CURVE USED IN COMPUTER GRAPHICS AND RELATED FIELDS
Bezier curve; Bezier curves; Bézier Curve; Bernstein-Bézier curve; Bernstein-Bezier curve; Besier curve; Bezier cubic; Bézier cubic; Bezier splines; Bezier Curve; Cubic bezier; Conic Bezier curve; Conic Bézier curve; Bezier path; Cubic bézier curve; Cubic Bézier curve
  • Animation of the construction of a fifth-order Bézier curve
  • cyan: ''y'' {{=}} ''t''<sup>3</sup>}}.
  • Cubic Bézier curve with four control points
  • Abstract composition of cubic Bézier curves ray-traced in 3D. Ray intersection with swept volumes along curves is calculated with Phantom Ray-Hair Intersector algorithm.<ref>Alexander Reshetov and David Luebke, Phantom Ray-Hair Intersector. In Proceedings of the ACM on Computer Graphics and Interactive Techniques (August 1, 2018). [https://research.nvidia.com/publication/2018-08_Phantom-Ray-Hair-Intersector]</ref>
  • Animation of a linear Bézier curve, ''t'' in [0,1
  • Animation of a quadratic Bézier curve, ''t'' in [0,1
  • Construction of a quadratic Bézier curve
  • Animation of a cubic Bézier curve, ''t'' in [0,1
  • Construction of a cubic Bézier curve
  • Animation of a quartic Bézier curve, ''t'' in [0,1
  • Construction of a quartic Bézier curve
  • Quadratic Béziers in [[string art]]: The end points ('''&bull;''') and control point ('''&times;''') define the quadratic Bézier curve ('''⋯''').

Bezier curve         
<graphics> A type of curve defined by mathematical formulae, used in computer graphics. A curve with coordinates P(u), where u varies from 0 at one end of the curve to 1 at the other, is defined by a set of n+1 "control points" (X(i), Y(i), Z(i)) for i = 0 to n. P(u) = Sum i=0..n [(X(i), Y(i), Z(i)) * B(i, n, u)] B(i, n, u) = C(n, i) * u^i * (1-u)^(n-i) C(n, i) = n!/i!/(n-i)! A Bezier curve (or surface) is defined by its control points, which makes it invariant under any affine mapping (translation, rotation, parallel projection), and thus even under a change in the axis system. You need only to transform the control points and then compute the new curve. The control polygon defined by the points is itself affine invariant. Bezier curves also have the variation-diminishing property. This makes them easier to split compared to other types of curve such as Hermite or B-spline. Other important properties are multiple values, global and local control, versatility, and order of continuity. [What do these properties mean?] (1996-06-12)
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.
Bezier         
WIKIMEDIA DISAMBIGUATION PAGE
Bezier; Bézier (disambiguation)
<graphics> (After Frenchman Pierre Bézier from Regie Renault) A collection of formulae for describing curved lines ({Bezier curve}) and surfaces (Bezier surface), first used in 1972 to model automobile surfaces. Curves and surfaces are defined by a set of "control points" which can be moved interactively making Bezier curves and surfaces convenient for interactive graphic design. ["Principles of interactive computer graphics", William M. Newman, Graw-Hill]. (1995-04-04)

Wikipédia

Bézier curve

A Bézier curve ( BEH-zee-ay) 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 limits of rasterized images and are intuitive to modify.

Bézier curves are also used in the time domain, particularly in animation, user interface design and smoothing cursor trajectory in eye gaze controlled interfaces. For example, a Bézier curve can be used to specify the velocity over time of an object such as an icon moving from A to B, rather than simply moving at a fixed number of pixels per step. When animators or interface designers talk about the "physics" or "feel" of an operation, they may be referring to the particular Bézier curve used to control the velocity over time of the move in question.

This also applies to robotics where the motion of a welding arm, for example, should be smooth to avoid unnecessary wear.