V2EX affine

Affine

定义 / Definition

affine(形容词):在数学中指“仿射的”,与仿射变换有关保持直线与平行关系不变的变换(例如平移、缩放、剪切、旋转的组合),但不一定保持长度与角度。

发音 / Pronunciation (IPA)

/fan/

例句 / Examples

An affine transformation can move and stretch a shape without bending it.
仿射变换可以移动并拉伸一个图形,而不会把它弯曲。

In computer vision, affine models are often used to approximate how a planar surface changes under different camera viewpoints.
在计算机视觉中,仿射模型常用于近似描述平面表面在不同相机视角下的变化。

词源 / Etymology

来自法语 affine,与拉丁语 affīnis(“相邻的、相关的、同一边界的”)有关。后来在数学语境中引申为“在某种结构上相关/对应”的概念,形成“仿射”的专门含义,强调在变换下保持直线与平行等关系。

相关词 / Related Words

文学与著作中的用例 / Literary & Notable Works

  • The Princeton Companion to Mathematics(介绍仿射空间、仿射几何等概念时出现 affine
  • Geometry(H. S. M. Coxeter,讨论仿射几何与射影几何的章节中出现 affine
  • Multiple View Geometry in Computer Vision(Hartley & Zisserman,计算机视觉几何模型中频繁使用 affine
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