CSCI 261 - Programming Concepts (C++)

This lab is due by October 05, 2016 08:00am.

For this lab we will get a very basic introduction to linear algebra in order to do some simple vector math. In linear algebra, we have a Point to represent a location in space and a Vector to represent a direction and distance. Linear algebra allows us to add a Vector to a Point to move that Point through space.

For instance, if we had a Point p at location (2, 3) and a Vector v with orientation <5, 1> we can add v to p to get a new Point located at (7, 4). We are going to create structs to define a container to store the information for a Point and a Vector. Then we will write a few functions to implement our basic vector math.

We are going to be using these structs and functions in Lab 06B and a future lab in a few weeks so you may want to consider defining these in a separate file. It is not necessary, but may save you some copy and paste later on.

First create a struct named Point that contains two doubles corresponding to the x and y location in cartesian space. In your main() function, create a Point variable and ask the user to enter the x and y coordinate of our point. You should be entering storing the user's response directly into the Point variable's data members. Print out the variable's data members to verify the values were stored correctly. Your program should look as follows at this point:

Enter the Point's x-coordinate: 2
Enter the Point's y-coordinate: 3
The point is (2, 3)

Printing a Point's value is an action we will wanting to be doing very often, so it makes sense to move that into a function (remember the DRY principle?). Create a function called PrintPoint that accepts a Point parameter passed by value and has no output. This function should now do the print the Point's location in a pretty manner.

Let's go ahead and repeat the above steps for our second struct, this time called Vector. The Vector struct should again have two double data members corresponding to the x and y directions in cartesian space. (Yes, the Vector struct will look very similar to the Point struct). Create a function called PrintVector accepts a Vector parameter passed by value and has no output. This function should prettily print the Vector direction. Ask the user to enter the Vector's direction and print out the values to verify. Your program should look as follows at this point:

Enter the Point's x-coordinate: 2
Enter the Point's y-coordinate: 3
The point is (2, 3)
Enter the Vector's x-direction: 5
Enter the Vector's y-direction: 1
The vector is <5, 1>

If the Point and Vector are so similar, then why do we want both? We need both so we can properly implement our vector math. In vector math, you can add (1) two vectors together or (2) a vector and a point, but you cannot add two points together. Creating these two new data types will help us enforce these rules. So let's do a little basic vector math.

The first vector math operation we want to support is adding a Vector to a Point. Create a function named MovePoint that takes a Point passed by value and a Vector passed by value as input. This function should return a Point as output. Inside the function, it should create a new Point and set its x component equal to the sum of the Point x-coordinate and the Vector x-direction. Do the same thing for y. Then return this new Point. In your main(), call this function with the values the user entered. Print out the resultant Point. Your program should look as follows at this point:

Enter the Point's x-coordinate: 2
Enter the Point's y-coordinate: 3
The point is (2, 3)
Enter the Vector's x-direction: 5
Enter the Vector's y-direction: 1
The vector is <5, 1>
After adding the vector to the point
The point is (7, 4)

Our last vector math operation will allow us to rotate a Vector by some angle. Create a function called RotateVector that takes a Vector passed by value and a double variable (representing the angle) passed by value. This function should return a Vector as output. Inside the function, it should create a new Vector and have it's x and y components set according to the following equations:

Then return this new Vector. In your main(), ask the user to enter an angle and then call this function with the values the user entered. Print out the resultant Vector. Your program should look as follows at this point:

Enter the Point's x-coordinate: 2
Enter the Point's y-coordinate: 3
The point is (2, 3)
Enter the Vector's x-direction: 5
Enter the Vector's y-direction: 1
The vector is <5, 1>
After adding the vector to the point
The point is (7, 4)
Enter an angle of rotation: 1.57
The vector is <-0.996, 5.001>

And you're done!

Here are some known input/output values that you can test against. Be sure to try your own to verify the code works! After our discussion following the coding quiz, think about the boundary conditions and edge cases that may arise.

You will submit your solution to this lab with the rest of Week06. Detailed instructions for doing this are posted in Assignment 06.

This lab is due by October 05, 2016 08:00am.