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单词 Affine mapping
释义

Affine mapping

中文百科

仿射变换 Affine transformation

（重定向自Affine mapping）
一个使用仿射变换所制造有自相似性的碎形
二维平面上的仿射变换可呈现于三维空间中。平移即为沿着z轴的错切，旋转则以z轴为轴心
一个实数平面上的简单仿射变换
将不同二维仿射变换作用到单位正方形上。注意镜射矩阵是缩放矩阵的特例。

仿射变换，又称仿射映射，是指在几何中，一个矢量空间进行一次线性变换并接上一个平移，变换为另一个矢量空间。

一个对矢量 \vec{x} 平移 \vec{b} ，与旋转放大缩小 A的仿射映射为

\vec{y} = A \vec{x} + \vec{b}

上式在齐次坐标上，等价于下面的式子

\begin{bmatrix} \vec{y} \\ 1 \end{bmatrix} = \begin{bmatrix} A & \vec{b} \ \\ 0, \ldots, 0 & 1 \end{bmatrix} \begin{bmatrix} \vec{x} \\ 1 \end{bmatrix}

在分形的研究里，收缩平移放射映射可以制造制具有自相似性的分形。

英语百科

Affine transformation 仿射变换

（重定向自Affine mapping）
An image of a fern-like fractal that exhibits affine self-similarity. Each of the leaves of the fern is related to each other leaf by an affine transformation. For instance, the red leaf can be transformed into both the small dark blue leaf and the large light blue leaf by a combination of reflection, rotation, scaling, and translation.
Affine transformations on the 2D plane can be performed in three dimensions. Translation is done by shearing along over the z axis, and rotation is performed around the z axis.
A central dilation. The triangles A1B1Z, A1C1Z, and B1C1Z get mapped to A2B2Z, A2C2Z, and B2C2Z, respectively.
A simple affine transformation on the real plane

In geometry, an affine transformation, affine map or an affinity (from the Latin, affinis, "connected with") is a function between affine spaces which preserves points, straight lines and planes. Also, sets of parallel lines remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line.
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更新时间：2025/6/17 5:13:34