Projective Transformation
Projective transformations come into play whenever perspective drawings of a scene are required. A projective transformation is defined by four preimage/image pairs of points. The definition is analogous to that of a
similarity, though with eight required points instead of four.
As an example we consider the situation of producing a projective image of a rectangular grid. We furthermore add a few circles to make visual effect of a projective transformation more visible. For this we simply have to draw a rectangular grid (and the circles) and the corners of the desired image. We define a projective transformation by mapping the corners of the rectangular grid to the corners of the image.
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Defining a projective transformation |
After this we apply the map to the elements to which we want to apply the projective transformation. The image of this operation is the desired projected rectangular grid.
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The image of the rectangular grid |