Describe in brief about the transformations Translations, Rotations, Scaling, reflections.
1) Transformation Translations
It is the straight line movement of an object from one position to another is called Translation. Here the object is positioned from one coordinate location to another.
Translation of point:
To translate a point from coordinate position (x, y) to another (x1 y1), we add algebraically the translation distances Tx and Ty to original coordinate.
x1=x+Tx
y1=y+Ty
The translation pair (Tx,Ty) is called as shift vector.
Translation is a movement of objects without deformation. Every position or point is translated by the same amount. When the straight line is translated, then it will be drawn using endpoints.
For translating polygon, each vertex of the polygon is converted to a new position. Similarly, curved objects are translated. To change the position of the circle or ellipse its center coordinates are transformed, then the object is drawn using new coordinates.
Let P is a point with coordinates (x, y). It will be translated as (x1 y1).
Rotations
It is a process of changing the angle of the object. Rotation can be clockwise or anticlockwise. For rotation, we have to specify the angle of rotation and rotation point. Rotation point is also called a pivot point. It is print about which object is rotated.
Types of Rotation:
1) Anticlockwise
2) Counterclockwise
The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-clockwise) direction.
The negative value of the pivot point (rotation angle) rotates an object in a clockwise direction.
When the object is rotated, then every point of the object is rotated by the same angle.
Straight Line: Straight Line is rotated by the endpoints with the same angle and redrawing the line between new endpoints.
Polygon: Polygon is rotated by shifting every vertex using the same rotational angle.
Curved Lines: Curved Lines are rotated by repositioning of all points and drawing of the curve at new positions.
Circle: It can be obtained by center position by the specified angle.
Ellipse: Its rotation can be obtained by rotating major and minor axis of an ellipse by the desired angle.
Scaling
It is used to alter or change the size of objects. The change is done using scaling factors. There are two scaling factors, i.e. Sx in x direction Sy in y-direction. If the original position is x and y. Scaling factors are Sx and Sy then the value of coordinates after scaling will be x1 and y1.
If the picture to be enlarged to twice its original size then Sx = Sy =2. If Sx and Sy are not equal then scaling will occur but it will elongate or distort the picture.
If scaling factors are less than one, then the size of the object will be reduced. If scaling factors are higher than one, then the size of the object will be enlarged.
If Sxand Syare equal it is also called as Uniform Scaling. If not equal then called as Differential Scaling. If scaling factors with values less than one will move the object closer to coordinate origin, while a value higher than one will move coordinate position farther from origin.
