For triangle (0,0), (4,0), (0,4), what are barycentric weights at (1,1)?
A (0.25, 0.25, 0.5)
B (0.5, 0.5, 0)
C (0.25, 0.5, 0.25)
D (0.5, 0.25, 0.25)
Answer: D. (0.5, 0.25, 0.25). The point has x/4 = 0.25 and y/4 = 0.25; the remaining weight is 0.5.
Which formula perspective-correctly interpolates attribute a?
A Σλaw
B Σλa
C Σλ/w
D (Σλa/w)/(Σλ/w)
Answer: D. (Σλa/w)/(Σλ/w). Perspective-correct interpolation divides the weighted a/w sum by the weighted 1/w sum.
Where is depth-buffer precision generally greatest with standard perspective depth?
A Near plane
B Far plane
C Viewport center
D Along edges
Answer: A. Near plane. Standard perspective depth values allocate more precision to geometry near the near plane.
What commonly causes z-fighting between nearly coplanar surfaces?
A Alpha blending
B Texture coordinates
C Finite depth precision
D Excess vertices
Answer: C. Finite depth precision. Limited depth precision can map very close surfaces to indistinguishable stored values.
Which matrix correctly transforms normals under nonuniform scaling?
A Projection matrix
B Viewport matrix
C Model matrix directly
D Inverse-transpose matrix
Answer: D. Inverse-transpose matrix. Normals transform with the inverse transpose so they remain perpendicular to transformed surfaces.
Which product rotates a point about pivot p using column vectors?
A R T(p) T(−p)
B T(p) T(−p) R
C T(−p) R T(p)
D T(p) R T(−p)
Answer: D. T(p) R T(−p). Move the pivot to the origin, rotate, then translate the pivot back.
Scaling followed by rotation is represented by which product?
A S R
B R S
C R − S
D S + R
Answer: B. R S. With column vectors, the rightmost transform acts first: S then R gives R×S.
What operation converts clip coordinates to normalized device coordinates?
A Add w to xyz
B Subtract w from xyz
C Divide xyz by w
D Multiply xyz by w
Answer: C. Divide xyz by w. Perspective division computes x/w, y/w, and z/w.
When is primitive clipping performed in the standard programmable pipeline?
A After display scanout
B After framebuffer blending
C Before vertex processing
D Before perspective division
Answer: D. Before perspective division. Primitives are clipped in homogeneous clip space before perspective division and viewport mapping.
What guarantees trivial rejection in Cohen–Sutherland clipping?
A Shared nonzero outcode bit
B Equal endpoint coordinates
C One outcode is zero
D Both outcodes are zero
Answer: A. Shared nonzero outcode bit. A common set bit means both endpoints are outside the same clipping half-plane.
Window x=5 maps from [2,10] into viewport [100,500]. What is x’?
A 200
B 250
C 350
D 300
Answer: B. 250. The fraction is (5−2)/(10−2)=3/8; 100+(3/8)×400 equals 250.
What is the derivative of a cubic Bézier at its start?
A P3 − P0
B P2 − P0
C 3(P1 − P0)
D 3(P3 − P2)
Answer: C. 3(P1 − P0). The cubic Bézier endpoint derivative at t=0 is 3(P1−P0).
De Casteljau evaluates a 1D quadratic with points 0, 4, 8 at t=0.5. What is the value?
A 6
B 4
C 2
D 8
Answer: B. 4. Interpolate 0-to-4 and 4-to-8 to get 2 and 6, then interpolate them to get 4.
Weights (0.2, 0.3, 0.5) combine values (10, 20, 40). What is the result?
A 30
B 34
C 24
D 28
Answer: D. 28. The weighted sum is 0.2×10 + 0.3×20 + 0.5×40 = 28.
Lambert diffuse response at a 60° light angle is proportional to what?
A 1
B 0.5
C 0
D √3
Answer: B. 0.5. The diffuse factor is max(cos 60°,0), which equals 0.5.
In Phong specular reflection, when is the highlight strongest?
A Camera faces away
B Normal aligns texture
C Reflected ray aligns view
D Light meets viewport
Answer: C. Reflected ray aligns view. The specular term peaks when the reflected light direction aligns with the viewing direction.
Opaque background, αf=0.25: what is foreground-over-background color?
A 0.25Cf + 0.75Cb
B 0.75Cf + 0.25Cb
C Cf + Cb
D 0.25Cf + Cb
Answer: A. 0.25Cf + 0.75Cb. Standard source-over compositing weights foreground by its alpha and background by one minus alpha.
Strong texture minification generally calls for which mipmap level?
A Lower-resolution level
B Depth-only level
C No texture level
D Highest-resolution level
Answer: A. Lower-resolution level. A smaller, prefiltered mip level better represents a texture footprint covering many source texels.
Four equal supersamples are 0, 20, 40, and 80. What average is resolved?
A 40
B 30
C 35
D 45
Answer: C. 35. Their sum is 140, and dividing by four yields 35.
Which interval must geometry intersect to block a shadow ray?
A Surface to light
B Camera to surface
C Beyond the light
D Behind the surface
Answer: A. Surface to light. An occluder between the shaded point and the light prevents direct illumination.
For a ray-sphere quadratic, what does a negative discriminant mean?
A Two forward hits
B No real intersection
C Sphere center hit
D One tangent hit
Answer: B. No real intersection. A negative discriminant gives no real roots, so the ray misses the sphere.
Using even-odd filling, a sample is inside after how many boundary crossings?
A Even crossings
B Exactly two crossings
C Zero crossings only
D Odd crossings
Answer: D. Odd crossings. The parity rule alternates in and out at every boundary crossing; an odd count means inside.
Where does a Bézier curve lie relative to its control points?
A Only on its tangent
B Inside their convex hull
C Outside every control point
D On the control polygon
Answer: B. Inside their convex hull. The convex-hull property keeps the Bézier curve inside the convex hull of its control points.
Changing one B-spline control point usually affects which region?
A The camera projection
B Only the endpoints
C Nearby spline spans
D Every curve in scene
Answer: C. Nearby spline spans. B-spline basis functions have local support, limiting a control point’s effect to nearby spans.
Triangle attribute interpolation at each fragment uses what weights?
A Barycentric coordinates
B Clip outcodes
C Texture dimensions
D Camera Euler angles
Answer: A. Barycentric coordinates. Rasterized triangle attributes are interpolated from vertices using barycentric weights.