“Bézier curve”的概念、定义、翻译、参考文献-科学参考

Bézier curve

Computer

A spline approximation developed by Pierre Bézier and widely used in computer-aided design. An nth-degree Bézier curve is an nth-degree polynomial defined by n + 1 control points, r₀…r_n. The Bézier curve is defined by
$r (u) = \sum_{i = 0}^{n} r_{i} B_{i}^{n} (u)$
where B_i ⁿ(u) is the Bernstein polynomial of degree n defined by
$\begin{array}{l} B_{i}^{n} (u) = n! / (i! (n - i)!) \times u^{i} {(1 - u)}^{n - i} \\ if 0 \leq i \leq n, \\ or = 0 otherwise . \end{array}$
Bézier curves have a number of important properties. For example, the curve passes through the first and last control points and is completely contained within the polygon that forms the convex hull of the control points; the gradient at each of the end points is the same as the gradient of the line joining the end point to its immediate neighbour; the control points exert a pull on the direction of the curve which is clamped by the slope at the end points.

单词	Bézier curve
释义	Bézier curve Computer A spline approximation developed by Pierre Bézier and widely used in computer-aided design. An nth-degree Bézier curve is an nth-degree polynomial defined by n + 1 control points, r₀…r_n. The Bézier curve is defined by $r (u) = \sum_{i = 0}^{n} r_{i} B_{i}^{n} (u)$ where B_i ⁿ(u) is the Bernstein polynomial of degree n defined by $\begin{array}{l} B_{i}^{n} (u) = n! / (i! (n - i)!) \times u^{i} {(1 - u)}^{n - i} \\ if 0 \leq i \leq n, \\ or = 0 otherwise . \end{array}$ Bézier curves have a number of important properties. For example, the curve passes through the first and last control points and is completely contained within the polygon that forms the convex hull of the control points; the gradient at each of the end points is the same as the gradient of the line joining the end point to its immediate neighbour; the control points exert a pull on the direction of the curve which is clamped by the slope at the end points.
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