A point mass consists of a 3-D location and an associated mass, such as Location

Question

A point mass consists of a 3-D location and an associated mass, such as

Location: (6, 0, 2) Mass: 3g

In a system of point masses, let p 1 , p 2 .......p n be the n 3-D points and m 1 , m 2 ....... m n be their associated masses. If m is the sum of the masses, the center of gravity C is calculated as

C=1/m(m1p1+m2p2+......+mnpn)

Write a program that repeatedly inputs point-mass system data sets from an input file until an input operation fails. For each data set, display the location matrix, the mass vector, n , and the center of gravity. Each data set includes a location matrix (a matrix in which each row is a point), a one-dimensional array of masses, and the number of point masses, n . Allow n to vary from 3 to 10.

Sample Data File

4

5 -4 3 2

4 3 -2 5

-4 -3 -1 2

-9 8 6 1

This sample should be stored as:

location 5 -4 3

4 3 -2

-4 -3 -1

-9 8 6

mass 2

5

2

1

n 4

Your main function should repeatedly input and process data sets from an input file until end of file is encountered. For each point-mass system data set, display the location matrix, the mass vector, n , and the center of gravity. Implement at least the following functions:

fget_point_mass : Takes an open input file and a maximum value for n as parameters and fills a two-dimensional array output parameter with a location matrix and a one-dimensional array output parameter with a mass vector from the data file. Returns as function value the actual value of n . center_grav : Takes a location matrix, mass vector, and n value as param- eters, and calculates and returns as the function value the center of gravity of the system. fwrite_point_mass : Takes an open output file and the location matrix, mass vector, and n value of a point-mass system as parameters and writes the system to the file with meaningful labels.

a). Name the input file lab12p1.in and the output file lab12p1.out. Open the input file inside the function fget_point_mass() and the output file inside the function fwrite_point_mass().

b). Using the sample data file (from the book), lab12p1.in should contain:

4     4 is the number of points in this data set. The maximum is 10.

5.0 -4.0 3.0 2.0

4.0 3.0 -2.0 5.0

-4.0 -3.0 -1.0 2.0

-9.0 8.0 6.0 1.0

c) For the above sample, the output file lab12p1.out should contain:

x                    y              z                 m

5.000          - 4.000     3.000      2.000

4.000          3.000      -2.000      5.000

-4.000        -3.000     -1.000      2.000

-9.000          8.000      6.000       1.000

Total mass: 10.000

Center of Gravity:     Cx            Cy         Cz

                                    1.300   0.900     z.zzz

d). For the function center_grav(), the center of gravity has three values. Thus, make the center of gravity a one-dimensional array of length 3. Do not include a return statement inside this function.

e). For the function fwrite_point_mass() pass the center of gravity (a one- dimensional array of length 3) as an input parame parameter

Explanation / Answer

#include<stdio.h>
// DECLARE MAX SIZE as 10.
const int max_size = 10;
// function to get location matrix and mass vector.
int fget_point_mass(FILE *fp,float location_matrix[max_size][max_size],float mass_vector[max_size])
{
// OPEN FILE lab12p1.in in read mode.
fp = fopen("lab12p1.in", "r");
// declare variable n to hold number of n point masses.
int n;
// declare row_index and column index to access location matrix.
int row_index,column_index;
if( fp != NULL ) // MAKING SURE THAT FILE IS available for READING.
{
// first row contain no of records. read that n.
fscanf(fp,"%d",&n);
// till end of file is reached.
while(!feof(fp ))
{
// start scanning row_index...
for(row_index=0; row_index<n; row_index++)
{
// // start scanning column_index...
for(column_index=0; column_index<n; column_index++)
{
// since last column contain mass once column index reaches n-1
// save that in mass vector
if(column_index==n-1)
fscanf(fp,"%f",&mass_vector[row_index]);
else
// else save it in location matrix.
fscanf(fp,"%f",&location_matrix[row_index][column_index]);
} // end local for
} // end outer for
} // end while.
// close file pointer.
fclose(fp);
} // end if.
return n; //return number of records i.e n.
}
// function to calculate center of gravity.
void center_grav(float location_matrix[max_size][max_size],float mass_vector[max_size],int n,float center_of_gravity[3])
{
// declare varible total_mass to hold total MASS.
float total_mass=0.0;
// declare i and j to access location matrix.
int i,j;
// first accesss mass vector and find total mass.
for(i=0; i<n; i++)
total_mass = total_mass + mass_vector[i];
// now start calculating centre of gravity in each direction i.e x,y,z...
for(i=0; i<3; i++)
{
// declare variable point_sum to hold point sum.
float point_sum = 0.0;
// now start scanning towards each column.
for(j=0; j<n; j++)
{
// point sum hold point sum = m1 p1 + m2 p2 +...........mn pn.
point_sum = point_sum + location_matrix[j][i]*mass_vector[j];
}
// now center of gravity is point_sum/total_mass;
// i.e   (m1 p1 + m2 p2 +...........mn pn)/m;
center_of_gravity[i] = point_sum/total_mass;
}
}
// function to write results to file.
void fwrite_point_mass(FILE* fp,float location_matrix[max_size][max_size],float mass_vector[max_size],int n,float center_of_gravity[3])
{
// open file lab12p1.out in write mode.
fp = fopen("lab12p1.out", "w");
// declare varible total_mass to hold total MASS.
float total_mass=0.0;
int i;
for(i=0; i<n; i++)
total_mass = total_mass + mass_vector[i];
// first write x y z m to output file.
fprintf(fp,"x y z m");
// declare row_index and column index to access location matrix.
int row_index,column_index;
// start scanning across row_index.
for(row_index=0; row_index<n; row_index++)
{
// for each row print a new line.
fprintf(fp," ");
// start scanning across column_index.
for(column_index=0; column_index<n; column_index++)
{
// if it is last column access mass_vector.
if(column_index==n-1)
{
fprintf(fp,"%f",mass_vector[row_index]);
}
//otherwise access location matrix.
else
{
fprintf(fp,"%.3f ",location_matrix[row_index][column_index]);
}
}
}
// write Total mass to file.
fprintf(fp," Total mass: %.3f,",total_mass);
// write Center of Gravity to file.
fprintf(fp," Center of Gravity: Cx Cy Cz");
// write Center of Gravity to file.
fprintf(fp," %.3f %.3f %.3f",center_of_gravity[0],center_of_gravity[1],center_of_gravity[2]);
// close file pointer.
fclose(fp);
}

int main()
{
//declare location matrix and matrix vector
float location_matrix[max_size][max_size];
float mass_vector[max_size];
// n to hold number of records.
int n;
// declare ceter of gravity.
float center_of_gravity[3];
// file pointer to hold input and output file.
FILE *fp;
// call fget_point_mass to fill location_matrix and to mass vector
n = fget_point_mass(fp,location_matrix,mass_vector);
// call center_grav to fill center of gravity vector.
center_grav(location_matrix,mass_vector,n,center_of_gravity);
// call fwrite_point_mass to write to file.
fwrite_point_mass(fp,location_matrix,mass_vector,n,center_of_gravity);
return 0;
}

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