Transformation - 2D Transformation in computer graphics

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Computer Graphics and Multimedia Application: Q1.Transformation? and its types? Q2.2D Transformation in computer graphics? Q3.Shearing Transformation? (Computer graphics and multimedia application All Notes)


Q1. What is Transformation? Explain the geometric transformation? 2D Transformation in computer graphics?

Ans. Transformation is the process by which we can change the shape, position, and direction of any object with respect to any coordinate system on background by translation, rotation, scaling and reflection.
Basically it is categorized into two categories :
1. Geometric transformation. 2. Co-ordinate transformation.

When the object is moved with respect to a stationary coordinate system this is referred to as geometric transformation and applied to each point of the object. And when the coordinate system is moved relative to the object and object is held stationary then this process is termed as co-ordinate transformation.

1. Geometric Transformation:

Every object in computer graphics is assumed as a set of points or pixels. In two-dimensional transformation, each object point P has coordinates (x, y) and the object is the sum of total of all co-ordinates points.
When any object is transformed to a new location then co-ordinate of new locations can be obtained by the application of geometric transformation.

Geometric transformation covers the following transformations :
(a) Translation
(b) Rotation about the origin.
(c) Scaling transformation.
(d) Mirror reflection about any axis.

(a) Translation:

Translation means an object is displaced a given distance and direction from its original position. If P(x, y) is the original point location and new object point P'(x', y') can be obtained by the following equation :
P' =Tv(P)
where x' = x +tx and y' = x +ty.

(b) Rotation about Origin:

The object is rotated 0° about the origin. We take 0° positive for counter clockwise and negative for anticlockwise direction.
The co-ordinates of the new point is given by the following equation :
P' = R0(P)
P(x, y) point location before the rotation and P'(x, y) point location after rotation.

(c) Scaling Transformation:

Scaling is the process of changing the size and position of the image. There are two factors in scaling transformation i.e. Sx and Sy , where Sx is scale factor or x-coordinate and Sy is the scale factor for the y-coordinate.

(d) Mirror Reflection about any axis:

Suppose we assume any axis as a mirror then the object has a mirror image or reflection. The reflection of object P is obtained at the same distance from the axis as P. Co-ordinate of P' is given by,

2. Coordinate Transformation:

When the coordinate system is moved with respect to object location, then it is called co-ordinate transformation. In co-ordinate transformation, the coordinate system is transformed and the object is made stationary.

Q2. What is 2-D Transformation? Explain 2D Transformation in computer graphics with example?

Ans. The fundamental objective of 2-D transformation is to simulate the movement and manipulation of objects in the plane. Points and lines which join them, along with appropriate drawing algorithm are used to represent objects.

The ability to transform these points and lines is achieved by translation, routing, scaling, and reflection. Two points of view are used for describing the object movement. The first of that the object itself is moved relative to a stationary coordinate system or background.

The mathematical statement of this viewpoint is described by geometric transformations applied to each point of the object. The second point of view holds that the object is held stationary, while the coordinate system is moved relative to the object. This effect is described by a coordinate transformation.

Basic 2D Transformation in computer graphics:

2D Transformation in computer graphics: There are three basic actions or movements, moving, scaling, and rotation which are widely used in the graphics applications. These movements are performed through some basic geometric.
Since these transformations are performed using geometry, they are also known as geometric transformations. There are three basic transformations, translation, scaling, and rotation. In the above figure, these three basic transformations are illustrated.

Q3. Define Shearing Transformation?

Ans. Shearing transformation is a linear mapping that displaces each point in fixed direction by an amount proportional to its signed distance from a line which is parallel to that direction. Such a transformation produces a shape distortion.

There are two shear transformations → X-shear and Y-shear. X-shear shifts X-coordinate values and Y-shear shifts Y-coordinate values.

[ Topic= 2D Transformation in computer graphics ]
[ Topic= 2D Transformation in computer graphics ]

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[ Topic= 2D Transformation in computer graphics ]

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