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A Bézier curve is defined by a set of control points P0 through Pn, where n is called the order of the curve (n = 1 for linear, 2 for quadratic, 3 for cubic, etc.). The first and last control points are always the endpoints of the curve; however, the intermediate control points generally do not lie on the curve.
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. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central ...
Composite Bézier curve. 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 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 ...
De Casteljau's algorithm. 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. De Casteljau's algorithm can also be used to split a single Bézier curve into two Bézier curves at an arbitrary ...
A quadratic ( ) Bézier triangle features 6 control points which are all located on the edges. The cubic ( ) Bézier triangle is defined by 10 control points and is the lowest order Bézier triangle that has an internal control point, not located on the edges. In all cases, the edges of the triangle will be Bézier curves of the same degree.
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. The idea is named after mathematician Sergei Natanovich Bernstein.
Properties. A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape ...
De Boor's algorithm. In the mathematical subfield of numerical analysis, de Boor's algorithm[1] is a polynomial-time and numerically stable algorithm for evaluating spline curves in B-spline form. It is a generalization of de Casteljau's algorithm for Bézier curves. The algorithm was devised by German-American mathematician Carl R. de Boor.