This example is taken from Nehe OpenGL Tutorial Lesson # 5 (@ http://nehe.gamedev.net/), which displays a 3D color-cube and a pyramid. The cube is made of 6 quads, each having different colors. The hollow pyramid is made up of 4 triangles, with different colors on each of the vertices. 
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/*
 *  3D Shapes
 */
#include <GLUT/glut.h> 
 
/* Global variables */
char title[] = "3D Shapes";
 
/* Initialize OpenGL Graphics */
void initGL() {
   glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set background color to black and opaque
   glClearDepth(1.0f);                   // Set background depth to farthest
   glEnable(GL_DEPTH_TEST);   // Enable depth testing for z-culling
   glDepthFunc(GL_LEQUAL);    // Set the type of depth-test
   glShadeModel(GL_SMOOTH);   // Enable smooth shading
   glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);  // Nice perspective corrections
}
 
/* Handler for window-repaint event.  */
void display() {
   glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // Clear color and depth buffers
   glMatrixMode(GL_MODELVIEW);     // To operate on model-view matrix
 
   // Render a color-cube consisting of 6 quads with different colors
   glLoadIdentity();                 // Reset the model-view matrix
   glTranslatef(1.5f, 0.0f, -7.0f);  // Move right and into the screen
 
   glBegin(GL_QUADS);                // Begin drawing the color cube with 6 quads
      // Top face (y = 1.0f)
      // Define vertices in counter-clockwise (CCW) order with normal pointing out
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f( 1.0f, 1.0f, -1.0f);
      glVertex3f(-1.0f, 1.0f, -1.0f);
      glVertex3f(-1.0f, 1.0f,  1.0f);
      glVertex3f( 1.0f, 1.0f,  1.0f);
 
      // Bottom face (y = -1.0f)
      glColor3f(1.0f, 0.5f, 0.0f);     // Orange
      glVertex3f( 1.0f, -1.0f,  1.0f);
      glVertex3f(-1.0f, -1.0f,  1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f( 1.0f, -1.0f, -1.0f);
 
      // Front face  (z = 1.0f)
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f( 1.0f,  1.0f, 1.0f);
      glVertex3f(-1.0f,  1.0f, 1.0f);
      glVertex3f(-1.0f, -1.0f, 1.0f);
      glVertex3f( 1.0f, -1.0f, 1.0f);
 
      // Back face (z = -1.0f)
      glColor3f(1.0f, 1.0f, 0.0f);     // Yellow
      glVertex3f( 1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f,  1.0f, -1.0f);
      glVertex3f( 1.0f,  1.0f, -1.0f);
 
      // Left face (x = -1.0f)
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(-1.0f,  1.0f,  1.0f);
      glVertex3f(-1.0f,  1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f,  1.0f);
 
      // Right face (x = 1.0f)
      glColor3f(1.0f, 0.0f, 1.0f);     // Magenta
      glVertex3f(1.0f,  1.0f, -1.0f);
      glVertex3f(1.0f,  1.0f,  1.0f);
      glVertex3f(1.0f, -1.0f,  1.0f);
      glVertex3f(1.0f, -1.0f, -1.0f);
   glEnd();  // End of drawing color-cube
 
   // Render a pyramid consists of 4 triangles
   glLoadIdentity();                  // Reset the model-view matrix
   glTranslatef(-1.5f, 0.0f, -6.0f);  // Move left and into the screen
 
   glBegin(GL_TRIANGLES);           // Begin drawing the pyramid with 4 triangles
      // Front
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f( 0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(-1.0f, -1.0f, 1.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(1.0f, -1.0f, 1.0f);
 
      // Right
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f(0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(1.0f, -1.0f, 1.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(1.0f, -1.0f, -1.0f);
 
      // Back
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f(0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(1.0f, -1.0f, -1.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(-1.0f, -1.0f, -1.0f);
 
      // Left
      glColor3f(1.0f,0.0f,0.0f);       // Red
      glVertex3f( 0.0f, 1.0f, 0.0f);
      glColor3f(0.0f,0.0f,1.0f);       // Blue
      glVertex3f(-1.0f,-1.0f,-1.0f);
      glColor3f(0.0f,1.0f,0.0f);       // Green
      glVertex3f(-1.0f,-1.0f, 1.0f);
   glEnd();   // Done drawing the pyramid
 
   glutSwapBuffers();  // Swap the front and back frame buffers (double buffering)
}
 
/* Handler for window re-size event. Called back when the window first appears and
   whenever the window is re-sized with its new width and height */
void reshape(GLsizei width, GLsizei height) {  // GLsizei for non-negative integer
   // Compute aspect ratio of the new window
   if (height == 0) height = 1;                // To prevent divide by 0
   GLfloat aspect = (GLfloat)width / (GLfloat)height;
 
   // Set the viewport to cover the new window
   glViewport(0, 0, width, height);
 
   // Set the aspect ratio of the clipping volume to match the viewport
   glMatrixMode(GL_PROJECTION);  // To operate on the Projection matrix
   glLoadIdentity();             // Reset
   // Enable perspective projection with fovy, aspect, zNear and zFar
   gluPerspective(45.0f, aspect, 0.1f, 100.0f);
}
 
/* Main function: GLUT runs as a console application starting at main() */
int main(int argc, char** argv) {
   glutInit(&argc, argv);            // Initialize GLUT
   glutInitDisplayMode(GLUT_DOUBLE|GLUT_DEPTH); // Enable double buffered mode
   glutInitWindowSize(640, 480);   // Set the window's initial width & height
   glutInitWindowPosition(50, 50); // Position the window's initial top-left corner
   glutCreateWindow(title);          // Create window with the given title
   glutDisplayFunc(display);       // Register callback handler for window re-paint event
   glutReshapeFunc(reshape);       // Register callback handler for window re-size event
   initGL();                       // Our own OpenGL initialization
   glutMainLoop();                 // Enter the infinite event-processing loop
   return 0;
}
GLUT Setup - main()

The program contains a initGL(), display() and reshape() functions.

The main() program:

  1. glutInit(&argc, argv);
    Initializes the GLUT.
  2. glutInitWindowSize(640, 480);
    glutInitWindowPosition(50, 50);
    glutCreateWindow(title);
    Creates a window with a title, initial width and height positioned at initial top-left corner.
  3. glutDisplayFunc(display);
    Registers display() as the re-paint event handler. That is, the graphics sub-system calls back display() when the window first appears and whenever there is a re-paint request.
  4. glutReshapeFunc(reshape);
    Registers reshape() as the re-sized event handler. That is, the graphics sub-system calls back reshape() when the window first appears and whenever the window is re-sized.
  5. glutInitDisplayMode(GLUT_DOUBLE|GLUT_DEPTH););
    Enables double buffering. In display(), we use glutSwapBuffers() to signal to the GPU to swap the front-buffer and back-buffer during the next VSync (Vertical Synchronization).
  6. initGL();
    Invokes the initGL() once to perform all one-time initialization tasks.
  7. glutMainLoop();
    Finally, enters the event-processing loop.
One-Time Initialization Operations - initGL()

The initGL() function performs the one-time initialization tasks. It is invoked from main() once.

glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set background color to black and opaque
glClearDepth(1.0f); // Set background depth to farthest
// In display()
glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
Set the clearing (background) color to black (R=0, G=0, B=0) and opaque (A=1), and the clearing (background) depth to the farthest (Z=1). In display(), we invoke glClear() to clear the color and depth buffer, with the clearing color and depth, before rendering the graphics.

glEnable(GL_DEPTH_TEST); // Enable depth testing for z-culling
glDepthFunc(GL_LEQUAL); // Set the type of depth-test
We need to enable depth-test to remove the hidden surface, and set the function used for the depth test.

glShadeModel(GL_SMOOTH); // Enable smooth shading
We enable smooth shading in color transition. The alternative is GL_FLAT.

glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST); // Nice perspective corrections
In graphics rendering, there is often a trade-off between processing speed and visual quality. We can use glHint() to decide on the trade-off. In this case, we ask for the best perspective correction, which may involve more processing. The default is GL_DONT_CARE.

Defining the Color-cube and Pyramid

The color-cube is made up of 6 quads. Each quad is made up of 4 vertices, defined in counter-clockwise (CCW) order, so that the normal vector is pointing out, indicating the front face. All 4 vertices have the same color. The color-cube is defined in its local space (called model space) with origin at the center of the cube with sides of 2 units.

Similarly, the pyramid is made up of 4 triangles (without the base). Each triangle is made up of 3 vertices, defined in CCW order. The 5 vertices of the pyramid are assigned different colors. The color of the triangles are interpolated (and blend smoothly) from its 3 vertices. Again, the pyramid is defined in its local space with origin at the center of the pyramid.

Model Transform

The objects are defined in their local spaces (model spaces). We need to transform them to the common world space, known as model transform.

To perform model transform, we need to operate on the so-called model-view matrix (OpenGL has a few transformation matrices), by setting the current matrix mode to model-view matrix:

glMatrixMode(GL_MODELVIEW); // To operate on model-view matrix

We perform translations on cube and pyramid, respectively, to position them on the world space:

// Color-cube
glLoadIdentity(); // Reset model-view matrix
glTranslatef(1.5f, 0.0f, -7.0f); // Move right and into the screen
// Pyramid
glLoadIdentity();
glTranslatef(-1.5f, 0.0f, -6.0f); // Move left and into the screen

View Transform

The default camera position is:

gluLookAt(0.0, 0.0, 0.0, 0.0, 0.0, -100.0, 0.0, 1.0, 0.0)

That is, EYE=(0,0,0) at the origin, AT=(0,0,-100) pointing at negative-z axis (into the screen), and UP=(0,1,0) corresponds to y-axis.

OpenGL graphics rendering pipeline performs so-called view transform to bring the world space to the camera's view space. In the case of the default camera position, no transform is needed.

Try using the gluLookAt function, change the eye position, where the camera is looking and the up vector. Explain what happens. Try setting the up vector to (0.0, -1.0, 0.0). This should be done in the reshape callback after the gluPerspective call.
Try moving around the two objects using only the gluLookAt function. The movement should be in the z=0 plane. Try to look at the back face of each object. Then the right and left sides of the cube.
Did you get it to work?
Viewport Transform

void reshape(GLsizei width, GLsizei height) {
   glViewport(0, 0, width, height);
The graphics sub-system calls reshape() when the window first appears and whenever the window is resized, given the new window's width and height, in pixels. We set our application viewport to cover the entire window, top-left corner at (0, 0) of width and height, with default minZ of 0 and maxZ of 1. We also use the same aspect ratio of the viewport for the projection view frustum to prevent distortion. In the viewport, a pixel has (x, y) value as well as z-value for depth processing.

Perspective
Projection Transform

GLfloat aspect = (GLfloat)width / (GLfloat)height; // Compute aspect ratio of window
glMatrixMode(GL_PROJECTION); // To operate on the Projection matrix
glLoadIdentity(); // Reset
gluPerspective(45.0f, aspect, 0.1f, 100.0f); // Perspective projection: fovy, aspect, near, far
 A camera has limited field of view. The projection models the view captured by the camera. There are two types of projection: perspective projection and orthographic projection. In perspective projection, object further to the camera appears smaller compared with object of the same size nearer to the camera. In orthographic projection, the objects appear the same regardless of the z-value. Orthographic projection is a special case of perspective projection where the camera is placed very far away. We shall discuss the orthographic projection in the later example.

To set the projection, we need to operate on the projection matrix. (Recall that we operated on the model-view matrix in model transform.)

We set the matrix mode to projection matrix and reset the matrix. We use the gluPerspective() to enable perspective projection, and set the fovy (view angle from the bottom-plane to the top-plane), aspect ratio (width/height), zNear and zFar of the View Frustum (truncated pyramid). In this example, we set the fovy to 45°. We use the same aspect ratio as the viewport to avoid distortion. We set the zNear to 0.1 and zFar to 100 (z=-100). Take that note the color-cube (1.5, 0, -7) and the pyramid (-1.5, 0, -6) are contained within the View Frustum.

The projection transform transforms the view frustum to a 2x2x2 cuboid clipping-volume centered on the plane (z=0). The subsequent viewport transform transforms the clipping-volume to the viewport in screen space. The viewport is set earlier via the glViewport() function.

Try changing the parameters of the gluProjection function. This should be done in the reshape callback. Try a fovy of 60 degrees, then 90 degrees, what about 120 degrees? Explain what happens. Try playing with the near and far clipping plane values. List the values you tried and explain what happened. Try modifying the aspect ratio, divide by 2.0 multiply by 2.0. What happens?
Do you understand how the perspective function works?

2.  Example 2 - This is to slow down animations using the GLUT Timer function, instead of the idle callback.

Let's modify the previous example to carry out animation (rotating the cube and pyramid).

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/*
 * 3D Shapes with animation
 */
#include <GLUT/glut.h>  // GLUT, include glu.h and gl.h
 
/* Global variables */
char title[] = "3D Shapes with animation";
GLfloat anglePyramid = 0.0f;  // Rotational angle for pyramid [NEW]
GLfloat angleCube = 0.0f;     // Rotational angle for cube [NEW]
int refreshMills = 15;        // refresh interval in milliseconds [NEW]
 
/* Initialize OpenGL Graphics */
void initGL() {
   glClearColor(0.0f, 0.0f, 0.0f, 1.0f); // Set background color to black and opaque
   glClearDepth(1.0f);                   // Set background depth to farthest
   glEnable(GL_DEPTH_TEST);   // Enable depth testing for z-culling
   glDepthFunc(GL_LEQUAL);    // Set the type of depth-test
   glShadeModel(GL_SMOOTH);   // Enable smooth shading
   glHint(GL_PERSPECTIVE_CORRECTION_HINT, GL_NICEST);  // Nice perspective corrections
}
 
/* Handler for window-repaint event. Called back when the window first appears and
   whenever the window needs to be re-painted. */
void display() {
   glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // Clear color and depth buffers
   glMatrixMode(GL_MODELVIEW);     // To operate on model-view matrix
 
   // Render a color-cube consisting of 6 quads with different colors
   glLoadIdentity();                 // Reset the model-view matrix
   glTranslatef(1.5f, 0.0f, -7.0f);  // Move right and into the screen
   glRotatef(angleCube, 1.0f, 1.0f, 1.0f);  // Rotate about (1,1,1)-axis [NEW]
 
   glBegin(GL_QUADS);                // Begin drawing the color cube with 6 quads
      // Top face (y = 1.0f)
      // Define vertices in counter-clockwise (CCW) order with normal pointing out
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f( 1.0f, 1.0f, -1.0f);
      glVertex3f(-1.0f, 1.0f, -1.0f);
      glVertex3f(-1.0f, 1.0f,  1.0f);
      glVertex3f( 1.0f, 1.0f,  1.0f);
 
      // Bottom face (y = -1.0f)
      glColor3f(1.0f, 0.5f, 0.0f);     // Orange
      glVertex3f( 1.0f, -1.0f,  1.0f);
      glVertex3f(-1.0f, -1.0f,  1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f( 1.0f, -1.0f, -1.0f);
 
      // Front face  (z = 1.0f)
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f( 1.0f,  1.0f, 1.0f);
      glVertex3f(-1.0f,  1.0f, 1.0f);
      glVertex3f(-1.0f, -1.0f, 1.0f);
      glVertex3f( 1.0f, -1.0f, 1.0f);
 
      // Back face (z = -1.0f)
      glColor3f(1.0f, 1.0f, 0.0f);     // Yellow
      glVertex3f( 1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f,  1.0f, -1.0f);
      glVertex3f( 1.0f,  1.0f, -1.0f);
 
      // Left face (x = -1.0f)
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(-1.0f,  1.0f,  1.0f);
      glVertex3f(-1.0f,  1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f, -1.0f);
      glVertex3f(-1.0f, -1.0f,  1.0f);
 
      // Right face (x = 1.0f)
      glColor3f(1.0f, 0.0f, 1.0f);     // Magenta
      glVertex3f(1.0f,  1.0f, -1.0f);
      glVertex3f(1.0f,  1.0f,  1.0f);
      glVertex3f(1.0f, -1.0f,  1.0f);
      glVertex3f(1.0f, -1.0f, -1.0f);
   glEnd();  // End of drawing color-cube
 
   // Render a pyramid consists of 4 triangles
   glLoadIdentity();                  // Reset the model-view matrix
   glTranslatef(-1.5f, 0.0f, -6.0f);  // Move left and into the screen
   glRotatef(anglePyramid, 1.0f, 1.0f, 0.0f);  // Rotate about the (1,1,0)-axis [NEW]
 
   glBegin(GL_TRIANGLES);           // Begin drawing the pyramid with 4 triangles
      // Front
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f( 0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(-1.0f, -1.0f, 1.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(1.0f, -1.0f, 1.0f);
 
      // Right
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f(0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(1.0f, -1.0f, 1.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(1.0f, -1.0f, -1.0f);
 
      // Back
      glColor3f(1.0f, 0.0f, 0.0f);     // Red
      glVertex3f(0.0f, 1.0f, 0.0f);
      glColor3f(0.0f, 1.0f, 0.0f);     // Green
      glVertex3f(1.0f, -1.0f, -1.0f);
      glColor3f(0.0f, 0.0f, 1.0f);     // Blue
      glVertex3f(-1.0f, -1.0f, -1.0f);
 
      // Left
      glColor3f(1.0f,0.0f,0.0f);       // Red
      glVertex3f( 0.0f, 1.0f, 0.0f);
      glColor3f(0.0f,0.0f,1.0f);       // Blue
      glVertex3f(-1.0f,-1.0f,-1.0f);
      glColor3f(0.0f,1.0f,0.0f);       // Green
      glVertex3f(-1.0f,-1.0f, 1.0f);
   glEnd();   // Done drawing the pyramid
 
   glutSwapBuffers();  // Swap the front and back frame buffers (double buffering)
 
   // Update the rotational angle after each refresh [NEW]
   anglePyramid += 0.2f;
   angleCube -= 0.15f;
}
 
/* Called back when timer expired [NEW] */
void timer(int value) {
   glutPostRedisplay();      // Post re-paint request to activate display()
   glutTimerFunc(refreshMills, timer, 0); // next timer call milliseconds later
}
 
/* Handler for window re-size event. Called back when the window first appears and
   whenever the window is re-sized with its new width and height */
void reshape(GLsizei width, GLsizei height) {  // GLsizei for non-negative integer
   // Compute aspect ratio of the new window
   if (height == 0) height = 1;                // To prevent divide by 0
   GLfloat aspect = (GLfloat)width / (GLfloat)height;
 
   // Set the viewport to cover the new window
   glViewport(0, 0, width, height);
 
   // Set the aspect ratio of the clipping volume to match the viewport
   glMatrixMode(GL_PROJECTION);  // To operate on the Projection matrix
   glLoadIdentity();             // Reset
   // Enable perspective projection with fovy, aspect, zNear and zFar
   gluPerspective(45.0f, aspect, 0.1f, 100.0f);
}
 
/* Main function: GLUT runs as a console application starting at main() */
int main(int argc, char** argv) {
   glutInit(&argc, argv);            // Initialize GLUT
   glutInitDisplayMode(GLUT_DOUBLE|GLUT_DEPTH); // Enable double buffered mode
   glutInitWindowSize(640, 480);   // Set the window's initial width & height
   glutInitWindowPosition(50, 50); // Position the window's initial top-left corner
   glutCreateWindow(title);          // Create window with the given title
   glutDisplayFunc(display);       // Register callback handler for window re-paint event
   glutReshapeFunc(reshape);       // Register callback handler for window re-size event
   initGL();                       // Our own OpenGL initialization
   glutTimerFunc(0, timer, 0);     // First timer call immediately [NEW]
   glutMainLoop();                 // Enter the infinite event-processing loop
   return 0;
}

The new code is:

GLfloat anglePyramid = 0.0f; // Rotational angle for pyramid [NEW]
GLfloat angleCube = 0.0f; // Rotational angle for cube [NEW]
int refreshMills = 15; // refresh interval in milliseconds [NEW]
 We define two global variables to keep track of the current rotational angles of the cube and pyramid. We also define the refresh period as 15 msec (66 frames per second).

void timer(int value) {
   glutPostRedisplay(); // Post re-paint request to activate display()
   glutTimerFunc(refreshMills, timer, 0); // next timer call milliseconds later
}
To perform animation, we define a function called timer(), which posts a re-paint request to activate display() when the timer expires, and then runs the timer again. In main(), we perform the first timer() call via glutTimerFunc(0, timer, 0).

glRotatef(angleCube, 1.0f, 1.0f, 1.0f); // Rotate the cube about (1,1,1)-axis [NEW]
......
glRotatef(anglePyramid, 1.0f, 1.0f, 0.0f); // Rotate about the (1,1,0)-axis [NEW]
......
anglePyramid += 0.2f; // update pyramid's angle
angleCube -= 0.15f; // update cube's angle
 In display(), we rotate the cube and pyramid based on their rotational angles, and update the angles after each refresh.

Play with this code to see how to slow/speed up your animations.