Intersection of circle with line (fixed radius)

intersection_circle_line.c

#define RHO 400.0 // Circle radius

typedef struct point2df_struct {
    float x;
    float y;
} point_2Df;

typedef struct segment_struct {
    float x1;
    float y1;
    float x2;
    float y2;
} segment;

short get_line_circle_intersection(
                                  segment line, segment circle,
                                  point_2Df *firstIntersection, point_2Df *secondIntersection /* Cannot be NULL */) {
    
    float dx = line.x2-line.x1, dy = line.y2-line.y1;
    float l = sqrtf(dx*dx+dy*dy); // Length of line
    float dxl = dx/l, dyl = dy/l;
    float t = dxl*(circle.x1-line.x1) + dyl*(circle.y1-line.y1); // Projection of circle center on line
    
    float ex = t*dxl + line.x1, ey = t*dyl + line.y1; // Coordinates of e on line and closest to circle center
    float lec = sqrtf((ex-circle.x1)*(ex-circle.x1) + (ey-circle.y1)*(ey-circle.y1)); // Distance e to circle center
    
    if (lec < RHO) { // Intersection
        float dt = sqrtf(RHO*RHO - lec*lec); // Distance to to circle intersection point
        int nbi = 0;
        if (t-dt >=0 && t-dt <= l) {
            firstIntersection->x = (t-dt) * dxl + line.x1;
            firstIntersection->y = (t-dt) * dyl + line.y1;
            nbi = 1;
        }
        if (t+dt >=0 && t+dt <= l) {
            if (nbi == 0) {
                firstIntersection->x = (t+dt) * dxl + line.x1;
                firstIntersection->y = (t+dt) * dyl + line.y1;
                nbi = 1;
            }
            else {
                secondIntersection->x = (t+dt) * dxl + line.x1;
                secondIntersection->y = (t+dt) * dyl + line.y1;
                nbi = 2;
            }
        }
        return nbi;
    }
    else if (lec == RHO && t >=0 && t <= l) { // Tangent
        firstIntersection->x = ex;
        firstIntersection->y = ex;
        return 1;
    }
    
    return 0;
    
}