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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 ...
Bernstein polynomials approximating a curve. In the mathematical field of numerical analysis, a Bernstein polynomial is a polynomial expressed as a linear combination of Bernstein basis polynomials.
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.
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.
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.
The bezier curve is defined by the a point moving through space. This point is the midpoint of the green line. As time goes by, the endpoints of the green line go from P0 to P1 and from P1 to P2 respectively, at a rate of distance/time.
Glaxnimate saves animations using a custom JSON-based format, but it also supports loading and saving animated SVG, Lottie, Android Vector Drawables, and After Effects Project files (.aep).