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The mathematical basis for Bézier curves—the Bernstein polynomials—was established in 1912, but the polynomials were not applied to graphics until some 50 years later when mathematician Paul de Casteljau in 1959 developed de Casteljau's algorithm, a numerically stable method for evaluating the curves, and became the first to apply them to computer-aided design at French automaker Citroën ...
In the mathematical field of numerical analysis, De Casteljau's algorithm is a recursive method to evaluate polynomials in Bernstein form or Bézier curves, named after its inventor Paul de Casteljau.
Blender is available for Windows 8.1 and above, and Mac OS X 10.13 and above. [243] [244] Blender 2.80 was the last release that had a version for 32-bit systems (x86). [245] Blender 2.76b was the last supported release for Windows XP, and version 2.63 was the last supported release for PowerPC.
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.
A béziergon (also called bézigon) is a closed path composed of Bézier curves. It is similar to a polygon in that it connects a set of vertices by lines, but whereas in polygons the vertices are connected by straight lines, in a béziergon the vertices are connected by Bézier curves.
A NURBS curve. (See also: the animated creation of a NURBS spline.) A NURBS surface. Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces.
An image rendered using path tracing, demonstrating notable features of the technique. Path tracing is a rendering algorithm in computer graphics that simulates how light interacts with objects, voxels, and participating media to generate realistic (physically plausible) images.
A space curve; the vectors T, N, B; and the osculating plane spanned by T and N. In differential geometry, the Frenet–Serret formulas describe the kinematic properties of a particle moving along a differentiable curve in three-dimensional Euclidean space, or the geometric properties of the curve itself irrespective of any motion.