How to find the intersection point of a vector and a radius?

[JohnnyBichevski]

Hello! I am trying to spawn an actor on a certain distance from a player, while determining the location by shooting a vector from a controller. How do I find the coordinates of an intersection point of the vector from controller and a radius around the player?

[ClockworkOcean]

You can get the angle between two vectors with

and if you know the distance of the controller from the player, then it’s Pythagoras ( if you mean in front of the player ).

[L1z4rD89]

Hey @JohnnyBichevski

you can use 2 methods to achieve this:

1. Use the law of sines and from here calculate all values for a triangle
   
   
   
   
   Triangle Calculator
   Start would be the triangle with g f h and then g f i

int main(){
    
    double xa,xb,xc,ya,yb,yc,za,zb,zc,r,dot,lenSq1,lenSq2,angle,intersect;
    r=6;

    cout << "Enter triangle coordinates\n";
    cout << "Point A: ";
    cin >> xa;
    cin >> ya;
    cin >> za;
    cout << "Enter triangle coordinates\n";
    cout << "Point B: ";
    cin >> xb;
    cin >> yb;
    cin >> zb;
    cout << "Enter triangle coordinates\n";
    cout << "Point C: ";
    cin >> xc;
    cin >> yc;
    cin >> zc;
    
    vector<double> v1 { xb-xa,yb-ya,zb-za};
    vector<double> v2 { xc-xa,yc-ya,zc-za};
    
    dot = v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2];
    lenSq1 = v1[0]*v1[0] + v1[1]*v1[1] + v1[2]*v1[2];
    lenSq2 = v2[0]*v2[0] + v2[1]*v2[1] + v2[2]*v2[2];
    angle = abs(acos(dot/sqrt(lenSq1 * lenSq2)));
    
    intersect = sin(3.14159265358979323846-angle-asin(sqrt(v2[0]*v2[0]+v2[1]*v2[1]+v2[2]*v2[2])*sin(angle)/r))*r/sin(angle);
    intersect  =  sqrt((intersect*intersect)/(v1[0]*v1[0]+v1[1]*v1[1]+v1[2]*v1[2]));
    cout << intersect;
}

2. Use the equations for the circle and the vector in paramteric form to create an quadratic equation and then solve this to get 0, 1 or 2 solutions / points / intersections.
   Get location of vector/circle intersection? - Mathematics Stack Exchange
   Quadratic equation - Wikipedia
   
   

int main() {
    double a,b,c,xa,xb,ya,yb,xc,yc,r,s,t,dx,dy;

    cout << "Enter triangle coordinates\n";
    cout << "Point A: ";
    cin >> xa;
    cin >> ya;
    cout << "Enter triangle coordinates\n";
    cout << "Point B: ";
    cin >> xb;
    cin >> yb;
    cout << "Enter triangle coordinates\n";
    cout << "Point C: ";
    cin >> xc;
    cin >> yc;
    
    r=6;
      
    
    a=pow((xb-xa),2)+pow((yb-ya),2);
    b=2*(xb-xa)*(xa-xc)+2*(yb-ya)*(ya-yc);
    c=pow((xa-xc),2)+pow((ya-yc),2)-pow(r,2);
    
    dx=xb-xa;
    dy=yb-ya;
    
    if(b*b-4*a*c==0){
        s=(b*(-1)+sqrt(b*b-4*a*c))/(2*a);
        cout << xa+s*dx << ", " << ya+s*dy;
    }
    else if(b*b-4*a*c>0){
        s=(b*(-1)+sqrt(b*b-4*a*c))/(2*a);
        t=(b*(-1)-sqrt(b*b-4*a*c))/(2*a);
        if(s>=0){
            cout << xa+s*dx << ", " << ya+s*dy << "\n";
            }
        if(t>=0){
            cout << xa+t*dx << ", " << ya+t*dy << "\n";
            }

        
    }
    else{
       cout << "No intersection";
    }
    
}

427Intersection.zip (188.2 KB)
503Intersection.zip (209.6 KB)
511Intersection.zip (215.8 KB)