столкновение окружностей

#include <iostream>
#include <list>
#include <cmath>
#include <algorithm>
#include <vector>

#include <GL/glut.h>
#include <GL/gl.h>
#include <GL/glu.h>

using namespace std;
int msec = 10;
double scale = 1.0;
double vx=0,vy=0;
double p=3.14,r_1=0;
double kx=5,ky=5;
double angle_step = p/30/100.0 * msec;
double k_;
double k_1;

void render_square(double x, double y) {
    glPushMatrix();

    double dx = 0.5;
    double dy = 0.5;
    glBegin(GL_POLYGON);
    glVertex2f(x, y);
    glVertex2f(x + dx, y);
    glVertex2f(x + dx, y - dy);
    glVertex2f(x, y - dy);
    glEnd();
    glPopMatrix();
}

void draw_line(double x, double y, double x1, double y1) {
    glBegin(GL_LINES);
    glVertex2d(x, y);
    glVertex2d(x1, y1);
    glEnd();
}
class circle{
public:
    double x,y,r,vx,vy;
    circle(double x_, double y_, double r_, double vx_, double vy_):r(r_), x(x_), y(y_){
        vx = vx_ / 1000.0 * msec;
        vy = vy_ / 1000.0 * msec;
    }
    void print_circle(){
        int n=40;
        double cx=x + r;
        double cy=y;
        double step = p/n;
        for (float f=step; f<=p*2;f+=step){
            draw_line(cx, cy ,cos(f)*r+x ,sin(f)*r+y);
             cx=x + cos(f)*r;
             cy=y + sin(f)*r;
        }
    }

    void update(){
        if(x+r>kx || x-r<-kx){
            vx*=-1;
        }
        if(y+r>ky || y-r<-ky){
            vy*=-1;
        }
        x+=vx;
        y+=vy;
    }
};
class Vector{
public:
    double x,y;
    Vector(float a,float b):x(a),y(b){
    }
    Vector operator +(Vector other){
        return Vector(x+other.x, y+other.y);
    }
    Vector operator -(Vector other){
        return Vector(x-other.x, y-other.y);
    }
    Vector operator *(float a){
        return Vector(x*a,y*a);
    }
    Vector operator /(float a){
        return Vector(x/a,y/a);
    }
    float dot (Vector other){
        return x*other.x+y*other.y;
    }
    void print(){
        cout<<'('<<x<<','<<y<<')'<<endl;
    }
    void draw(){
        static double d = 6.0;
        Vector n1(-y, x);
        Vector n2(y, -x);
        Vector a(x,y);
        Vector ar_1 = (n1 - a*2)/d;
        Vector ar_2 = (n2 - a*2)/d;
        draw_line(0,0,x,y);
        draw_line(x, y, ar_1.x + x, ar_1.y + y);
        draw_line(x, y, ar_2.x + x, ar_2.y + y);
    }
};
/*class Liniya{
public:
    double x,y;
    Liniya(float a,float b):x(a),y(b){
    }
    Liniya operator +(Liniya other){
        return Liniya(x+other.x, y+other.y);
    }
    Liniya operator -(Liniya other){
        return Liniya(x-other.x, y-other.y);
    }
    Liniya operator *(float a){
        return Liniya (x*a,y*a);
    }
    Liniya operator /(float a){
        return Liniya (x/a,y/a);
    }
    float dot (Liniya  other){
        return x*other.x+y*other.y;
    }
    void print(){
        cout<<'('<<x<<','<<y<<')'<<endl;
    }
    void draw(){
        static double d = 6.0;
        Liniya  n1(-y, x);
        Liniya  n2(y, -x);
        Liniya  a(x,y);
        //Liniya  ar_1 = (n1 - a*2)/d;
        //Liniya  ar_2 = (n2 - a*2)/d;
        draw_line(0,0,x,y);
        //draw_line(x, y, ar_1.x + x, ar_1.y + y);
        //draw_line(x, y, ar_2.x + x, ar_2.y + y);
    }
};*/
//Liniya c(2,2);
Vector b(2,2);
vector<circle> particles;
circle a(-4, 0, 0.4, 1, 0);
circle n(4, 0, 0.4, -1, 0);



/*void draw_clocks(float stop_angle){
    int j = 0;
    float coef = 0.8;
    for(float  angle = 0; angle <  2 * p; angle += p/30.0, j++){
        float x = cos(angle);
        float y = sin(angle);
        if(j % 5 == 0) coef = 0.6;
        else coef = 0.8;
        draw_line(x, y, x * coef, y * coef);
    }
}*/
void modul(float a){
    if(a < 0)
        a = -a;
}
void colide(vector <circle> & part){
    for(int i = 0; i < part.size(); i++){
        for(int j = i + 1; j < part.size(); j++){
            float l = (part[i].x - part[j].x) * (part[i].x - part[j].x) + (part[i].y - part[j].y) * (part[i].y - part[j].y);
            float r = (part[i].r + part[j].r) * (part[i].r + part[j].r);

            if(l <= r){
                //cout << i << " - " << j << endl;
                double k= r-l;
                k_=sqrt(k)/2;
            }
        }
    }
}
void Render() {
        static double cur_angle = 1.5*p;
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
        glLoadIdentity();
        glTranslatef(0, 0, -10);
        glColor3d(1, 1, 1);
        glScalef(scale, scale, scale);
        for(int i = 0; i < particles.size(); i++){
            particles[i].print_circle();
            particles[i].update();
        }
        colide(particles);
        //draw_clocks(cur_angle);
        //Vector b(cos(-cur_angle),sin(-cur_angle));
       // Liniya c()
        //cur_angle += angle_step;
        //if (cur_angle - 1.5 * p > 2 * p) cur_angle -= 2*p;
        draw_line(-kx,-ky,kx,-ky);
        draw_line(kx,-ky,kx,ky);
        draw_line(kx,ky,-kx,ky);
        draw_line(-kx,ky,-kx,-ky);

        //b.draw();
        //n.print_circle();


        glFlush();
}

void update(int t) {
    Render();
    glutTimerFunc(msec, update, 0);
}

void keyb(unsigned char key, int x, int y) {
    if(key == '+') {
        scale *= 1.1;
    }
    if(key == '-') {
        scale *= 0.9;
    }
    if(key == 'w') {
        kx *= 1.1;
    }
    if(key == 's') {
        kx *= 0.9;
    }
    if(key == 'd') {
        ky *= 1.1;
    }
    if(key == 'a') {
        ky *= 0.9;
    }
    Render();
}

void reshape(int w, int h) {

    // предупредим деление на ноль
    // если окно сильно перетянуто будет
    if(h == 0)
        h = 1;
    float ratio = 1.0* w / h;

    // используем матрицу проекции
    glMatrixMode(GL_PROJECTION);

        // Reset матрицы
    glLoadIdentity();

    // определяем окно просмотра
    glViewport(0, 0, w, h);

    // установить корректную перспективу.
    gluPerspective(45,ratio,1,1000);

    // вернуться к модели
    glMatrixMode(GL_MODELVIEW);
}

int main(int argc, char **argv)
{
    particles.push_back(a);
    particles.push_back(n);

    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(800, 600);
    glutCreateWindow("Physics Engine");
    glEnable(GL_DEPTH_TEST);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    glClearColor(0, 0, 0.0, 0.0);

    glutTimerFunc(50, update, 0);
    glutReshapeFunc(reshape);
    glutDisplayFunc(Render);
    glutKeyboardFunc(keyb);
    glutMainLoop();
}