What is Scaling in Computer Graphics?

By Priyanshu Vaish|Updated : August 26th, 2022

Scaling in Computer Graphics is one of the fundamental transformations. Transformation is a process of modifying and re-positioning the existing graphics. 

Transformations help change the object's position, size, orientation, shape, etc. There are three basic rigid transformations: reflections, rotations, and translations. There is a fourth common transformation called dilation. Further, we have discussed scaling in computer graphics, transformation, and a lot more in the upcoming sections.

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What is Transformation in Computer Graphics?

Transformation in Computer Graphics means a change some graphics into something else by applying rules. In other words, transformation is the change of an object(position and size) after creation. Transformation can be done in 2D as well as 3D.

Transformation plays a vital role in computer graphics, repositioning the graphics on the screen and changing their size or orientation. The different types of basic geometrical transformation are as follows:

  • Translation
  • Scaling
  • Rotation

The derived geometrical transformation is:

  • Reflection
  • Shearing

2D Scaling in Computer Graphics

Scaling is the transformation that is used to change the object's size. The operation is carried out for polygon by multiplying the coordinate value(X, Y) of each vertex with the scaling factors.

Rules for Scaling in Computer Graphics

Scaling is performed about the origin as

If scale > 1, it enlarges the object and moves it away from the origin.

If scale = 1, then it leaves the object the same.

If scale < 1, it shrinks/reduces the object and moves it towards its origin.

What is the Equation for Scaling in Computer Graphics?

Let us suppose the coordinate(X, Y) is the original coordinate before the scaling, Sx, and Sy are the X-axis and Y-axis scaling factors. The new coordinate(X', Y') after the scaling is given by the equation:

X' = X . SX and Y' = Y . SY

The scaling factor SX and SY scale the object in the X and Y direction, respectively. The above equations may also be represented in matrix form as below:

What is the Equation for Scaling in Computer Graphics?


P’ = P . S

The following figure shows the scaling process where S is the scaling matrix.

Scaling in Computer Graphics 2

Computer scaling

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FAQs on Scaling in Computer Graphics

  • A scaling transformation alters the size of an object. In the scaling process, we either compress or expand the dimension of the object. The scaling operation can be achieved by multiplying each vertex coordinate (x, y) of the polygon by scaling factor sx and sy to produce the transformed coordinates as (x', y')

  • In computer graphics, scaling is a process of modifying or altering the size of objects. Scaling may be used to increase or reduce the size of the object. Scaling subjects the coordinate points of the original object to change. The scaling factor determines whether the object size is to be increased or reduced.

  • It is used to alter or change the size of objects. The change is done using scaling factors. There are two scaling factors that is Sx in the x-direction and Sy in the y-direction.

  • In the scaling method of nearest-neighbor interpolation, every pixel is replaced by four pixels of the same size. Scaling is also used for performing zooming in and zooming out the operation on digital images. Zooming affects all the portions of the display image or text uniformly.

  • Zooming is a transformation often provided with imaginary software. The transformation effectively scales down or blows up a pixel map or a portion of it with the instructions from the user. Such scaling is commonly implemented at the pixel level rather than the coordinates level.

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