V2EX parametric curve

Parametric Curve

定义 Definition

参数曲线:用一个或多个“参数”(常记为 t)来表示平面或空间中点的坐标,从而描述曲线的方式。典型形式如 \(x=f(t),\ y=g(t)\)(或再加 \(z=h(t)\))。除“显式函数曲线”外,参数化特别适合描述圆、螺旋线、摆线等。

发音 Pronunciation (IPA)

/prmtrk kv/

例句 Examples

A circle can be described as a parametric curve with \(x=\cos t\) and \(y=\sin t\).
圆可以用参数曲线表示:\(x=\cos t\),\(y=\sin t\)。

In computer graphics, a parametric curve lets us control the shape smoothly by adjusting a few parameters.
在计算机图形学中,参数曲线可以通过调整少量参数来平滑地控制形状。

词源 Etymology

parametric 来自 parameter(参数),源于希腊语 *para-*(“旁边、辅助”)与 metron(“度量”)相关词根,强调“用可调的量来刻画”。curve 来自拉丁语 curvus(“弯曲的”)。合起来即“用参数刻画的曲线”。

相关词 Related Words

文学与著作中的用例 Literary Works

  • Calculus: Early Transcendentals(James Stewart)
  • Calculus(Michael Spivak)
  • Differential and Integral Calculus(Richard Courant)
  • The Princeton Companion to Mathematics(Timothy Gowers 主编)
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