Midterm Exam Details

The exam will be 50 minutes long and done on paper during class. If you have approved accommodations on file, you must make sure to register at least two business days (M-F) in advance to take your exam in the Academic Resource Center or it will be assumed that you will take the exam at our usual class time and for the standard duration.

Format

The exam will have 15 questions. Some questions have multiple formats (such as multiple choice and a short answer), but a general distribution is as follows:

• 7 short Answer (sometimes very short answer)
• 3 expression questions (write a vector/transformation/mathematical expression)
• 2 multiple choice
• 1 drawing
• 2 fill in the blank

Test taking environment and exam rules

Since seating in our classroom is very tight test questions will be randomized and there will be ZERO talking to avoid distracting others and to ensure the integrity of the exam process. Conversing with another student will result in the immediate submission of both student examinations and grading penalties. If you have a clarification question, you must raise your hand and I will come by to assist you.

While taking the exam, your table must be completely cleared except for your exam, one or more writing utensils, and white scratch paper provided by the professor during the exam. All devices, bags, notebooks, etc. must be put away and out of sight.

Study Guide

This is the pool of potential test questions for the exam. The context, wording, or presentation of each question may differ from the content below, but the concepts will remain the same. Each question is associated with resources to find/derive an answer to the question.

Chapter 1 - Slides

• List the 6 components of a graphics system (Ch 1.2)
• List and describe the 4 components of the graphics Pipeline. What is the input and output for the graphics pipeline? (Ch1.7.3 / Slides)

Chapter 2/3

• What are the two shaders required for a WebGL program? What are each of them used for? (Ch 2.8.3/ 2.8.4)
• Identify a convex or concave polygon. (Ch 2.4.1)
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• What is the basic tenet of three-color theory? (Ch 2.5)
• What type of color model is RGB? What type of color model is CMY? (Ch 2.5)
• In webGL color is described with four components. What is the fourth component? (Ch 2.5.1)
• We discussed 3 types of variables that are unique to the shaders. What are the names of those three variable types and what are they used for? (Ch 2.8.1, Ch 2.10.1, Ch 3.1.1 )
• What is the default algorithm for hidden-surface-removal that is enabled with the following code gl.enable(gl.DEPTH_TEST); ? (Ch 2.10.4)
• What is picking? Briefly explain the process of picking using an extra color buffer. (Ch 3.9)

Chapter 4 - Vector Slides / Matrices Slides

Vectors

• Show the result of the vector u multiplied by the following scalar value? (Slides)
• Given the vectors u and v, show the result of u+v. (Slides)
• What is the result of point-vector addition? (Slides)
• Given two points A and B, write a mathematical expression find the vector from A to B. (Slides)
• What does it mean to normalize a vector? (Slides)
• Given the dot product result of two vectors u and v, does the value represent? (Slides)
• What are the spatial relationships between the two vectors if the dot product is 0, 1, or -1 (there is a different relationship for each case)? (Slides)
• A vector created from the cross product of two vectors has what kind of spatial relationship to the other vectors? (Slides)
• How can you tell what direction the vector resulting from a cross product will point? (Slides)
• What does the length of a cross product vector tell you? (Slides)
• Suppose we have the vector V^T = [1, 2, 3]. What is V^T in homogeneous coordinates? What is the homogeneous coordinate if V^T is a point? (Slides / Ch 4.3.4)

Matrices

• What is the transpose of the following matrix? (Slides)
• What is the identity matrix? (Slides)
• Given the matrix Q and W what is the result of QW (multiplication)? (Slides)
  • If a test question involves matrix multiplication it will be simple and no larger than multiplying a 3x3 by a 3x2
• Given matrix Q and W with the following dimensions, can the matrices be multiplied together? (Slides)
• Given matrix Q and W with the following dimensions what are the dimensions of the matrix resulting from QW (multiplication)? (Slides)
• Row Major / Column Major Order (Slides / Ch 4.5.1)
  • What order are Javascript matrices?
  • What order are GLSL matrices?
• What does it mean if a matrix has a determinant of 0? (Slides)

Transformations

Notation

NOTE: I will use the following notation (similar to the book) to represent transformations unless explicitly stated otherwise in a question:

• R_x(θ) / R_x - Rotation around x-axis (θ is angle of rotation)
• R_y(θ) / R_y - Rotation around y-axis (θ is angle of rotation)
• R_z(θ) / R_z - Rotation around z-axis (θ is angle of rotation)
• H_x(θ) / H_x - Shear along x-axis (θ is angle of shear)
• H_y(θ) / H_y - Shear along y-axis (θ is angle of shear)
• H_z(θ) / H_z - Shear along z-axis (θ is angle of shear)
• T(p_f) / T - Translation (p_f is the dispersion factor)
• S(p_f) / S - Scale (p_f is the scaling factor)

Questions

• How are matrices used in computer graphics? (Ch 4.3.2 / Ch 4.7)
• What do the components highlighted in orange (left) and blue (right) in the transformation matrix below represent? (Ch 4.8 - 4.9.4 and board notes)
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• Name the first 3 of the 6 coordinate frames in the WebGL pipeline? (Ch 4.4)
• What is a proper vertex traversal order for creating the polygon face shown below? Why? (Ch 4.6.2)
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• Around what axis is the following rotation taking place? (Ch 4.9.3)
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• Assuming a cube with side lengths 2 positioned at the origin. What is the correct transformation order for the cube to rotate around the z-axis by 35°, around the y-axis by 15°, reduce the cube’s size by 20%, position the cube in the top left corner of the viewport, and rotate around the x-axis by 45°? The result should be a small cube in the top left corner of the viewport rotated in z, y, x order. (Ch 4.10 /Ch 4.11.5)
• To perform an instance transformation, what is the correct order to apply the following transformations: (Ch 4.10.3)
  • Transformation
  • Scaling
  • Rotation
• What are the necessary transformations to rotate an object about it’s center (p_f) along the z-axis if it were NOT located at the origin? (Ch 4.10.1)
• What is a drawback of using Euler Angles for rotations? How can we avoid this issue? (Ch 4.14.3)

Chapter 5 - Viewing Slides

• How does an object’s distance from the camera affect its scale in an orthographic projection? Why? (Slides)
• What are the steps to form a perspective projection? (Slides)