Description

Full Marks: 40
You are given with a partial implementation of three classes: Point2D, Circle, and Rectangle in your homework 1. Extend the implementation according to the following instructions. Note that the numbers inside brackets specify the marks allotted to each task.
Point2D: [8 Marks]
– Let, = ( , ) and = ( , ) be two points. Overload the following operators according to their definitions given:
Operator Type Expression Expression output
+ Binary + A new point = ( , ) where
= + and = + . This
operation represents a translation of the point by the amount specified by
* Binary ∗
where is a real number A new point = ( , ) where = ∗
and = ∗ . This operation represents a scaling of the point by the amount . The scaling is done with respect to the origin (0,0).
== Binary == TRUE (Boolean) if both points have same coordinates; otherwise FALSE
!= Binary ! = TRUE (Boolean) if the points are different; otherwise FALSE

Circle: [20 Marks]
-Let, and be two circles having centers and and radiuses and . Overload the following operators according to their definitions given:
Operator Type Expression Expression output
+ Binary + where is a 2D point. A new circle whose center is translated by the amount specified by the point . This operation represents a translation of the circle with respect to the origin (0,0).
* Binary ∗
where is a real number A new circle whose radius and center is scaled by the amount . This operation represents a scaling operation for the circle with respect to the origin (0,0).
+ binary + A new circle whose center is the
Homework prepared by Sukarna Barua, Asst. Professor, CSE, BUET
weighted average ∗ + ∗ (1 − ) and radius is + .
where = /( + )
– Binary − A new circle whose center is the
weighted average ∗ + ∗ (1 − ) and radius is − .
where = /( + )
== Binary == TRUE (Boolean) if both circles are of equal area; otherwise FALSE
> Binary > TRUE (Boolean) if the area of is larger than the area of ; otherwise FALSE
>= Binary >= TRUE (Boolean) if the area of is larger than or equal to the area of ; otherwise FALSE
< Binary < TRUE (Boolean) if the area of is smaller than the area of ; otherwise FALSE
<= Binary <= TRUE (Boolean) if the area of is smaller than or equal to the area of ; otherwise FALSE
++ Unary + +
+ + Increments of radius of by 1 unit. Should support both prefix and postfix version.

Rectangle: [6 Marks]
-Let, and be rectangles. Overload the following operators according to their definitions given:
Operator Type Expression Expression output
+ Binary + where is a 2D point. A new rectangle translated by point . This operation represents a translation of the rectangle with respect to the origin (0,0).
* Binary ∗
where is a real number A new rectangle whose points are scaled by the amount . This operation represents a scaling operation for the rectangle with respect to the origin (0,0).

Main: [6 Marks]
-Create suitable examples to demonstrate all functionalities as specified in the cpp file.
More practice: [For online]
-Extend your program to include facilities for other geometric objects such as square, triangle, ellipse, etc.
Homework prepared by Sukarna Barua, Asst. Professor, CSE, BUET