Week 6 Tutorial

Question 1: Winding Order and Culling

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: Depth buffer and transparency

Use bilinear interpolation to work out the pixel depths for the triangle below, given the coordinates and pseudo-depth values for the vertices as stated. Calculate depth values to two decimal places.

Show the result of copying the triangle into the depth buffer that already has the rectangle below in it

Suppose the green rectangle is transparent (with alpha = 0.25) and rgb values of (0.3,0.6,0.15) and the triangle is opaque (with alpha value = 1) and the rgb values of the triangle are (0.7,0,0.9). What does the resulting image look like in this case with standard alpha blending? What are the rgb values of the different pixels?

Suppose the rectangle is opaque( with alpha 1) and the triangle is transparent (with alpha = 0.25). What does the resulting image look like in this case? What are the rgb values of the different pixels?

Question 3: BSP trees

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?

Question 4: Illumination

float amb[]  = {0.0f, 0.0f, 0.1f, 1.0f};
float diff[] = {0.0f, 0.0f, 0.5f, 1.0f};
float spec[] = {1.0f, 1.0f, 1.0f, 1.0f};
float f[] = { 10.0f }; //phong exponent

gl.glMaterialfv(GL2.GL_FRONT_AND_BACK, GL2.GL_AMBIENT, amb,0);
gl.glMaterialfv(GL2.GL_FRONT_AND_BACK, GL2.GL_DIFFUSE, diff,0);
gl.glMaterialfv(GL2.GL_FRONT_AND_BACK, GL2.GL_SPECULAR, spec,0);
gl.glMaterialfv(GL2.GL_FRONT_AND_BACK, GL2.GL_SHININESS, f,0);        	

And a light source with the following properties

float lightAmb[] = { 0.2f, 0.2f, 0.2f, 1.0f };
float lightDifAndSpec[] = { 1, 1, 1, 1 };
gl.glLightfv(GL2.GL_LIGHT0, GL2.GL_AMBIENT,  lightAmb,0);
gl.glLightfv(GL2.GL_LIGHT0, GL2.GL_DIFFUSE,  lightDifAndSpec,0);
gl.glLightfv(GL2.GL_LIGHT0, GL2.GL_SPECULAR, lightDifAndSpec,0);

float[] globAmb =  {0.1f, 0.1f, 0.1f, 1.0f};
gl.glLightModelfv(GL_LIGHT_MODEL_AMBIENT, globAmb, 0);

//Calculate the camera viewpoint properly instead of using hack.
gl.glLightModeli(GL2.GL_LIGHT_MODEL_LOCAL_VIEWER, GL2.GL_TRUE); 

Assume

• The vertex is at position(0,0,-2)
• The normal at the vertex is (0,0,1)
• The light source is a point light at position (0,3,2)

1. Calculate the diffuse component rgb values for the vertex
2. Calculate the specular component rgb values assuming we are using the blinn-phong specular model.
3. Calculate the total rgb values for the vertex.