Exam 2 Review Problems

Problem 1:
Consider the 3D object defined by the following 4 vertices:

P0 = (0,0,1), P1 = (0,0,3), P2 = (4, 0, 1), P3 = (0,3,1)

The four faces are defined by the triangles formed by all possible groups of the three of these vertices.

Part a. Find the surface normal for each of the four faces of the object. Normalize the length of the normals to length 1.0.

Part b. Suppose you want to shade this object using Gouraud shading. Calculate the normals that would be associated with each vertex for this type of shading.

Problem 2:
Assume you are given the pyramid defined by the following five vertices:

The base is defined by: (0,0,200), (0,0,100), (100,0,100), (100,0,200)
The tip is defined by: (50, 150, 150)

Part a: What set of 3D transformations would move the pyramid to a position defined by the following coordinates:

The base is defined by: (100,0,0), (200, 0,0), (200, -100, 0), (100, -100, 0) (Not necessarily in the same order as the above specification).
The tip is defined by: (150, -50, 150).

Part b:Draw the final position of the pyramid that results from applying the following sequence of transformations:

T(-50, 0, -150)

S(2.0, 2.0, 2.0)

Ry(45.0)

Problem 3:
Suppose you are given a pyramid defined by the following 5 vertices:

The Base is defined by: (100, 200, 200), (100, 100, 200), (200, 100, 200), (200, 200, 200)
The tip is defined by: (150, 150, 100)

Part a: Suppose the pyramid is projected onto a 2-D projection plane that coincides with the XY plane. Assuming orthographic projection is used, derive the (x,y) coordinates of each of the five vertices onto this projection plane.

Part b: Now assume that perspective projection is used and that the center of projection is at the origin of the coordinate system and the projection plane is a distance of 10 from the origin along the Z axis (and parallel to the XY plane). Derive the (x,y) coordinates of the projections of each of the five vertices onto the projection plane.

Problem 4:
Suppose you have a light source that is positioned at an angle of 45 degrees from the normal vector of a surface. Assume you have the following parameters for the light source and the material reflection properties:

kd = 0.5
ka = 0.5
Ld = 1000
La = 100
Ls = ks = 0
d (distance to light source) = 10
Attenuation coeeficients: a = 0, b = 0.1, c = 0.09

Calculate the intensity of the light reflected from the surface according to the Phong reflection model. How would this intensity change if the angle between N and L were decreased? How would it change if kd were increased?

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Constance Royden--croyden@mathcs.holycross.edu
Computer Science 384, Computer Graphics
Date Created: August 17, 1999
Last Modified: November 4, 2003
Page Expires: August 17, 2004