The Algorithm that MarkS give you draw only the outline of the circle. If you want a circle filed with a texture, you can use triangle fan. First, draw the vertex at the center of the circle. Then draw the vertex on the contour of the circle, use cos(angle)*radius for x and sin(angle)*radius for y. Since texture coordinates s and t are in the range [0 1] => s = (cos(angle)+1.0)*0.5 and t = (sin(angle)+1.0)*0.5 . The texture coordinate for the vertex at the center of the circle is (0.5,0.5).

Here is an unoptimized sample code that you can test:

```
GLvoid draw_circle(const GLfloat radius,const GLuint num_vertex)
{
GLfloat vertex[4];
GLfloat texcoord[2];
const GLfloat delta_angle = 2.0*M_PI/num_vertex;
glEnable(GL_TEXTURE_2D);
glBindTexture(GL_TEXTURE_2D,texID);
glTexEnvi(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_REPLACE);
glBegin(GL_TRIANGLE_FAN);
//draw the vertex at the center of the circle
texcoord[0] = 0.5;
texcoord[1] = 0.5;
glTexCoord2fv(texcoord);
vertex[0] = vertex[1] = vertex[2] = 0.0;
vertex[3] = 1.0;
glVertex4fv(vertex);
for(int i = 0; i < num_vertex ; i++)
{
texcoord[0] = (std::cos(delta_angle*i) + 1.0)*0.5;
texcoord[1] = (std::sin(delta_angle*i) + 1.0)*0.5;
glTexCoord2fv(texcoord);
vertex[0] = std::cos(delta_angle*i) * radius;
vertex[1] = std::sin(delta_angle*i) * radius;
vertex[2] = 0.0;
vertex[3] = 1.0;
glVertex4fv(vertex);
}
texcoord[0] = (1.0 + 1.0)*0.5;
texcoord[1] = (0.0 + 1.0)*0.5;
glTexCoord2fv(texcoord);
vertex[0] = 1.0 * radius;
vertex[1] = 0.0 * radius;
vertex[2] = 0.0;
vertex[3] = 1.0;
glVertex4fv(vertex);
glEnd();
glDisable(GL_TEXTURE_2D);
}
```

Notice that only the portion of a circle inside the square texture image will be displayed to avoid deformation.