For a 640 × 480 viewport, what ratio describes its width and height?
A 16:9
B 3:4
C 5:4
D 4:3
Answer: D. 4:3. Dividing both dimensions by 160 reduces 640:480 to 4:3.
Given x=2 in window [0,10] and viewport [100,500], where does x map?
A 200
B 160
C 240
D 180
Answer: D. 180. The scale is 400/10; thus x’ = 100 + 2×40 = 180.
Scaling point (2, −3) by factors (2, 1) gives which point?
A (4, −3)
B (2, −3)
C (4, −6)
D (1, −3)
Answer: A. (4, −3). Apply each scale factor to its matching coordinate: (2×2, −3×1).
Translating (2, −1) by (3, 4) gives which point?
A (5, 3)
B (6, 3)
C (−1, −5)
D (5, −5)
Answer: A. (5, 3). Translation adds coordinates componentwise: (2+3, −1+4).
Which point results from rotating (1, 0) 90° counterclockwise?
A (0, 1)
B (1, 0)
C (−1, 0)
D (0, −1)
Answer: A. (0, 1). A positive quarter-turn maps the positive x-axis onto the positive y-axis.
Rotating (2, 1) by 90° counterclockwise about (1, 1) gives what?
A (2, 1)
B (1, 0)
C (0, 2)
D (1, 2)
Answer: D. (1, 2). Translate relative to the pivot to (1,0), rotate to (0,1), then translate back to (1,2).
With column vectors, which product applies scaling before rotation?
A S − R
B R + S
C R × S
D S × R
Answer: C. R × S. Matrix operations act right to left, so R×S scales first and rotates second.
After perspective division, which coordinates are produced?
A (x+w, y+w, z+w)
B (x/w, y/w, z/w)
C (x, y, z)
D (wx, wy, wz)
Answer: B. (x/w, y/w, z/w). Perspective division divides clip-space x, y, and z by homogeneous w.
Given a camera pose from camera to world space, what gives view coordinates?
A Texture transform
B Viewport transform
C Inverse camera pose
D Camera pose
Answer: C. Inverse camera pose. View coordinates are obtained by applying the inverse of the camera’s world pose.
Geometry crossing the near view boundary is handled by which operation?
A Curve subdivision
B Near-plane clipping
C Texture filtering
D Color quantization
Answer: B. Near-plane clipping. Clipping trims or rejects geometry against the near plane before rasterization.
What must the three barycentric weights of a triangle point sum to?
A One
B The area
C Zero
D Three
Answer: A. One. Barycentric coordinates of a point inside a triangle sum to one.
How are vertex attributes interpolated over a rasterized triangle?
A Nearest face normal
B Sorted vertex indices
C Average edge lengths
D Weighted vertex attributes
Answer: D. Weighted vertex attributes. Barycentric weights combine the values at the triangle’s vertices.
Under a conventional smaller-is-nearer depth convention, which sample passes?
A Nearer depth value
B Higher alpha value
C Larger depth value
D Older color value
Answer: A. Nearer depth value. With smaller normalized depth representing nearer geometry, the lower value wins the depth test.
During triangle rasterization, what can an edge function determine?
A Polygon material index
B Inside orientation tests
C Camera roll angle
D Texture color depth
Answer: B. Inside orientation tests. Edge functions evaluate signed orientation and can test whether sample points lie inside a triangle.
For DDA with dx = 12 and dy = 5, how many steps are taken?
A 60
B 5
C 12
D 17
Answer: C. 12. DDA uses max(|12|,|5|), which is 12.
While drawing a line, what does Bresenham update?
A Texture matrix
B Camera basis
C Color histogram
D Decision error
Answer: D. Decision error. Bresenham incrementally updates a decision or error term to choose the next raster sample.
The segment (0,0) to (10,10) meets y = 6 at which point?
A (10, 6)
B (4, 6)
C (6, 6)
D (6, 4)
Answer: C. (6, 6). The segment follows x=y, so at y=6 its x-coordinate is also 6.
How does Sutherland–Hodgman build a clipped polygon?
A Each texture layer
B Each depth value
C Each screen pixel
D Each clipping boundary
Answer: D. Each clipping boundary. It processes the polygon against each clip boundary in sequence.
Scan-line filling uses which crossings to define spans?
A Texture mip levels
B Sorted edge intersections
C Sorted surface normals
D Camera ray lengths
Answer: B. Sorted edge intersections. Ordered intersections with polygon edges mark alternating inside and outside spans.
Why can Gouraud shading miss a small specular highlight?
A It uses no vertices
B It interpolates vertex intensities
C It removes the depth buffer
D It clips every highlight
Answer: B. It interpolates vertex intensities. A narrow highlight may fall between vertices after lighting is computed only at vertices.
Four texels have values 0, 10, 20, and 30. What is their bilinear value at the center?
A 20
B 10
C 15
D 30
Answer: C. 15. At the center all four texels have equal weight, so their mean is 15.
Supersampling combines multiple subpixel colors using what operation?
A Maximum sample depth
B Mean sample color
C Median polygon size
D First vertex color
Answer: B. Mean sample color. A common resolve averages the subpixel samples to estimate the pixel color.
For highest image frequency f, what minimum sampling rate avoids aliasing ideally?
A Exactly f/4
B At least f/2
C Any positive rate
D At least 2f
Answer: D. At least 2f. The Nyquist criterion requires a sampling rate greater than twice the highest frequency.
How many control points define a cubic Bézier curve?
A Six
B Five
C Four
D Three
Answer: C. Four. A degree-three Bézier curve uses four control points, from P0 through P3.
At its start, what is the derivative of a cubic Bézier curve?
A 3(P1 − P0)
B P2 − P1
C 3(P3 − P2)
D P3 − P0
Answer: A. 3(P1 − P0). Differentiating the cubic Bézier at t=0 yields three times the first control-edge vector.