2D Geometric Transformation (Published on dated Oct 10, 2021)

1.1 Introduction of 2D Transformation

Transformation is the process of changing graphics into something else by applying rules. There are several different transformations like translation, scaling up or down, rotation, shearing, etc. When a change takes place on a 2D plane, it is called 2D transformation.

Transformations are used to reposition the graphics on the screen and alter their size and/or their orientation.

Homogeneous Coordinates

To perform a sequence of transformation such as translation followed by rotation and scaling, we follow a sequential process −

Translate the coordinates,

Rotate the translated coordinates

Scale the rotated coordinates.

1.2 Basic Types of 2D Transformation

· 2D Translation

· 2D Rotation

· 2D Scaling

· 2D Reflection

· 2D Shearing

1.2.1 2D Translation

1.2.2 2D Rotation

Example of 2-D Rotation –

1.2.3 2D Scaling

Scaling is used to change the size of an object. During Scaling, we either expand or compress the dimensions of the object. Scaling is done by multiplying the original coordinates of the object with the scaling factor.

1.2.4 2D Reflection

Generating the mirror image of an object is called as reflection. In other words, we can say that it is rotation operation with 180° of rotation. The size of the object does not change.

1.2.5 2D Shearing

Shear transformation changes the shape of an object. There are two shear transformations X-Shear and Y-Shear. X-shear shifts X coordinates values while Y-Shear shifts Y coordinate values. However, in both the cases only one coordinate is changed, the other coordinate other preserves its values. Shearing is also termed as Skewing.

X-Shear

In X-Shear the value of X-coordinate is preserved, and the value of the Y-coordinate is changed. The figure in turn becomes skewed to the right or left.

References:

1. https://link.springer.com/chapter/10.1007/978-3-642-46514-7_6
2. Computer Graphics by AP Godse
3. Computer Graphics and Multimedia Techniques By Neetu Agrwal
4. Computer Graphics by Dincy Paul