Projective Transformation

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.

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.

The image of the rectangular grid