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A commonly desired property of splines is for them to join their individual curves together with a specified level of parametric or geometric continuity.While individual curves in the spline are fully continuous within their own interval, there is always some amount of discontinuity where different curves meet.
Form·Z allows design in 3D or in 2D, using numeric or interactive graphic input through either line or smooth shaded drawings ().Modeling features include Boolean solids to generate complex composite objects; the ability to create curved surfaces from splines, including NURBS and Bézier/Coons patches; mechanical and organic forms using the previous as well as metaforms, patches, subdivisions ...
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.
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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 ...
OCAF persistence without dynamically loaded plugins. Improved STEP AP242 support, including PMI, dimensions and annotations. Improved rendering performance of Wireframe AIS_Shape presentation. Added AIS_Manipulator for interactive object transformations in 3D viewer. TKOpenGl now uses GLSL programs by default. Open CASCADE Technology 7.0 2016 ...
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.
In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object.