Introduction

The aim of this assignment is to develop a set of mathematical calculation in term of matrix transformation. All of the
transformation are in 2D included translate, scale, rotate and shear. Other than that student also need to develop a set of class vector. All of the programming code need to be write by using C++ programming.

Objective

- to refresh back how to do C++ programming.
- to solve the mathematical calculation (matrix) using programming.
- to develop a set of class vector.

The Problem

This assignment are divided into two parts.

        Part 1

        Solve all of these problem using C++ programming :-

        1. To translate a point 2D coordinate (30,30) to a new point (?,?). Translation in x-direction = -18
            and translation in y-direction  = -15.

        2. To scale a point from 2D coordinate (30,30) by 7 in the x-direction and 8 in y-direction

        3. To rotate a point from 2D coordinate (30,30) by 35 degrees

        4. To shear a point from 2D coordinate (35,35) by 10.5 in the x-direction and 20.5 in the y-direction
            (a = 10.5, b = 20.5)

        Part 2

        Develop a class vector that encapsulate the behaviour of a 3D vector i.e (3,4,5). The vector should contain at
        least the following functionality:-

            - Vector Addition

                            V₁ + V₂ = (V_1x + V_2x, V_1y + V_2y, V_1z + V_2z)

            - Vector Subtraction

                    V₁ - V₂ = (V_1x - V_2x, V_1y - V_2y, V_1z - V_2z)

            - Cross product

                            V₁ . V₂ = (V_1x V_2x + V_1yV_2y + V_1zV_2z)

            - Dot Product

                    V₁ x V₂ = (V_1yV_2z - V_1zV_2y ,V_1zV_2x - V_1xV_2z , V_1xV_2y - V_1yV_2x)

            - Scalar Multiplication

                            a (V₁ ) = ( aV_1x , aV_2y , aV_1z )

            - Length of Vector

                            | V | =  sqrt (V_x² + V_y² + V_z² )

        Test all of these functionality using a vector.
 

Report

An overall project report is required. This should include:
    - A statement of problem AND
    - what has been accomplished
    - Conclusions, problems, etc.
    - Code Listing
 

Deadline

Work must be submitted to me or En. Zaimufarruddin by: Saturday 12 July 2003