how to write this program

Question

• In this specific case (2D space), all vectors exist on the same plane. Hence, a vector v is defined by its x- and y-coordinates and cross-product can mathematically computed as follows:

• v1 x v2 = v1.x * v2.y – v1.y * v2.x

Where V1.x represents the x coordinate of vector V1 and V1.y represents the y coordinate of vector V1.  Similar meaning for V2.x and V2.y.

• Vector multiplication is defined as follows:

• v1 * v2 = v1.x * v2.x + v1.y * v2.y

• The values of t and u in the parametric equations of the line segments can be computed as follows:

• t = q x s / r x s
• u = q x r / r x s

where the operator x indicates the cross-product operation as defined above. q, s, and r are auxiliary vectors whose x- and y-coordinates are computed as follows:

• r = (x2 – x1, y2 – y1)    represents the vector P1P2
• s = (x4 – x3, y4 – y3)    represents the vector P3P4
• q = (x3 – x1, y3 – y1)   represents the vector P3P1

Algorithm

• Read x1, y1, x2, y2
• Read x3, y3, x4, y4
• Compute vectors r, s, and q
• Compute cross-products qxs, qxr, and rxs
• Compute auxiliary values: q*r, r*r, q*s, and s*s
• If rxs is zero and qxr is zero, then
  • The two lines are collinear
    • If 0 <= q*r <= r*r or 0 <= q*s <= s*s
      • The two lines are overlapping
    • else
      • The two lines are disjoint
• If rxs is zero and qxr is not zero
  • The two lines are parallel and not intersecting
• If rxs is not zero , compute t and u
  • If   0 <= t <= 1 and 0 <= u <= 1
    • The two lines intersect at P1+t*r
  • else
    • The two line segments do not intersect

Answer 1

Pretty simple implementation, hope it helps!

#include <iostream>

using namespace std;

int crossProduct(int* v1, int* v2){
    int product = v1[1]*v2[2] - v1[2]*v2[1];
    return product;
}

int pointProduct(int* v1, int* v2){
    int product = v1[1]*v2[1] + v1[2]*v2[2];
    return product;
}

int main()
{
    //Variables inputs
    int x1,x2,x3,x4,y1,y2,y3,y4,t,u;
    cout << "Insert x1 ";
    cin >> x1;
    cout << "Insert y1 ";
    cin >> y1;
    cout << "Insert x2 ";
    cin >> x2;
    cout << "Insert y2 ";
    cin >> y2;
    
    cout << "Insert x3 ";
    cin >> x3;
    cout << "Insert y3 ";
    cin >> y3;
    cout << "Insert x4 ";
    cin >> x4;
    cout << "Insert y4 ";
    cin >> y4;
    
    
    //Array assignments
    int r[2],s[2],q[2];
    r[1] = x2 - x1;
    r[2] = y2 - y1;
    cout << "r: " << r[1] << ","<< r[2] << endl;
    s[1] = x4 - x3;
    s[2] = y4 - y3;
    cout << "s: " << s[1] << "," << s[2] << endl;
    q[1] = x3 - x1;
    q[2] = y3 - y1;
    cout << "q: " << q[1] << "," << q[2] << endl;
    cout << "Assignments done\n";
    
    //CrossProduct
    int qsProd = crossProduct(q,s);
    cout << "q x s: " << qsProd << endl;
    int qrProd = crossProduct(q,r);
    cout << "q x s " << qrProd << endl;
    int rsProd = crossProduct(r,s);
    cout << "r x s " << rsProd << endl;
    
    if(rsProd != 0){
        t = qsProd/rsProd;
        u = qrProd/rsProd;
    }
    else{
        cerr << "Cannot divide by zero!";
        exit(1);
    }
    
    //PointProduct
    int qrPoint = pointProduct(q,r);
    int rrPoint = pointProduct(r,r);
    int qsPoint = pointProduct(q,s);
    int ssPoint = pointProduct(s,s);
    
    //Conditions PrintOut
    if(rsProd == 0 && qrProd == 0)
        cout << "Lines are Collinear!\n";
    if((rrPoint >= qrPoint && qrPoint >= 0) || (ssPoint >= qsPoint >= 0))
        cout << "Lines are Overlapping!\n";
    else
        cout << "lines are Disjoint!\n";

    if(rsProd == 0 && qrProd != 0)
        cout << "The two lines are parallel and not intersecting\n";
    if(rsProd != 0){
        if((1 >= t && t >= 0) && (1 >= u && u >= 0))
            cout << "The two lines intersect at P1+t*r\n";
        else
            cout << "The two line segments do not intersect\n";
    }
        
}