125 lines
3.8 KiB
Java
125 lines
3.8 KiB
Java
package Maths;
|
|
|
|
/**
|
|
* @file
|
|
*
|
|
* @brief Calculates the [Cross Product](https://en.wikipedia.org/wiki/Cross_product) and the magnitude of two mathematical 3D vectors.
|
|
*
|
|
*
|
|
* @details Cross Product of two vectors gives a vector.
|
|
* Direction Ratios of a vector are the numeric parts of the given vector. They are the tree parts of the
|
|
* vector which determine the magnitude (value) of the vector.
|
|
* The method of finding a cross product is the same as finding the determinant of an order 3 matrix consisting
|
|
* of the first row with unit vectors of magnitude 1, the second row with the direction ratios of the
|
|
* first vector and the third row with the direction ratios of the second vector.
|
|
* The magnitude of a vector is it's value expressed as a number.
|
|
* Let the direction ratios of the first vector, P be: a, b, c
|
|
* Let the direction ratios of the second vector, Q be: x, y, z
|
|
* Therefore the calculation for the cross product can be arranged as:
|
|
*
|
|
* ```
|
|
* P x Q:
|
|
* 1 1 1
|
|
* a b c
|
|
* x y z
|
|
* ```
|
|
*
|
|
* The direction ratios (DR) are calculated as follows:
|
|
* 1st DR, J: (b * z) - (c * y)
|
|
* 2nd DR, A: -((a * z) - (c * x))
|
|
* 3rd DR, N: (a * y) - (b * x)
|
|
*
|
|
* Therefore, the direction ratios of the cross product are: J, A, N
|
|
* The following Java Program calculates the direction ratios of the cross products of two vector.
|
|
* The program uses a function, cross() for doing so.
|
|
* The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
|
|
*
|
|
* Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
|
|
*
|
|
*
|
|
* For maintaining filename consistency, Vector class has been termed as VectorCrossProduct
|
|
*
|
|
* @author [Syed](https://github.com/roeticvampire)
|
|
*/
|
|
|
|
|
|
public class VectorCrossProduct {
|
|
int x;
|
|
int y;
|
|
int z;
|
|
//Default constructor, initialises all three Direction Ratios to 0
|
|
VectorCrossProduct(){
|
|
x=0;
|
|
y=0;
|
|
z=0;
|
|
}
|
|
|
|
/**
|
|
* constructor, initialises Vector with given Direction Ratios
|
|
* @param _x set to x
|
|
* @param _y set to y
|
|
* @param _z set to z
|
|
*/
|
|
VectorCrossProduct(int _x,int _y, int _z){
|
|
x=_x;
|
|
y=_y;
|
|
z=_z;
|
|
}
|
|
|
|
/**
|
|
* Returns the magnitude of the vector
|
|
* @return double
|
|
*/
|
|
double magnitude(){
|
|
return Math.sqrt(x*x +y*y +z*z);
|
|
}
|
|
|
|
/**
|
|
* Returns the dot product of the current vector with a given vector
|
|
* @param b: the second vector
|
|
* @return int: the dot product
|
|
*/
|
|
int dotProduct(VectorCrossProduct b){
|
|
return x*b.x + y*b.y +z*b.z;
|
|
}
|
|
|
|
/**
|
|
* Returns the cross product of the current vector with a given vector
|
|
* @param b: the second vector
|
|
* @return vectorCrossProduct: the cross product
|
|
*/
|
|
VectorCrossProduct crossProduct(VectorCrossProduct b){
|
|
VectorCrossProduct product=new VectorCrossProduct();
|
|
product.x = (y * b.z) - (z * b.y);
|
|
product.y = -((x * b.z) - (z * b.x));
|
|
product.z = (x * b.y) - (y * b.x);
|
|
return product;
|
|
}
|
|
|
|
/**
|
|
* Display the Vector
|
|
*/
|
|
void displayVector(){
|
|
System.out.println("x : "+x+"\ty : "+y+"\tz : "+z);
|
|
}
|
|
|
|
public static void main(String[] args) {
|
|
test();
|
|
}
|
|
static void test(){
|
|
//Create two vectors
|
|
VectorCrossProduct A=new VectorCrossProduct(1,-2,3);
|
|
VectorCrossProduct B=new VectorCrossProduct(2,0,3);
|
|
|
|
//Determine cross product
|
|
VectorCrossProduct crossProd=A.crossProduct(B);
|
|
crossProd.displayVector();
|
|
|
|
//Determine dot product
|
|
int dotProd=A.dotProduct(B);
|
|
System.out.println("Dot Product of A and B: "+dotProd);
|
|
|
|
}
|
|
|
|
}
|