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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. [3] Other uses include the design of computer fonts and animation. [3] Bézier curves can be combined to form a Bézier spline, or generalized to higher dimensions to form Bézier ...
The geometry of a single bicubic patch is thus completely defined by a set of 16 control points. These are typically linked up to form a B-spline surface in a similar way as Bézier curves are linked up to form a B-spline curve. Simpler Bézier surfaces are formed from biquadratic patches (m = n = 2), or Bézier triangles.
The variation diminishing property of Bézier curves is that they are smoother than the polygon formed by their control points. If a line is drawn through the curve, the number of intersections with the curve will be less than or equal to the number of intersections with the control polygon.
The edges of the triangle are themselves Bézier curves, with the same control points as the Bézier triangle. By removing the γ u term, a regular Bézier curve results. Also, while not very useful for display on a physical computer screen, by adding extra terms, a Bézier tetrahedron or Bézier polytope results.
The curve named after Pierre Bézier. Bézier popularized but did not actually create the Bézier curve — using such curves to design automobile bodies. The curves were first developed in 1959 by Paul de Casteljau using de Casteljau's algorithm, a numerically stable method to evaluate Bézier curves. The curves remain widely used in computer ...
Béziergon – The red béziergon passes through the blue vertices, the green points are control points that determine the shape of the connecting Bézier curves. 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 continuous. In other words, a ...
English: Illustration of use of cubic Bezier splines to smooth a polyline, based on algorithm at . The different colours indicate different "curviness" values (black lowest and red highest). Triangles and squares indicate control points for the Bezier spline of the corresponding colour.
Paul de Casteljau (19 November 1930 – 24 March 2022) was a French physicist and mathematician. In 1959, while working at Citroën, he developed an algorithm for evaluating calculations on a certain family of curves, which would later be formalized and popularized by engineer Pierre Bézier, leading to the curves widely known as Bézier curves.