CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
Part 1: Ray Tracing & Perspective (Questions 1-20)
1. In Whitted-style ray tracing, when a primary ray hits a transparent surface, which of the following
is recursively cast?
A) Shadow rays only
B) Reflected rays only
C) Refracted and reflected rays
D) Ambient occlusion rays
Correct Answer: C
Rationale: Whitted-style ray tracing recursively spawns reflection and refraction (transmission) rays
at the intersection point. Shadow rays are cast towards light sources, but not recursively from the hit
point for further bounces.
2. The "pinhole camera" model in ray tracing is typically implemented by:
A) Placing the camera at the origin and generating rays parallel to the view direction.
B) Generating rays from the image plane through the center of projection (COP).
C) Defining a lens aperture and sampling multiple points on the lens.
D) Using a single ray per pixel with no variation.
Correct Answer: B
Rationale: The pinhole model assumes an infinitely small aperture. Rays originate from the camera
position (the pinhole) and pass through each pixel on the virtual image plane.
3. A common technique to reduce aliasing in ray tracing is:
A) Increasing the ray depth.
B) Using a higher resolution framebuffer without changing the scene.
C) Stochastic sampling (e.g., jittering) of rays within a pixel.
D) Using a single sample per pixel with a sharper filter.
Correct Answer: C
Rationale: Aliasing is caused by undersampling. Stochastic (Monte Carlo) sampling, including
jittering, distributes samples within a pixel to convert high-frequency aliasing into lower-frequency
noise, which is less visually objectionable.
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
4. The primary purpose of the Z-buffer in the rendering pipeline is to:
A) Store texture coordinates.
B) Determine visibility for opaque objects.
C) Store surface normals for lighting.
D) Accelerate ray-triangle intersections.
Correct Answer: B
Rationale: The Z-buffer (or depth buffer) stores the depth of the closest fragment rendered so far.
When a new fragment is drawn, its depth is compared to the stored value; only closer fragments are
written, solving the visibility problem.
5. In the context of a perspective transformation matrix (4x4 in clip space), the term in the
w
w component (after multiplication) is used for:
A) Perspective divide (converting to NDC).
B) Calculating ambient occlusion.
C) Determining the radius of a point sprite.
D) Modulating the alpha channel.
Correct Answer: A
Rationale: In perspective projection, the matrix modifies the
z
z and
w
w components. After matrix multiplication, the hardware performs a homogeneous divide (
x
/
w
,
y
/
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
w
,
z
/
w
x/w,y/w,z/w), which creates the perspective foreshortening effect.
6. Which of the following is NOT a valid Ray-Box intersection test accelerator?
A) Slabs method (Kay-Kajiya)
B) BVH (Bounding Volume Hierarchy)
C) Phong Reflection Model
D) Grid-based spatial subdivision
Correct Answer: C
Rationale: The Phong model is a local illumination model for shading surfaces, not a data structure
or algorithm for accelerating ray intersection tests.
7. A transformation matrix that is defined as the transpose of its inverse is guaranteed to be:
A) Skew-symmetric
B) Orthogonal
C) Perspective
D) Shear
Correct Answer: B
Rationale: A matrix
M
M is orthogonal if
M
T
=
M
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
−
1
M
T
=M
−1
. Orthogonal matrices preserve lengths and angles; they are used for pure rotations and reflections.
8. What does the "cross product" of two vectors in 3D space produce?
A) A scalar representing the dot product.
B) A vector perpendicular to both input vectors.
C) A vector projected onto the plane of the two vectors.
D) A scalar representing the area of the parallelogram.
Correct Answer: B
Rationale: The cross product
a
×
b
a×b results in a vector that is orthogonal to both
a
a and
b
b. Its magnitude equals the area of the parallelogram spanned by the two vectors.
9. In a homogeneous coordinate system, a point (as opposed to a vector) is represented with a
w
w component of:
A) 0
B) 1
and correct answers and rationale
graded A+ updated 2026 new!!
Part 1: Ray Tracing & Perspective (Questions 1-20)
1. In Whitted-style ray tracing, when a primary ray hits a transparent surface, which of the following
is recursively cast?
A) Shadow rays only
B) Reflected rays only
C) Refracted and reflected rays
D) Ambient occlusion rays
Correct Answer: C
Rationale: Whitted-style ray tracing recursively spawns reflection and refraction (transmission) rays
at the intersection point. Shadow rays are cast towards light sources, but not recursively from the hit
point for further bounces.
2. The "pinhole camera" model in ray tracing is typically implemented by:
A) Placing the camera at the origin and generating rays parallel to the view direction.
B) Generating rays from the image plane through the center of projection (COP).
C) Defining a lens aperture and sampling multiple points on the lens.
D) Using a single ray per pixel with no variation.
Correct Answer: B
Rationale: The pinhole model assumes an infinitely small aperture. Rays originate from the camera
position (the pinhole) and pass through each pixel on the virtual image plane.
3. A common technique to reduce aliasing in ray tracing is:
A) Increasing the ray depth.
B) Using a higher resolution framebuffer without changing the scene.
C) Stochastic sampling (e.g., jittering) of rays within a pixel.
D) Using a single sample per pixel with a sharper filter.
Correct Answer: C
Rationale: Aliasing is caused by undersampling. Stochastic (Monte Carlo) sampling, including
jittering, distributes samples within a pixel to convert high-frequency aliasing into lower-frequency
noise, which is less visually objectionable.
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
4. The primary purpose of the Z-buffer in the rendering pipeline is to:
A) Store texture coordinates.
B) Determine visibility for opaque objects.
C) Store surface normals for lighting.
D) Accelerate ray-triangle intersections.
Correct Answer: B
Rationale: The Z-buffer (or depth buffer) stores the depth of the closest fragment rendered so far.
When a new fragment is drawn, its depth is compared to the stored value; only closer fragments are
written, solving the visibility problem.
5. In the context of a perspective transformation matrix (4x4 in clip space), the term in the
w
w component (after multiplication) is used for:
A) Perspective divide (converting to NDC).
B) Calculating ambient occlusion.
C) Determining the radius of a point sprite.
D) Modulating the alpha channel.
Correct Answer: A
Rationale: In perspective projection, the matrix modifies the
z
z and
w
w components. After matrix multiplication, the hardware performs a homogeneous divide (
x
/
w
,
y
/
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
w
,
z
/
w
x/w,y/w,z/w), which creates the perspective foreshortening effect.
6. Which of the following is NOT a valid Ray-Box intersection test accelerator?
A) Slabs method (Kay-Kajiya)
B) BVH (Bounding Volume Hierarchy)
C) Phong Reflection Model
D) Grid-based spatial subdivision
Correct Answer: C
Rationale: The Phong model is a local illumination model for shading surfaces, not a data structure
or algorithm for accelerating ray intersection tests.
7. A transformation matrix that is defined as the transpose of its inverse is guaranteed to be:
A) Skew-symmetric
B) Orthogonal
C) Perspective
D) Shear
Correct Answer: B
Rationale: A matrix
M
M is orthogonal if
M
T
=
M
, CS 559 Midterm Exam with questions
and correct answers and rationale
graded A+ updated 2026 new!!
−
1
M
T
=M
−1
. Orthogonal matrices preserve lengths and angles; they are used for pure rotations and reflections.
8. What does the "cross product" of two vectors in 3D space produce?
A) A scalar representing the dot product.
B) A vector perpendicular to both input vectors.
C) A vector projected onto the plane of the two vectors.
D) A scalar representing the area of the parallelogram.
Correct Answer: B
Rationale: The cross product
a
×
b
a×b results in a vector that is orthogonal to both
a
a and
b
b. Its magnitude equals the area of the parallelogram spanned by the two vectors.
9. In a homogeneous coordinate system, a point (as opposed to a vector) is represented with a
w
w component of:
A) 0
B) 1
