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Modern vector graphics and computer font systems like PostScript, Asymptote, Metafont, OpenType, and SVG use composite Bézier curves composed of cubic Bézier curves (3rd order curves) for drawing curved shapes. Sinc function approximated using a smooth Bézier spline, i.e., a series of smoothly-joined Bézier curves
With information of the given vertex positions ,, of a flat triangle and the according normal vectors ,, at the vertices a cubic Bézier triangle is constructed. In contrast to the notation of the Bézier triangle page the nomenclature follows G. Farin (2002), [2] therefore we denote the 10 control points as with the positive indices holding the condition + + =.
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.
An example Bézier triangle with control points marked. A cubic Bézier triangle is a surface with the equation (,,) = (+ +) = + + + + + + + + +where α 3, β 3, γ 3, α 2 β, αβ 2, β 2 γ, βγ 2, αγ 2, α 2 γ and αβγ are the control points of the triangle and s, t, u (with 0 ≤ s, t, u ≤ 1 and s + t + u = 1) are the barycentric coordinates inside the triangle.
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.
SolveSpace v3.0 is able to export 2D sketches and surfaces into DXF/DWG (AutoCAD version 2007), PDF, SVG, EPS, and HPGL file formats. Wireframes can be exported as DXF and STEP files. Polygon meshes can be exported as STL and Wavefront OBJ; NURBS as STEP. SolveSpace is able to export models in STEP, STL, and G-code for reuse in third-party CAM ...
Cubic polynomial splines can be specified in other ways, the Bezier cubic being the most common. However, these two methods provide the same set of splines, and data can be easily converted between the Bézier and Hermite forms; so the names are often used as if they were synonymous.