Affine transformation - Wikipedia
网页In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles.
网页Affine transformations of the plane in two dimensions include pure translations, scaling in a given direction, rotation, and shear. An affine transformation is usually and conveniently represented in matrix notation: using homogeneous coordinates. The advantage of using homogeneous coordinates is that one can combine any number of affine ...
仿射变换（Affine Transformation）在2D和3D坐标下的变换矩阵和 …
网页An affine transformation is a type of geometric transformation which preserves collinearity (if a collection of points sits on a line before the transformation, they all sit on a line afterwards) and the ratios of distances between points on a line.
二维仿射变换 Two-dimensional Affine Transformations - 知乎
网页在平面中，包含了移动、缩放（给定方向的）、旋转、和切变的变换，统称为【仿射变换】（Affine Transformations)。 通常，我们会用在齐次坐标(Homogeneous Coordinates)的矩阵来表示仿射变换， 以便于将上述所有的变换，集成到少量矩阵中以相乘的形式来表示。
Affine Transformation -- from Wolfram MathWorld
网页2024年8月22日 · An affine transformation is any transformation that preserves collinearity (i.e., all points lying on a line initially still lie on a line after transformation) and ratios of distances (e.g., the midpoint of a line segment remains the midpoint after transformation).
Computing 2D affine transformations using only matrix ... - Medium
网页2018年1月12日 · This is a short visual description of computing a 2D affine transformation using a single matrix multiplication step, something that requires a bit of dimensional trickery.
Affine Transformation - A Comprehensive Guide on Affine …
网页2023年8月31日 · What is an Affine Transformation? An affine transformation is a specific type of transformation that maintains the collinearity between points (i.e., points lying on a straight line remain on a straight line) and preserves the ratios of distances between points lying on a straight line.
Affine transformations | Brilliant Math & Science Wiki
网页An affine transformation is a type of geometric transformation which preserves collinearity (if a collection of points sits on a line before the transformation, they all sit on a line afterwards) and the ratios of distances between points on a line. Types of affine transformations include translation (moving a figure), scaling (increasing or ...
网页What all the elements of a 2 x 2 transformation matrix do and how these generalize to 3 x 3 transformations. What homogeneous coordinates are and how they work for affine transformations. How to concatenate transformations. The mathematical properties of affine transformations.
网页Geometric transformations will map points in one space to points in another: (x', y‘, z‘ ) = f (x, y, z). These transformations can be very simple, such as scaling each coordinate, or complex, such as non-linear twists and bends. We'll focus on transformations that can be represented easily with matrix operations. 5.
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