Programming and Graphics

150 Introduction to C++ Programming and Graphics

Generic: Group Member Action

Maths: Space Element Operation

OOP: Class Object Member function

Science: Discipline Phenomenon Dynamics

Table 6.1 Equivalence of groups, spaces, and objects and their relation in object
oriented programming (OOP).

The set of real numbers registered as floating-point numbers in computer science:

The member function “multiplication by zero” operating on a member

produces the null member “0”.

Vector spaces in mathematics:

The member function “inner product” operating on a pair of members

produces a number that is a measure of the angle subtended between the

two vectors. If the inner product is zero, the two vectors are orthogonal.

The set of all two-index matricesaij:

Each member is identified by the pair of integersiandj.

In calculus, a “member function” defined on the set of real numbers is a
device that receives real numbers (input) and produces new numbers (output).
Stated differently, a function maps the input to the output. When the output
is the null point “0”, the input has been annihilated.

In object oriented programming (OOP), a group is a “class,” a member is
an “object,” and a “member function” implements an operation. By operating
on an object with a “function,” we can read, record, and change some or all
of its attributes. As an example, consider the class of all polygons. A member
function can be defined that transforms a rectangle into a triangle in some
sensible fashion.

Classes in object oriented programming can be as simple as the set of
integers (int) or the set of floating point numbers stored in double precision
(double), and as complex as a database whose members (entries) are described
by names, numbers, and other fields.

Table 6.1 displays the equivalence of groups, spaces, and objects and their
relation in object oriented programming (OOP).