Question

The world of shapes is much richer than the shapes included in the inheritance hierarchy of Fig, \(12.3 .\) Write down all the shapes you can think ofboth two- dimensional and three-dimensionaland form them into a more complete Shape hierarchy with as many levels as possible. Your hierarchy should have base class shape from which class Two imensionalshape and class ThreeDimensionalshape are derived. [Note: You do not need to write any code for this exercise.] We will use this hierarchy in the exercises of Chapter 13 to process a set of distinct shapes as objects of base-class shape. (This technique, called polymorphism, is the subject of Chapter \(13 .\).

Short answer

The hierarchy starts with `Shape`, with two subclasses: `TwoDimensionalShape` and `ThreeDimensionalShape`, each with specific shape subclasses.

Step-by-step solution

Identify Two-Dimensional Shapes

Two-dimensional shapes have width and height but no depth. Common examples include: - Circle - Square - Rectangle - Triangle - Pentagon - Hexagon - Octagon - Trapezoid - Parallelogram - Ellipse These can be part of the `TwoDimensionalShape` subclass.

Identify Three-Dimensional Shapes

Three-dimensional shapes have width, height, and depth. Common examples include: - Sphere - Cube - Cuboid (Rectangular prism) - Pyramid - Cone - Cylinder - Tetrahedron - Octahedron These can be part of the `ThreeDimensionalShape` subclass.

Overall Shape Hierarchy Structure

The base class will be `Shape`. From `Shape`, there will be two derived classes: `TwoDimensionalShape` and `ThreeDimensionalShape`. Subclasses derived from `TwoDimensionalShape` include `Circle`, `Square`, `Rectangle`, `Triangle`, `Pentagon`, `Hexagon`, `Octagon`, `Trapezoid`, `Parallelogram`, and `Ellipse`. Subclasses derived from `ThreeDimensionalShape` include `Sphere`, `Cube`, `Cuboid`, `Pyramid`, `Cone`, `Cylinder`, `Tetrahedron`, and `Octahedron`.

Key concepts

Polymorphism

Polymorphism is a powerful concept in object-oriented programming that allows objects to be treated as instances of their parent class. This feature is particularly useful when dealing with shapes because it lets us define a single interface, like `Shape`, and use it to manage diverse behaviors in different shapes.
For instance, you could create a function that calculates the area of a shape, and use the same function to handle circles, squares, and triangles, as they all derive from the base class `Shape`. Polymorphism simplifies code management:

• Promotes code reusability by allowing a general class to handle various cases.
• Makes it easier to add new shape types without altering existing code.
• Facilitates the management of groups of objects through a common interface.

Whenever you call a method on a `Shape` object, the correct version of the method is executed depending on the shape's actual class, making your programs versatile and easily extensible.

Shapes Hierarchy

In programming, establishing a hierarchy is crucial for organizing data. When dealing with shapes, creating a shapes hierarchy helps to categorize and structure different kinds of shapes logically. At the top of this hierarchy, we have the base class `Shape`, which represents the most generalized concept.
Underneath this, shapes can be divided into two major subclasses: `TwoDimensionalShape` and `ThreeDimensionalShape`. These subclasses branch out into more specific shapes, each with its own properties and methods:

• `TwoDimensionalShape` includes classic shapes like circles, squares, and triangles.
• `ThreeDimensionalShape` covers shapes like spheres, cubes, and pyramids.

A well-constructed hierarchy makes your program more organized and easier to navigate. It also ensures a clear path for inheritance and polymorphism, where specialized behaviors of shapes can be implemented at different levels of the hierarchy.

Inheritance

Inheritance is a core principle of object-oriented programming, allowing new classes to adopt the properties and methods of existing classes. This is particularly useful in shaping hierarchies where general attributes and behaviors can be defined in a base class like `Shape` and then be automatically available to derived classes such as `TwoDimensionalShape` and `ThreeDimensionalShape`.
The advantages of using inheritance in shape hierarchies include:

• Code reuse, as common features and properties need to be written only once.
• Clear understanding of relationships between different classes based on a hierarchy.
• Simplification of code modifications and maintenance, as changes to a base class can propagate to derived classes.

With inheritance, you can create more complex and nuanced classes based on simpler ones, enriching the functionality of the shapes within your program while keeping the code clean and efficient.

2D Shapes

Two-dimensional shapes, or 2D shapes, have width and height but lack depth. These shapes are flat and exist in the plane, making them simpler to analyze geometrically compared to their 3D counterparts. Common examples are:

• Circle - Defined by its radius; every point is equidistant from a center.
• Square - A polygon with four equal sides and right angles.
• Triangle - Defined by three sides and three vertices.
• Rectangle - Similar to a square but with opposite sides equal and right angles.
• Ellipse - An oval shape determined by its major and minor axes.

Each of these shapes can have unique properties and formulas, such as area or perimeter calculations, making them important for many practical applications like graphic design, architecture, and more.

3D Shapes

Three-dimensional shapes, or 3D shapes, have width, height, and depth, making them more complex as they occupy space. They are not flat like 2D shapes and are used extensively in modeling and simulations. Some common 3D shapes are:

• Sphere - All points are equidistant from its center, like a ball.
• Cube - All sides are equal squares, forming a regular polyhedron.
• Cylinder - Composed of two parallel circular bases connected by a curved surface.
• Cone - Has a circular base and a point called the apex; tapering smoothly from base to apex.
• Pyramid - A polygonal base and triangular faces converging at a point.

Each 3D shape has properties that can be leveraged in volume and surface area calculations, making them critical in fields such as construction, 3D modeling, and virtual reality.