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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 ...
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 optimization methods. [5]
The key points, placed by the artist, are used by the computer algorithm to form a smooth curve either through, or near these points. For a typical example of 2-D interpolation through key points see cardinal spline. For examples which go near key points see nonuniform rational B-spline, or Bézier curve. This is extended to the forming of ...
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 ...
The Pen tool creates Bézier curves and the Line tool allows easy creation of straight line segments. All of these tools can also be used to manipulate existing curves. Arc, Spiral, and Triangle tools create curves; B-Spline tool creates B-Spline curves; Context-sensitive Node tool provides control over post-editing objects and nodes.
The drafter uses several technical drawing tools to draw curves and circles. Primary among these are the compasses, used for drawing arcs and circles, and the French curve, for drawing curves. A spline is a rubber coated articulated metal that can be manually bent to most curves.
B C Cubic spline Common implementations 0 Any: Cardinal splines: 0 0.5 Catmull-Rom spline: Bicubic filter in GIMP: 0 0.75 Unnamed: Bicubic filter in Adobe Photoshop [5] 1/3 1/3 Mitchell–Netravali Mitchell filter in ImageMagick [4] 1 0 B-spline: Bicubic filter in Paint.net
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. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae ) and modeled shapes .