Week 6 Tutorial

Question 1:

Consider the following code for drawing a pyramid.

Which way are the faces pointing? If you drew this in OpenGL with back face culling turned on, what would you see?

        // the base
        gl.glBegin(GL2.GL_POLYGON);
        {
            gl.glVertex3d(1, 1, 0);
            gl.glVertex3d(-1, 1, 0);
            gl.glVertex3d(-1,-1, 0);
            gl.glVertex3d(1, -1, 0);
        }
        gl.glEnd();        

        // the sides
        gl.glBegin(GL2.GL_POLYGON);
        {
            gl.glVertex3d(0, 0, 2);
            gl.glVertex3d(1, 1, 0);
            gl.glVertex3d(-1, 1, 0);
        }
        gl.glEnd();        

        gl.glBegin(GL2.GL_POLYGON);
        {
            gl.glVertex3d(0, 0, 2);
            gl.glVertex3d(-1, -1, 0);
            gl.glVertex3d(-1, 1, 0);
        }
        gl.glEnd();        

        gl.glBegin(GL2.GL_POLYGON);
        {
            gl.glVertex3d(0, 0, 2);
            gl.glVertex3d(-1, -1, 0);
            gl.glVertex3d(1, -1, 0);
        }
        gl.glEnd();        

        gl.glBegin(GL2.GL_POLYGON);
        {
            gl.glVertex3d(0, 0, 2);
            gl.glVertex3d(1, -1, 0);
            gl.glVertex3d(1, 1, 0);
        }
        gl.glEnd();        

Question 2: 3D Modeling

• Write a vertex list, normal list and face list for a mesh describing a triangular prism. The front face should be a triangle with its top point in local co-ordinates at (0,1,-1). Assume it lies on the z=-1 plane. The back face should lie on the z=-3 plane at corresponding x and y values. The two faces should be connected by quads.

• Write code/pseudocode to generate a cylinder. The front face of the cylinder should be a circle of radius 1 at (0,0,-1), lying on the z=-1 plane with a back face at z=-3. The two faces should be connected by quads or a quadstrip. Make sure you do not forget to specify normals.
• Discuss different ways you could calculate normals for the following triangle mesh. For example, how would you calculate the normal for vertex P when drawing the triangle PDR? You may assume that each triangle is 1 unit in the x direction and 1 unit in the z direction, but has arbitrary y values.

       
       |/   |/   |/   |/
  ...--+----+----+----+--...
      /|   /|   /|   /|           Z
     / |  / |  / |  / |           ^
       | /  | /  | /  | /         |
       |/   |/   |/   |/          |
  ...--+----P----R----+--...      +-----> X
      /|   /|   /|   /|          
     / |  / |  / |  / |         
       | /  | /  | /  | /      
       |/   |/   |/   |/
  ...--+----D----+----+--...
      /|   /|   /|   /|
  
  
  

Question 3:

Use bilinear interpolation to work out the pixel depths for the triangle below, given the coordinates for the vertices as stated. Calculate depth values to one decimal place.

Show the result of copying the triangle into a depth buffer.

Use this depth buffer to add the rectangle below. Draw the resulting image.

Suppose the green rectangle is transparent (with alpha = 0.5). What does the resulting image look like in this case?

Question 4:

Consider the dungeon map below:

Assuming each wall is a single polygon, and assigning normals as you see fit, build a BSP tree for this map. There are many possible trees, depending on the order in which you choose polygons. What is the smallest tree you can find?

If the player is in the position marked, what order should the polygons be drawn so that all hidden surfaces are renderered properly?