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1 | 1 | /** |
2 | 2 | * @file |
3 | 3 | * |
4 | | - * @brief Calculates the [Cross Product](https://en.wikipedia.org/wiki/Cross_product) and the magnitude of two mathematical 3D vectors. |
| 4 | + * @brief Calculates the [Cross |
| 5 | + *Product](https://en.wikipedia.org/wiki/Cross_product) and the magnitude of two |
| 6 | + *mathematical 3D vectors. |
5 | 7 | * |
6 | 8 | * |
7 | 9 | * @details Cross Product of two vectors gives a vector. |
8 | | - * Direction Ratios of a vector are the numeric parts of the given vector. They are the tree parts of the |
9 | | - * vector which determine the magnitude (value) of the vector. |
10 | | - * The method of finding a cross product is the same as finding the determinant of an order 3 matrix consisting |
11 | | - * of the first row with unit vectors of magnitude 1, the second row with the direction ratios of the |
12 | | - * first vector and the third row with the direction ratios of the second vector. |
13 | | - * The magnitude of a vector is it's value expressed as a number. |
14 | | - * Let the direction ratios of the first vector, P be: a, b, c |
15 | | - * Let the direction ratios of the second vector, Q be: x, y, z |
16 | | - * Therefore the calculation for the cross product can be arranged as: |
| 10 | + * Direction Ratios of a vector are the numeric parts of the given vector. They |
| 11 | + *are the tree parts of the vector which determine the magnitude (value) of the |
| 12 | + *vector. The method of finding a cross product is the same as finding the |
| 13 | + *determinant of an order 3 matrix consisting of the first row with unit vectors |
| 14 | + *of magnitude 1, the second row with the direction ratios of the first vector |
| 15 | + *and the third row with the direction ratios of the second vector. The |
| 16 | + *magnitude of a vector is it's value expressed as a number. Let the direction |
| 17 | + *ratios of the first vector, P be: a, b, c Let the direction ratios of the |
| 18 | + *second vector, Q be: x, y, z Therefore the calculation for the cross product |
| 19 | + *can be arranged as: |
17 | 20 | * |
18 | 21 | * ``` |
19 | 22 | * P x Q: |
|
28 | 31 | * 3rd DR, N: (a * y) - (b * x) |
29 | 32 | * |
30 | 33 | * Therefore, the direction ratios of the cross product are: J, A, N |
31 | | - * The following C++ Program calculates the direction ratios of the cross products of two vector. |
32 | | - * The program uses a function, cross() for doing so. |
33 | | - * The direction ratios for the first and the second vector has to be passed one by one seperated by a space character. |
| 34 | + * The following C++ Program calculates the direction ratios of the cross |
| 35 | + *products of two vector. The program uses a function, cross() for doing so. The |
| 36 | + *direction ratios for the first and the second vector has to be passed one by |
| 37 | + *one seperated by a space character. |
34 | 38 | * |
35 | | - * Magnitude of a vector is the square root of the sum of the squares of the direction ratios. |
| 39 | + * Magnitude of a vector is the square root of the sum of the squares of the |
| 40 | + *direction ratios. |
36 | 41 | * |
37 | 42 | * ### Example: |
38 | 43 | * An example of a running instance of the executable program: |
|
45 | 50 | * @author [Shreyas Sable](https://github.com/Shreyas-OwO) |
46 | 51 | */ |
47 | 52 |
|
48 | | -#include <iostream> |
49 | 53 | #include <array> |
50 | | -#include <cmath> |
51 | 54 | #include <cassert> |
| 55 | +#include <cmath> |
52 | 56 |
|
53 | 57 | /** |
54 | 58 | * @namespace math |
55 | 59 | * @brief Math algorithms |
56 | 60 | */ |
57 | 61 | namespace math { |
58 | | - /** |
59 | | - * @namespace vector_cross |
60 | | - * @brief Functions for Vector Cross Product algorithms |
61 | | - */ |
62 | | - namespace vector_cross { |
63 | | - /** |
64 | | - * @brief Function to calculate the cross product of the passed arrays containing the direction ratios of the two mathematical vectors. |
65 | | - * @param A contains the direction ratios of the first mathematical vector. |
66 | | - * @param B contains the direction ration of the second mathematical vector. |
67 | | - * @returns the direction ratios of the cross product. |
68 | | - */ |
69 | | - std::array<double, 3> cross(const std::array<double, 3> &A, const std::array<double, 3> &B) { |
70 | | - std::array<double, 3> product; |
71 | | - /// Performs the cross product as shown in @algorithm. |
72 | | - product[0] = (A[1] * B[2]) - (A[2] * B[1]); |
73 | | - product[1] = -((A[0] * B[2]) - (A[2] * B[0])); |
74 | | - product[2] = (A[0] * B[1]) - (A[1] * B[0]); |
75 | | - return product; |
76 | | - } |
| 62 | +/** |
| 63 | + * @namespace vector_cross |
| 64 | + * @brief Functions for Vector Cross Product algorithms |
| 65 | + */ |
| 66 | +namespace vector_cross { |
| 67 | +/** |
| 68 | + * @brief Function to calculate the cross product of the passed arrays |
| 69 | + * containing the direction ratios of the two mathematical vectors. |
| 70 | + * @param A contains the direction ratios of the first mathematical vector. |
| 71 | + * @param B contains the direction ration of the second mathematical vector. |
| 72 | + * @returns the direction ratios of the cross product. |
| 73 | + */ |
| 74 | +std::array<double, 3> cross(const std::array<double, 3> &A, |
| 75 | + const std::array<double, 3> &B) { |
| 76 | + std::array<double, 3> product; |
| 77 | + /// Performs the cross product as shown in @algorithm. |
| 78 | + product[0] = (A[1] * B[2]) - (A[2] * B[1]); |
| 79 | + product[1] = -((A[0] * B[2]) - (A[2] * B[0])); |
| 80 | + product[2] = (A[0] * B[1]) - (A[1] * B[0]); |
| 81 | + return product; |
| 82 | +} |
77 | 83 |
|
78 | | - /** |
79 | | - * @brief Calculates the magnitude of the mathematical vector from it's direction ratios. |
80 | | - * @param vec an array containing the direction ratios of a mathematical vector. |
81 | | - * @returns type: double description: the magnitude of the mathematical vector from the given direction ratios. |
82 | | - */ |
83 | | - double mag(const std::array<double, 3> &vec) { |
84 | | - double magnitude = sqrt((vec[0] * vec[0]) + (vec[1] * vec[1]) + (vec[2] * vec[2])); |
85 | | - return magnitude; |
86 | | - } |
87 | | - } /// namespace vector_cross |
88 | | -} /// namespace math |
| 84 | +/** |
| 85 | + * @brief Calculates the magnitude of the mathematical vector from it's |
| 86 | + * direction ratios. |
| 87 | + * @param vec an array containing the direction ratios of a mathematical vector. |
| 88 | + * @returns type: double description: the magnitude of the mathematical vector |
| 89 | + * from the given direction ratios. |
| 90 | + */ |
| 91 | +double mag(const std::array<double, 3> &vec) { |
| 92 | + double magnitude = |
| 93 | + sqrt((vec[0] * vec[0]) + (vec[1] * vec[1]) + (vec[2] * vec[2])); |
| 94 | + return magnitude; |
| 95 | +} |
| 96 | +} // namespace vector_cross |
| 97 | +} // namespace math |
89 | 98 |
|
90 | 99 | /** |
91 | 100 | * @brief test function. |
92 | 101 | * @details test the cross() and the mag() functions. |
93 | 102 | */ |
94 | 103 | static void test() { |
95 | | - /// Tests the cross() function. |
96 | | - std::array<double, 3> t_vec = math::vector_cross::cross({1, 2, 3}, {4, 5, 6}); |
97 | | - assert(t_vec[0] == -3 && t_vec[1] == 6 && t_vec[2] == -3); |
| 104 | + /// Tests the cross() function. |
| 105 | + std::array<double, 3> t_vec = |
| 106 | + math::vector_cross::cross({1, 2, 3}, {4, 5, 6}); |
| 107 | + assert(t_vec[0] == -3 && t_vec[1] == 6 && t_vec[2] == -3); |
| 108 | + |
| 109 | + /// Tests the mag() function. |
| 110 | + double t_mag = math::vector_cross::mag({6, 8, 0}); |
| 111 | + assert(t_mag == 10); |
98 | 112 |
|
99 | | - /// Tests the mag() function. |
100 | | - double t_mag = math::vector_cross::mag({6, 8, 0}); |
101 | | - assert(t_mag == 10); |
| 113 | + /// Tests A ⨯ A = 0 |
| 114 | + std::array<double, 3> t_vec2 = |
| 115 | + math::vector_cross::cross({1, 2, 3}, {1, 2, 3}); |
| 116 | + assert(t_vec2[0] == 0 && t_vec2[1] == 0 && |
| 117 | + t_vec2[2] == 0); // checking each element |
| 118 | + assert(math::vector_cross::mag(t_vec2) == |
| 119 | + 0); // checking the magnitude is also zero |
102 | 120 | } |
103 | 121 |
|
104 | 122 | /** |
105 | 123 | * @brief Main Function |
106 | | - * @details Asks the user to enter the direction ratios for each of the two mathematical vectors using std::cin |
| 124 | + * @details Asks the user to enter the direction ratios for each of the two |
| 125 | + * mathematical vectors using std::cin |
107 | 126 | * @returns 0 on exit |
108 | 127 | */ |
109 | 128 | int main() { |
110 | | - |
111 | | - /// Tests the functions with sample input before asking for user input. |
112 | | - test(); |
113 | | - |
114 | | - std::array<double, 3> vec1; |
115 | | - std::array<double, 3> vec2; |
116 | | - |
117 | | - /// Gets the values for the first vector. |
118 | | - std::cout << "\nPass the first Vector: "; |
119 | | - std::cin >> vec1[0] >> vec1[1] >> vec1[2]; |
120 | | - |
121 | | - /// Gets the values for the second vector. |
122 | | - std::cout << "\nPass the second Vector: "; |
123 | | - std::cin >> vec2[0] >> vec2[1] >> vec2[2]; |
124 | | - |
125 | | - /// Displays the output out. |
126 | | - std::array<double, 3> product = math::vector_cross::cross(vec1, vec2); |
127 | | - std::cout << "\nThe cross product is: " << product[0] << " " << product[1] << " " << product[2] << std::endl; |
128 | | - |
129 | | - /// Displays the magnitude of the cross product. |
130 | | - std::cout << "Magnitude: " << math::vector_cross::mag(product) << "\n" << std::endl; |
131 | | - |
132 | | - return 0; |
| 129 | + /// Tests the functions with sample input before asking for user input. |
| 130 | + test(); |
| 131 | + return 0; |
133 | 132 | } |
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