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Worked solutions

IB Computer Science HL · Paper 3

Computer Science, Higher Level

Session: May 2016
Marks: 30
Duration: 1 hour
Calculator: Not allowed
Questions: 4

Keep your copy of the paper open alongside. We don't reproduce the questions: each part below is labelled to match the May 2016 Global paper, which your school or the IB can provide.

Practice mode

Hide our working until you've had a go.

Questions

Questions 1–4 · 30 marks

Question 1

4 marks

Defining the rendering equation and role of cels in 2D animation

Modelling and simulation

(a)

2 marks

Define the rendering equation in computer graphics:
The rendering equation is an integral equation based on the physical law of conservation of light energy that calculates the total spectral radiance exiting a point on a surface in a given direction.
It computes the total emitted light from the surface plus the integral of all incoming incident light arriving from all directions across the hemisphere, scaled by the material's bidirectional reflectance distribution function (BRDF) and the surface normal angle.

L_{o} (x, ω_{o}) = L_{e} (x, ω_{o}) + \int_{Ω} f_{r} (x, ω_{i}, ω_{o}) L_{i} (x, ω_{i}) (ω_{i} \cdot n) d ω_{i}

Mentor tip

State that it is an integral equation computing total outgoing light as the sum of self-emitted light and reflected incoming light from all surrounding directions.

(b)

2 marks

Outline the use of transparent cels in constructing a 2D animated scene:
A cel is a transparent celluloid or acetate sheet onto which individual foreground characters, moving components, or visual props are drawn and painted.
Multiple cels are layered on top of each other over a single static painted background to produce a complete animated frame, eliminating the need to redraw static background elements for every individual frame.

Mentor tip

Explain that layering transparent sheets over a static background allows animators to update only the moving character elements from frame to frame.

Question 2

8 marks

Comparing tweening with morphing and evaluating the uncanny valley effect

Modelling and simulation

(a)

4 marks

Compare the animation techniques of tweening and morphing:
1) Common underlying concept: Both methods generate intermediate transition frames between two designated keyframes or states to create smooth, continuous visual transformation.
2) Purpose and scope of tweening: In-betweening (tweening) interpolates position, rotation, scale, or limb joint variables (avars) of the exact same geometric object over time across a scene, simulating natural physical movement or camera translation without modifying the underlying structural identity of the object.
3) Purpose and scope of morphing: Morphing transforms one distinct visual entity into an entirely different visual entity (e.g., transforming a human face into a feline face) by combining geometric shape warping with cross-dissolve color blending.
4) Algorithmic distinction: While tweening calculates mathematical trajectory curves (e.g., Bézier interpolation) along consistent control coordinates, morphing requires establishing feature correspondence mesh points between disparate source and target images to deform coordinate grids progressively.

Mentor tip

Distinguish between moving the same object across space (tweening) versus altering one visual entity into a completely different entity via warping and blending (morphing).

(b)

4 marks

Explain the uncanny valley effect and its implications for 3D animators:
1) Definition of the phenomenon: The uncanny valley describes a psychological response where an artificial figure (such as a 3D animated human) appears almost indistinguishable from a living person, but exhibits subtle flaws in eye motion, skin elasticity, or micro-expressions, evoking strong feelings of revulsion, unease, or visual discomfort in observers.
2) Human visual sensitivity: Human neural processing is acutely attuned to detecting tiny anomalies in facial cadence and emotional responses; near-human models that fail to achieve absolute perfection appear lifeless or diseased rather than appealing.
3) Stylized alternative strategy: Animators frequently adopt stylized, cartoon aesthetics (such as exaggerated proportions and whimsical facial features), stopping well short of realism where audiences readily form emotional empathy without expecting biological accuracy.
4) Photorealistic alternative strategy: If realistic humans are necessary, production teams must invest extensive computational and rendering resources to cross the valley entirely, capturing authentic human motion capture and simulating complex subsurface light scattering across skin layers.

Mentor tip

Explain that the uncanny valley occurs when an animation is near-human but slightly flawed, creating revulsion, requiring animators either to adopt stylized aesthetics or achieve near-flawless realism.

Question 3

6 marks

Terrain generation using midpoint displacement fractal algorithms

Modelling and simulation

6 marks

Explain how fractal midpoint displacement algorithms generate realistic 3D mountainous terrain starting from a simple initial rectangle:
1) Boundary initialization: The algorithm defines an initial planar rectangular grid, assigning elevation (height) values to the four corner vertices $(z_{1}, z_{2}, z_{3}, z_{4})$ , which may be randomized or preset.
2) Subdividing edges and center: The algorithm calculates midpoint coordinates along all four perimeter edges and determines the center intersection point of the rectangle, bisecting the geometry into four smaller rectangular quadrants.
3) Midpoint height calculation: The elevation value for each newly generated midpoint is computed by calculating the arithmetic mean of the adjacent bounding corner heights.
4) Stochastic displacement injection: To simulate natural geographic ruggedness rather than flat geometric planes, the algorithm adds a pseudo-random displacement perturbation $Δ z$ to each calculated midpoint elevation: $z_{mid} = \frac{1}{2} (z_{a} + z_{b}) + R \cdot s$ , where $R$ is a random scalar and $s$ represents the current scale factor.
5) Recursive roughness decay: The displacement perturbation amplitude is scaled down by a roughness factor $2^{- H}$ (where $H$ relates to fractal dimension) at each successive subdivision level, ensuring large macro-features (peaks and valleys) emerge in early passes while fine surface texture (rocks and crags) develops in late passes.
6) Termination condition: The diamond-square or midpoint division process executes recursively across all generated sub-rectangles until reaching a predetermined recursion depth or until triangle polygon sizes correspond to individual screen pixel dimensions.

z_{mid} = \frac{z _{A} + z _{B}}{2} + random (- 1, 1) \times σ \times 2^{- i \cdot H}

Mentor tip

Structure the explanation through initial boundary corners, midpoint averaging, adding random displacement, reducing the perturbation amplitude recursively, and terminating at the target resolution.

Question 4

12 marks

Technical evaluation of 3D modeling and rendering pipelines for home computer gaming

Modelling and simulation

12 marks

Discuss the technical considerations for selecting 3D modeling and rendering methodologies for Pacific FX's animated human computer game targeting consumer home hardware:
Target platform constraints and operational requirements:
- Hardware limitations of home computers: Unlike offline film production clusters that spend hours rendering individual frames, interactive PC video games must execute all geometry transformations, physics simulations, and surface rendering in real time at sustained display rates (30 to 60+ frames per second) on varied consumer GPU and CPU configurations.
Techniques for creating 3D wireframe models:
- Manual polygon modeling and subdivision surfaces: Artists construct base low-polygon control cages using 3D modeling suites, applying subdivision surfaces to smooth curved body contours during authoring. Low-polygon models conserve runtime memory and geometry pipeline processing, making them ideal for consumer graphics cards.
- 3D laser/optical scanning: Captures dense point-cloud geometry directly from physical human actors. While providing exceptional anatomical fidelity, raw scanned meshes produce millions of unstructured polygons that saturate consumer RAM and bus bandwidth, requiring labor-intensive manual retopology to convert into game-ready meshes.
Character animation methodologies:
- Keyframe animation with algorithmic tweening: Animators establish primary key poses, and interpolation algorithms (linear, cubic, or spherical Bézier splines) compute intermediate positions for articulated avars (animation variables). This approach offers creative control and minimal file storage, though complex human motion can occasionally appear mechanical.
- Optical Motion Capture (Mo-Cap): Multiple synchronized cameras track reflective markers on live actors, recording real-world 3D joint rotations frame by frame. Mo-cap delivers exceptionally natural physical cadence and authentic nuance, neutralizing uncanny valley risks, but requires specialized studio facilities and cleaning up noisy capture data before runtime integration.
Scene rendering architectures:
- Ray-tracing pipeline: Traces optical ray paths through each screen pixel into the 3D scene, recursively calculating reflections, refractions, and global illumination by resolving light-surface intersections. While physically accurate, recursive ray-intersection tests across complex scenes demand immense computational processing that exceeds the real-time capabilities of mainstream consumer hardware in 2016.
- Scanline rendering / rasterization with programmable shaders: Projects 3D polygonal primitives onto a 2D viewport line-by-line, utilizing hardware Z-buffering for depth sorting and applying programmable vertex and pixel shaders for localized lighting (Phong, Blinn-Phong, texture mapping, and normal mapping). This pipeline aligns directly with modern consumer GPU rasterization architectures, delivering high-speed, interactive frame rates.
Balanced strategic synthesis and recommendation:
Pacific FX should implement an optimized rasterization pipeline. For character construction, they should combine motion capture data mapped onto clean, retopologized polygon meshes with skeletal inverse kinematics. For rendering, they should deploy scanline rasterization enhanced by normal mapping, specular highlights, and pre-baked ambient occlusion, achieving compelling visual realism while maintaining fluid 60 FPS gameplay on consumer home computers.

Mentor tip

Address both 3D wireframe modeling/animation (manual modeling vs 3D scanning, tweening vs Mo-cap) and rendering (scanline rasterization vs ray-tracing), firmly grounded in real-time consumer PC constraints.

Our analysis

Where the marks are

Each part sorted by the topic it mostly tests. Modelling and simulation carries the most marks on this paper.

Modelling and simulation30 marks · 100%
Q1, Q2, Q3, Q4

Mentor insights

Traps to watch for

01
Viewing the rendering equation as a simple linear formula · Q1
The rendering equation is an integral equation that models global illumination across all hemisphere directions, not a simple linear shading equation like basic Phong.
02
Confusing tweening between keyframes with morphing between meshes · Q2
Tweening animates the position or rotation of an identical object across time, whereas morphing algorithmically reshapes one visual object into another via spatial warping and color interpolation.
03
Recommending offline ray-tracing for a real-time home computer game · Q4
Pure recursive ray-tracing was computationally prohibitive for real-time 60 FPS consumer PC games in 2016; scanline rasterization with GPU shaders was the industry standard.

Solutions and tips are GeorgeTheTutor's own; the questions are not reproduced here. Not affiliated with or endorsed by the International Baccalaureate Organization.

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Worked solutions

IB Computer Science HL · Paper 3

Computer Science, Higher Level

Session: May 2016
Marks: 30
Duration: 1 hour
Calculator: Not allowed
Questions: 4

Q1 Q2 Q3 Q4

Keep your copy of the paper open alongside. We don't reproduce the questions: each part below is labelled to match the May 2016 Global paper, which your school or the IB can provide.

Practice mode

Hide our working until you've had a go.

Questions

Questions 1–4 · 30 marks

Question 1

4 marks

Defining the rendering equation and role of cels in 2D animation

Modelling and simulation

(a)

2 marks

Define the rendering equation in computer graphics:
The rendering equation is an integral equation based on the physical law of conservation of light energy that calculates the total spectral radiance exiting a point on a surface in a given direction.
It computes the total emitted light from the surface plus the integral of all incoming incident light arriving from all directions across the hemisphere, scaled by the material's bidirectional reflectance distribution function (BRDF) and the surface normal angle.

L_{o} (x, ω_{o}) = L_{e} (x, ω_{o}) + \int_{Ω} f_{r} (x, ω_{i}, ω_{o}) L_{i} (x, ω_{i}) (ω_{i} \cdot n) d ω_{i}

Mentor tip

State that it is an integral equation computing total outgoing light as the sum of self-emitted light and reflected incoming light from all surrounding directions.

(b)

2 marks

Outline the use of transparent cels in constructing a 2D animated scene:
A cel is a transparent celluloid or acetate sheet onto which individual foreground characters, moving components, or visual props are drawn and painted.
Multiple cels are layered on top of each other over a single static painted background to produce a complete animated frame, eliminating the need to redraw static background elements for every individual frame.

Mentor tip

Explain that layering transparent sheets over a static background allows animators to update only the moving character elements from frame to frame.

Question 2

8 marks

Comparing tweening with morphing and evaluating the uncanny valley effect

Modelling and simulation

(a)

4 marks

Compare the animation techniques of tweening and morphing:
1) Common underlying concept: Both methods generate intermediate transition frames between two designated keyframes or states to create smooth, continuous visual transformation.
2) Purpose and scope of tweening: In-betweening (tweening) interpolates position, rotation, scale, or limb joint variables (avars) of the exact same geometric object over time across a scene, simulating natural physical movement or camera translation without modifying the underlying structural identity of the object.
3) Purpose and scope of morphing: Morphing transforms one distinct visual entity into an entirely different visual entity (e.g., transforming a human face into a feline face) by combining geometric shape warping with cross-dissolve color blending.
4) Algorithmic distinction: While tweening calculates mathematical trajectory curves (e.g., Bézier interpolation) along consistent control coordinates, morphing requires establishing feature correspondence mesh points between disparate source and target images to deform coordinate grids progressively.

Mentor tip

Distinguish between moving the same object across space (tweening) versus altering one visual entity into a completely different entity via warping and blending (morphing).

(b)

4 marks

Explain the uncanny valley effect and its implications for 3D animators:
1) Definition of the phenomenon: The uncanny valley describes a psychological response where an artificial figure (such as a 3D animated human) appears almost indistinguishable from a living person, but exhibits subtle flaws in eye motion, skin elasticity, or micro-expressions, evoking strong feelings of revulsion, unease, or visual discomfort in observers.
2) Human visual sensitivity: Human neural processing is acutely attuned to detecting tiny anomalies in facial cadence and emotional responses; near-human models that fail to achieve absolute perfection appear lifeless or diseased rather than appealing.
3) Stylized alternative strategy: Animators frequently adopt stylized, cartoon aesthetics (such as exaggerated proportions and whimsical facial features), stopping well short of realism where audiences readily form emotional empathy without expecting biological accuracy.
4) Photorealistic alternative strategy: If realistic humans are necessary, production teams must invest extensive computational and rendering resources to cross the valley entirely, capturing authentic human motion capture and simulating complex subsurface light scattering across skin layers.

Mentor tip

Question 3

6 marks

Terrain generation using midpoint displacement fractal algorithms

Modelling and simulation

6 marks

Explain how fractal midpoint displacement algorithms generate realistic 3D mountainous terrain starting from a simple initial rectangle:
1) Boundary initialization: The algorithm defines an initial planar rectangular grid, assigning elevation (height) values to the four corner vertices $(z_{1}, z_{2}, z_{3}, z_{4})$ , which may be randomized or preset.
2) Subdividing edges and center: The algorithm calculates midpoint coordinates along all four perimeter edges and determines the center intersection point of the rectangle, bisecting the geometry into four smaller rectangular quadrants.
3) Midpoint height calculation: The elevation value for each newly generated midpoint is computed by calculating the arithmetic mean of the adjacent bounding corner heights.
4) Stochastic displacement injection: To simulate natural geographic ruggedness rather than flat geometric planes, the algorithm adds a pseudo-random displacement perturbation $Δ z$ to each calculated midpoint elevation: $z_{mid} = \frac{1}{2} (z_{a} + z_{b}) + R \cdot s$ , where $R$ is a random scalar and $s$ represents the current scale factor.
5) Recursive roughness decay: The displacement perturbation amplitude is scaled down by a roughness factor $2^{- H}$ (where $H$ relates to fractal dimension) at each successive subdivision level, ensuring large macro-features (peaks and valleys) emerge in early passes while fine surface texture (rocks and crags) develops in late passes.
6) Termination condition: The diamond-square or midpoint division process executes recursively across all generated sub-rectangles until reaching a predetermined recursion depth or until triangle polygon sizes correspond to individual screen pixel dimensions.

z_{mid} = \frac{z _{A} + z _{B}}{2} + random (- 1, 1) \times σ \times 2^{- i \cdot H}

Mentor tip

Structure the explanation through initial boundary corners, midpoint averaging, adding random displacement, reducing the perturbation amplitude recursively, and terminating at the target resolution.

Question 4

12 marks

Technical evaluation of 3D modeling and rendering pipelines for home computer gaming

Modelling and simulation

12 marks

Discuss the technical considerations for selecting 3D modeling and rendering methodologies for Pacific FX's animated human computer game targeting consumer home hardware:
Target platform constraints and operational requirements:
- Hardware limitations of home computers: Unlike offline film production clusters that spend hours rendering individual frames, interactive PC video games must execute all geometry transformations, physics simulations, and surface rendering in real time at sustained display rates (30 to 60+ frames per second) on varied consumer GPU and CPU configurations.
Techniques for creating 3D wireframe models:
- Manual polygon modeling and subdivision surfaces: Artists construct base low-polygon control cages using 3D modeling suites, applying subdivision surfaces to smooth curved body contours during authoring. Low-polygon models conserve runtime memory and geometry pipeline processing, making them ideal for consumer graphics cards.
- 3D laser/optical scanning: Captures dense point-cloud geometry directly from physical human actors. While providing exceptional anatomical fidelity, raw scanned meshes produce millions of unstructured polygons that saturate consumer RAM and bus bandwidth, requiring labor-intensive manual retopology to convert into game-ready meshes.
Character animation methodologies:
- Keyframe animation with algorithmic tweening: Animators establish primary key poses, and interpolation algorithms (linear, cubic, or spherical Bézier splines) compute intermediate positions for articulated avars (animation variables). This approach offers creative control and minimal file storage, though complex human motion can occasionally appear mechanical.
- Optical Motion Capture (Mo-Cap): Multiple synchronized cameras track reflective markers on live actors, recording real-world 3D joint rotations frame by frame. Mo-cap delivers exceptionally natural physical cadence and authentic nuance, neutralizing uncanny valley risks, but requires specialized studio facilities and cleaning up noisy capture data before runtime integration.
Scene rendering architectures:
- Ray-tracing pipeline: Traces optical ray paths through each screen pixel into the 3D scene, recursively calculating reflections, refractions, and global illumination by resolving light-surface intersections. While physically accurate, recursive ray-intersection tests across complex scenes demand immense computational processing that exceeds the real-time capabilities of mainstream consumer hardware in 2016.
- Scanline rendering / rasterization with programmable shaders: Projects 3D polygonal primitives onto a 2D viewport line-by-line, utilizing hardware Z-buffering for depth sorting and applying programmable vertex and pixel shaders for localized lighting (Phong, Blinn-Phong, texture mapping, and normal mapping). This pipeline aligns directly with modern consumer GPU rasterization architectures, delivering high-speed, interactive frame rates.
Balanced strategic synthesis and recommendation:
Pacific FX should implement an optimized rasterization pipeline. For character construction, they should combine motion capture data mapped onto clean, retopologized polygon meshes with skeletal inverse kinematics. For rendering, they should deploy scanline rasterization enhanced by normal mapping, specular highlights, and pre-baked ambient occlusion, achieving compelling visual realism while maintaining fluid 60 FPS gameplay on consumer home computers.

Mentor tip

Our analysis

Where the marks are

Each part sorted by the topic it mostly tests. Modelling and simulation carries the most marks on this paper.

Modelling and simulation30 marks · 100%
Q1, Q2, Q3, Q4

Mentor insights

Traps to watch for

01
Viewing the rendering equation as a simple linear formula · Q1
The rendering equation is an integral equation that models global illumination across all hemisphere directions, not a simple linear shading equation like basic Phong.
02
Confusing tweening between keyframes with morphing between meshes · Q2
Tweening animates the position or rotation of an identical object across time, whereas morphing algorithmically reshapes one visual object into another via spatial warping and color interpolation.
03
Recommending offline ray-tracing for a real-time home computer game · Q4
Pure recursive ray-tracing was computationally prohibitive for real-time 60 FPS consumer PC games in 2016; scanline rasterization with GPU shaders was the industry standard.

Solutions and tips are GeorgeTheTutor's own; the questions are not reproduced here. Not affiliated with or endorsed by the International Baccalaureate Organization.

Want someone to go through your paper with you?

Our maths mentors took these exams recently. One-to-one, they'll find where your marks are going and fix it before May.

Find your maths mentor More past papers