In computer graphics, lighting calculations often use the angle between vectors.

Question

In computer graphics, lighting calculations often use the angle between vectors.

Write a program that asks a user to input two 3-dimensional vectors and calculates and displays the angle

between them. Vectors are input using the following format (square brackets and commas required), e.g, :

[23.5, 22.1, 99.6]

The angle should be printed out in radians. It does not need to be formatted or rounded.

Your program must do the following:

1. Include a void function named inputVector that takes an empty array as its only argument and

returns a 3 dimensional vector entered from the console. The inputVector function must use

getline to read a string from the console that contains a vector in the format as described above.

You will need to parse the string to obtain the three values and store them in the array [Hint: convert

values to c-strings and use the atof function]. If the string is not entered correctly (wrong number of

values, missing brackets, etc.) provide an error message and exit the program using the exit(1)

function.

2. Include a second function named printVector that will take an array of double values representing

a 3-dimensional vector and display it in the following format (square brackets and commas required),

e.g.,:

[23.5, 22.1, 99.6]

3. Include a third function named dotProduct that will take two array arguments representing 3

dimensional vectors and return the scalar dot product.

4. Include a fourth function named magnitude that will take a single array representing a 3 dimensional

vector and return the scalar vector magnitude. The magnitude function should call dotProduct.

5. Include the following main function in your source code (exactly as it appears):

int main()

{ double vector1[3],vector2[3],theta;

cout << "Enter first vector: ";

inputVector(vector1);

cout << "Enter second vector: ";

inputVector(vector2);

printVector(vector1);

printVector(vector2);

theta = acos(dotProduct(vector1,vector2)/

(magnitude(vector1)*magnitude(vector2)));

cout << "The angle between the vectors is: " << theta << endl;

return 0;

}

Example:

Enter first vector: [0,0,4]

Enter second vector: [0,8,0]

[0,0,4]

[0,8,0]

The angle between the vectors is: 1.5708

Explanation / Answer

#include <iostream>

#include <cstdio>

#include <cstdlib>

#include <string>

#include <cmath>

using namespace std;

void inputVector(double* v){

string s;

cin>>s;

cout<<s<<endl;

unsigned pos = s.find(",");

v[0]=atof((s.substr(1,pos-1)).c_str());

unsigned pos2 = s.find(",",pos+1);

v[1]=atof((s.substr(pos+1,pos2-pos-1)).c_str());

unsigned pos3 = s.find("]");

v[2]=atof((s.substr(pos2+1,pos3-pos2-1)).c_str());

}

void printVector(double* v){

cout<<"["<<v[0]<<","<<v[1]<<","<<v[2]<<"]"<<endl;

}

double dotProduct(double* v1,double* v2){

return (v1[0]*v2[0])+(v1[1]*v2[1])+(v1[2]*v2[2]);

}

double magnitude(double* v1){

return sqrt((v1[0]*v1[0])+(v1[1]*v1[1])+(v1[2]*v1[2]));

}

int main()

{ double vector1[3],vector2[3],theta;

cout << "Enter first vector: ";

inputVector(vector1);

cout << "Enter second vector: ";

inputVector(vector2);

printVector(vector1);

printVector(vector2);

theta = acos(dotProduct(vector1,vector2)/(magnitude(vector1)*magnitude(vector2)));

cout << "The angle between the vectors is: " << theta << endl;

return 0;

}

Output:

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