//cylinder
int nslice = 36;
glBegin( GL_QUAD_STRIP);
	   GLfloat t = 0.;
	   GLfloat dt = (360. / nslice) * 3.1416 / 180.;
		for  (int j = 0; j <= nslice; ++j) {
			 glNormal3f( cos(t), 0., sin(t));
			 glVertex3f( cos( t), 0., sin( t));
			 glVertex3f( cos( t), 2., sin( t));
			 t = t + dt;
		 }
glEnd();


// torus
// return a point on the torus for u,v both on [0, 2pi]
// where v = radians around a meridian
// u = radians "swept" around the axis
Vector p( float u, float v ) {
	float r_maj = 5.0; // distance from origin to center of a meridian
	float r_min = 2.0; // radius of a meridian
	return( Vector(cos(u)*(r_maj+r_min*cos(v)),
					 sin(u)*(r_maj+r_min*cos(v)),
					 r_min*sin(v) ) );
}

Vector n( float u, float v ) {
	Vector N;
	N.x = cos(v)*cos(u);
	N.y = cos(v)*sin(u);
	N.z = sin(v);
	N.normalize();
	return( N );
}

int num_steps_u = 30;
int num_steps_v = 15;
const float PI = 3.14159265359;

float step_u = (2*PI)/(float)num_steps_u;
float step_v = (2*PI)/(float)num_steps_v;

glBegin( GL_QUADS );

for( float u = 0; u < 2 * PI; u += step_u ) {
	for( float v = 0; v < 2 * PI; v += step_v ) {

		Vector P[4], N[4];

		P[0] = p( u, v );
		P[1] = p( u+step_u, v );
		P[2] = p( u+step_u, v+step_v );
		P[3] = p( u, v+step_v );

		N[0] = n( u, v );
		N[1] = n( u+step_u, v );
		N[2] = n( u+step_u, v+step_v );
		N[3] = n( u, v+step_v );

		for( int c = 0; c < 4; c++ ) {
			glNormal3f( N[c].x, N[c].y, N[c].z );
			glVertex3f( P[c].x, P[c].y, P[c].z );
		}
	}
}
glEnd();


//helix curve
int angle = 0, spcount = 5;
GLfloat x, y, z=0;
GLfloat r = 2,  b = 0.002;
GLfloat radia= 3.1415926/180, theta = 0;

glBegin(GL_LINE_STRIP);
	for(angle = 0; angle < 360*spcount; angle += 1)
	{
		theta = angle*radia;
		x = r * cos(theta);
		y = r * sin(theta);

		glVertex3f(x,y,z);
		z+= b;
	}
 glEnd();
 
 
//duble helix suface
int angle = 0, spcount = 1;
GLfloat x, y, z, x1, y1, z1=0;
GLfloat r = 2,  b = 0.02;
GLfloat pi = 3.1415926;
GLfloat radia= pi/180, theta = 0;

glBegin(GL_QUAD_STRIP);
//glBegin(GL_LINE_STRIP);
	for(angle = 0; angle < 360*spcount; angle += 1)
	{
		theta = angle*radia;
		x = r * cos(theta);
		y = r * sin(theta);
		glVertex3f(x,y,z);
		z+= b;

		x1 = r * cos(theta+pi);
		y1 = r * sin(theta+pi);
		glVertex3f(x1,y1,z1);
		z1+= b;
	}
  glEnd();
 
 
//mobius strip 
int angle = 0, spcount = 1;
GLfloat x, y, z, x1, y1, z1=0;
GLfloat r = 2,  l = 1;
GLfloat pi = 3.1415926;
GLfloat radia= pi/180, theta = 0;

glBegin(GL_QUAD_STRIP);
	for(angle = 0; angle <= 360; angle += 1)
	{
		theta = angle*radia;
		x1 = l*sin(theta/2)*cos(theta);
		y1 = l*sin(theta/2)*sin(theta);
		z1 = l*cos(theta/2);

		glVertex3f(r*cos(theta)+x1, r*sin(theta)+y1,  z1);
		glVertex3f(r*cos(theta)-x1, r*sin(theta)-y1,  -z1);
	}
glEnd();

 //Mobuis strip wired mesh
int angle = 0, spcount = 1;
GLfloat x, y, z, x1, y1, z1=0;
GLfloat r = 2,  l = 1;
GLfloat pi = 3.1415926;
GLfloat radia= pi/180, theta = 0;

glPolygonMode( GL_FRONT, GL_LINE );
glPolygonMode( GL_BACK, GL_LINE );

glColor3f(1.0, 1.0, 0);
glBegin(GL_QUAD_STRIP);
	for(angle = 0; angle <= 360; angle += 5)
	{
		theta = angle*radia;
		x1 = l*sin(theta/2)*cos(theta);
		y1 = l*sin(theta/2)*sin(theta);
		z1 = l*cos(theta/2);
		glVertex3f(r*cos(theta)+x1, r*sin(theta)+y1,  z1);
		glVertex3f(r*cos(theta)-x1, r*sin(theta)-y1,  -z1);

	}
glEnd();