Homework 5

• Download an example changing the viewpoint by a mouse.
• Download and execute sample solution to Question 2.

1. Implement a simple 3D function plotter that can plot a function of 2 variables. For example:

   GLfloat fy( GLFloat x, GLfloat z) { return 2*x*x+2*z*z-1.0; }

   when plotted for values x=-1..1 and z=-1..1 produces a 3D graph similar to the figure at right centered at the origin, when looking directly down the negative z-axis.

   • Test using f(x,z)=2x²+2z²-1.0. Choose your own range for x and z.
   • Use polygon offset mode described on page 267 to improve the appearance of the graph.
   • Add the ability to view all sides of the plot by mouse movements.
   • Add an xz-plane at y=0.

   Hint: To implement a general function plotter requires passing the function to be plotted. A function f can be passed a function as parameter p in C or C++ by defined as:

   void f( int p( int ), int y ) { printf( "%d", p( y ) ); }

   int square( int x ) { return x*x; }

   f( square, 3);        // Prints 9

    

2. Create a cube world of a plane where a large cube is fixed and a smaller cube that can move and has the ability to walk through the sides of the large cube.

   There should be two viewing modes, one from a viewpoint on a hemisphere (from Question 1) viewing both cubes, the second from the small cube able to view its surroundings.

   • Use the up and down keys to move the small cube forward and backward, choose one of the faces as the head for orientation,
   • turn left and right with the left and right keys, choose whether its your left or the cubes left,
   • when the Enter key is pressed, toggle the viewpoint between the viewer and the small cube,
   • use the mouse to pan around the scene from the eye position of the viewer or the small cube.

   Hints:

   • Remember the Turtle, the small cube can be oriented and moved in much the same way.
   • The cube viewing example places the eye of the viewer on the surface of a hemisphere (at the mouse location) always looking at the origin. The cube view just reverse that and has the eye(s) at the cube and look at a point on the hemisphere indicated by the mouse position. Calculating the same angles for different uses by the viewer and cube will create some relatively minor but odd visual artifacts from the cube view that can be tolerated for now.
   • Special keys such as arrows can be used through the callback:

     • glutSpecialFunc(specialKey);

     and:

     • void specialKey(int key, int x, int y) {
           if(key==GLUT_KEY_UP)  { ... }
       
        

3. Modify Question 2 solution so that the big cube is replaced by the function plot from Question 1 and that the small cube can move through the plot.

EMAIL

1. To  with subject: YOUR NAME: B481 and Homework 5.
2. Send a Web accessible link to a zip file with your last name as Lastname.zip containing three directories:
   1. Directory named ONE for Question 1:
   • capture of plot of your favorite 3D function,
   • all code files (include exe) for Question 1.
   2. Directory named TWO for Question 2:
   • all code files (include exe) for Question 2.
   2. Directory named THREE for Question 3:
   • all code files (include exe) for Question 3.
3. Instructions on executing.