CMPT 102: Assignment #3

Due October 30, 2006


NOTE1: YOU MUST USE THE VARIABLE NAMES SPECIFIED IN THE ASSIGNMENT, failure to do so will result in deduction of points.
NOTE2: If you were unable to get the program in assignment 2 working you may (with a small penalty) use the solution code in assignment 2's solution as a starting point. If you choose to use the solution code there will be a 4 point deduction from the 100 points available for assignment 3.

PART 1: Function for finding the intersection of two circles. (40 points)

Take your program for determining the intersection of two circles and convert the program into a function. The prototype for the function should be:

void CircIntersect(double XCentre1, double YCentre1, double Radius1, double XCentre2, double YCentre2, double Radius2, double *XIntersect1p, double *YIntersect1p, double *XIntersect2p, double *YIntersect2p, int *NumIntersectp);

In your function you will have five double variables, XIntersect1, YIntersect1, XIntersect2, YIntersect2, and NumIntersect. (XIntersect1, YIntersect1) is the (x,y) location of the first intersection point if there is one. (XIntersect2, YIntersect2) is the (x,y) location of the second intersection point if there is one. NumIntersect is the number of intersection points between the pair of circles. In your CircIntersect function, after determining the number and location of the intersections, instead of printing the messages indicating the number of intersections and the locations of the intersection points, add the following statements used to pass the values of your results back to main program.
In all cases add
*NumIntersectionp = NumIntersection;
If there are one or more points of intersecton also add
*XIntersect1p = XIntersect1;
*YIntersect1p = YIntersect1;
If there are two points of intersection also add
*XIntersect2p = XIntersect2;
*YIntersect2p = YIntersect2;

Write a main program to test your CircIntersect function. Remember that input and output should be done outside of your function. When you are sure your CircIntersect function is working you are ready to begin implementation of the detailed algorithm you have developed to solve the problem in PART 2. If your circle intersection program is not reliable you may use the program provided as a solution to problem 1. Using the solution rather than your own program will result is a penalty of 4 points.

PART 2: Finding the location of an Earthquake (60 points)

While developing your program follow the software development method, you will need to submit each of the following as part of your solution:

• A test plan for the problem.
• A refined algorithm (need not include what is inside the function CircIntersect)
• The C code, stored in a file called eq.c

How can we locate an Earthquake? A simple geometric method of locating an earthquake on the surface of the Earth can be outlined as follows:

• Assume that the earthquake is recorded at three seismic stations. We will specify the locations of each of each of these stations as a point in the (x,y) plane. For simplicity we will assume that all (x,y) coordinates of stations are positive numbers, that is, x>=0, y>=0.
• Plot the locations of the stations on the surface of the Flat Earth (plot each x,y) on the (x,y) plane)
• Draw a circle around each (x,y) location, the radius of the circle will represent the distance from the station to the earthquake. We can measure the time the wave takes to travel to the station then divide that time by the speed at which the wave travels to give the distance. We will assume the distance has already been determined and provided.
• Locate the point where the three circles intersect. (EqX, EqY). This point, (EqX,EqY), is the location of the earthquake.

Your problem is to translate this algorithm into a computer program. This inputs to this program will be the (x,y) locations of the three recording stations and the distances from each of the recording stations to the earthquake.
You will use your CircIntersect function in your earthquake location program. In the development of the earthquake location program, you may call this functions without providing the detailed algorithm or flowchart for what happens inside the functions.
A summary algorithm for approaching the translation of the algorithm above into a computer algorithm is given below:

• Consider the three circles two at a time.
• Find the intersection of two of the three circles.
• Find the intersection of the third circle with one of the other two circles
• Compare the two sets of intersection points, and choose the common intersection if there is one
• When determining if the three circles intersect at a common point remember that we are using experimental measurements to determine the answer. Consider that two solutions are the 'same' solution if the distance between the two intersection points (for example an intersection point of circle 1 and circle 2, and an intersection of circle 1 and circle 3) is less than 0.001 units.