I am trying to oscillate a 2D object about a point, while the object has already been drawn then later I want to oscillate it by specifying the pivot point, how to proceed, please help me.It is for a mini project.I am using codeblocks and using c programing language along with OpenGL to do this, I have attached main .c file and .cpb file below (For reference I have attached the code for that object also below .) I have attached a .png file as what is my 2D image looks like.I want to oscillate that image about its top point(i.e cap tip).

#include <GL/glut.h>
#include <math.h>
#define PI 3.14159265358979324

void myinit()
{
	glClearColor(1.0,1.0,1.0,0.0);
	glMatrixMode (GL_PROJECTION);
	gluOrtho2D(0.0, 200.0, 0.0, 150.0);
	//glutPostRedisplay();
}

void display(void)
{

    float r3 = 4.0; // Radius of circle.
    float x3 = 80.0; // X-coordinate of center of circle.
    float y3 = 67.0;

    float r1 = 1.0; // Radius of circle.
    float x1 = 77.0; // X-coordinate of center of circle.
    float y1 = 73.0;

    float r2 = 1.0; // Radius of circle.
    float x2 = 83.0; // X-coordinate of center of circle.
    float y2 = 73.0;

    float R = 3.0; // Radius of circle.
    float X = 80.0; // X-coordinate of center of circle.
    float Y = 103.0; // Y-coordinate of center of circle.
    int numVertices = 25; // Number of vertices on circle.
    float t = 0; // Angle parameter.
    int i;

	glClear(GL_COLOR_BUFFER_BIT);
	//glColor3f(0.5, 0.5, 0.5);
	glLineWidth(2.0);
    glEnable(GL_LINE_STIPPLE);
    //glLineStipple(1,0x00ff);
	//draw a line
	glBegin(GL_LINES);
        glColor3f(0.92, 0.78, 0.62);
        glVertex2f(80.0,60.0);
		glVertex2f(90.0,65.0);

		glVertex2f(90.0,65.0);
		glVertex2f(90.0,75.0);

        glColor3f(0.137255, 0.556863, 0.137255);//0.0, 0.5, 0.0);
		glVertex2f(90.0,75.0);
		glVertex2f(80.0,80.0);

		glVertex2f(80.0,80.0);
		glVertex2f(70.0,75.0);

        glColor3f(0.92, 0.78, 0.62);
		glVertex2f(70.0,75.0);
		glVertex2f(70.0,65.0);

		glVertex2f(70.0,65.0);
		glVertex2f(80.0,60.0);

        glColor3f( 0.137255, 0.556863, 0.137255);
		glVertex2f(90.0,75.0);
		glVertex2f(80.0,100.0);

		glVertex2f(80.0,100.0);
		glVertex2f(70.0,75.0);

	glEnd();
	glFlush();

	glBegin(GL_POLYGON);
	glColor3f(0.1, 0.9, 0.0);
    for(int i = 0; i < numVertices; ++i)
    {
        //glColor3ub(rand()%256, rand()%256, rand()%256);
        glVertex3f(X + R * cos(t), Y + R * sin(t), 0.0);
        t += 2 * PI / numVertices;
    }
    glEnd();
    glFlush();

    glBegin(GL_POLYGON);
    glColor3f(0.647059, 0.164706, 0.164706);
    for(int i = 0; i < numVertices; ++i)
    {
        glVertex3f(x1 + r1 * cos(t), y1 + r1 * sin(t), 0.0);
        t += 2 * PI / numVertices;
    }
    glEnd();
    glFlush();

    glBegin(GL_POLYGON);
    glColor3f(0.647059, 0.164706, 0.164706);
    for(int i = 0; i < numVertices; ++i)
    {
        glVertex3f(x2 + r2 * cos(t), y2 + r2 * sin(t), 0.0);
        t += 2 * PI / numVertices;
    }
    glEnd();
    glFlush();

    glBegin(GL_POLYGON);
    glColor3f(1.0, 0.7, 0.0);
    for(int i = 0; i < numVertices; ++i)
    {
        glVertex3f(x3 + r3 * cos(t), y3 + r3 * sin(t), 0.0);
        t += - PI / numVertices;
    }
    glEnd();
    glFlush();
}

void main(int argc,char *argv[])
{
	glutInit(&argc,argv);
	glutInitDisplayMode (GLUT_SINGLE | GLUT_RGB);
	glutInitWindowSize (1000, 1000);
	glutInitWindowPosition (0, 0);
	glutCreateWindow ("joker");
	myinit();
	glutDisplayFunc(display);
	glutMainLoop();
}

thanks in advance, please help me

joker.cbp

main.c

glVertex3f(x1 + r1 * cos(t), y1 + r1 * sin(t), 0.0);

You may want to read up a bit more on openGL and how transforms work, glLoadIdentity(), glRotatef(), glScalef(). You shouldn't be recalculating vertices this way.