void DisplayMelc() {
    double pi = 4 * atan(1.0);
    double a = 0.3;
    double b = 0.2;
    double tmin = -1 * pi,tmax=pi;
    double ratia = 0.005;
    double proportia = 0.80;
    double x, y;

    glColor3f(1, 0.1, 0.1); // rosu
    glBegin(GL_LINE_STRIP);
    for (double t = tmin + ratia; t < tmax; t+= ratia) {
        x = 2.0 * (a * cos(t) + b)*cos(t);
        y = 2.0 * (a * cos(t) + b) * sin(t);


        glVertex2f(x*proportia, y*proportia);
    }
    glEnd();
}

void DisplayCicloida() {
    double a = 0.1;
    double b = 0.2;
    double tmin = -9.5, tmax = 9.5;
    double ratia = 0.005;
    double proportia=0.9;
    double x, y;


    glColor3f(1, 0.1, 0.1); // rosu
    glBegin(GL_LINE_STRIP);
    for (double t = tmin ; t < tmax; t += ratia) {
        x = a * t - b * sin(t);
        y = a-b*cos(t);
        glVertex2f(x , y  );
    }
    glEnd();
}

void DisplayHipocicloida() {
    double pi = 4 * atan(1.0);
    double R = 0.1;
    double r = 0.3;
    double tmin = 0, tmax = 2 * pi;
    double ratia = 0.005;
    double x, y;

    glColor3f(1, 0.1, 0.1); // rosu
    glBegin(GL_LINE_STRIP);
    for (double t = tmin; t < tmax; t += ratia) {
        x = (R-r)*cos(r/R*t)-r*cos(t-r/R*t);
        y = (R - r) *sin(r / R * t) - r * sin(t - r / R * t);


        glVertex2f(x , y);
    }
    glEnd();
}
void DisplaySpiralaLogaritmica() {

    double ratia = 0.05;
    double a = 0.02;

    glColor3f(1, 0.1, 0.1); // rosu
    glBegin(GL_LINE_STRIP);
    for (double t = 0 + ratia; t <=3; t += ratia) {
       double r=a*exp(1+t);
       double x = r * cos(t);
       double y = r * sin(t);

        glVertex2f(x ,y );
    }
    glEnd();
}