On the ultimate explanation of affine transformation and perspective transformation

Recently to use some of the graphics to learn things, naturally unavoidable involves the concept of affine transformation and perspective transformation, unfortunately, the past textbooks and online interpretation of a large number of consensus is still not clear concept, the following quote "Learning OpenCV" a picture, simple and clear explanation:

Visible:

Affine transformation: In fact, it includes the translation, rotation, scaling, in fact, the concept in three-dimensional space is more able to explain, nothing else is to add a z-coordinate, but its value is zero, then the transformation of the translation transformation matrix to another three-dimensional coordinate system, and the newly generated z-coordinate ignored on the line, because, The essence of affine transformation is the projection mapping of parallel light, and for scaling the result is multiplied by a scale factor.

Perspective transformation: In fact, it is the transformation matrix of the keyhole imaging model, the result of which is the image acquired by the camera to acquire the actual object.

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On the ultimate explanation of affine transformation and perspective transformation