Shear

In computer graphics, shear is a transformation that distorts an object by stretching or compressing it in a particular direction. Shear can be applied in different directions and along different axes.

One of the most common types of shear is the shear parallel to the x-axis. This is also known as horizontal shear or x-shear. It involves shifting the y-coordinates of the object's vertices based on their x-coordinates. The amount of shift is determined by a shearing factor, which is a scalar value that specifies the amount of shear. The transformation matrix for horizontal shear can be defined as follows:

```

Sx = [ 1   Shx   0   0 ]

     [ 0   1     0   0 ]

     [ 0   0     1   0 ]

     [ 0   0     0   1 ]

```

Here, `Shx` is the shearing factor along the x-axis. To apply horizontal shear to an object, we multiply its vertices by this matrix.

Similarly, we can define vertical shear or y-shear, which involves shifting the x-coordinates of the object's vertices based on their y-coordinates. The transformation matrix for vertical shear can be defined as follows:

```

Sy = [ 1     0   0   0 ]

     [ Shy   1   0   0 ]

     [ 0     0   1   0 ]

     [ 0     0   0   1 ]

```

Here, `Shy` is the shearing factor along the y-axis. To apply vertical shear to an object, we multiply its vertices by this matrix.

There are also other types of shear, such as shear along the z-axis or diagonal shear, which involves shifting both x and y coordinates simultaneously. These types of shear can be defined similarly by modifying the appropriate elements of the transformation matrix.

It's important to note that shear, like other transformations, can be combined with other transformations, such as rotation, scaling, and translation, to create more complex transformations.