Computer Graphics Flashcards

Question 1

(a) Motion Capture

• Motion capture captures the motion of a model from a real-life actor.
• Markers are placed on the actor's body, typically at joints, to record motion in real time.
• Multiple calibrated cameras track the markers.
• Joint positions are estimated using triangulation.

(b) Rendering Pipeline in 3D Graphics

• The rendering pipeline includes stages like modelling, transformation, lighting, rasterisation, and pixel shading.
• It transforms 3D objects into a 2D image by projecting vertices onto the screen.
• It applies lighting and shading calculations.
• The result is rasterised into pixels for display.

(c) Significance of the Alpha Channel

• The alpha channel in texture maps represents transparency.
• It allows textures to have varying levels of opacity.
• Enables the rendering of transparent objects, maintaining realistic interactions with other objects.

(d) MIP Mapping in OpenGL

• MIP mapping improves texture rendering by creating prefiltered texture images at different resolutions.
• Advantages include better texture quality at varying distances.
• It enhances performance.
• It prevents texture popping artefacts.
• Particularly useful in real-time graphics.
• It is also useful in scenarios where consistent texture quality across distances is critical.

(e) Global vs. Local Illumination

• Global illumination simulates how light interacts with surfaces and scatters throughout a scene, considering specular and diffuse lighting.
• Local illumination models do not consider object-to-object interactions.
• Examples of global illumination techniques include ray tracing, path tracing, and radiosity.

(f) Characterizing Rendering Capabilities

• Gouraud shading: $L[D|S]E$ (single diffuse or specular reflection).
• Phong shading: $L[D|S]E$ (single diffuse or specular reflection).
• Ray tracing: $LDS^*E$ (single diffuse but multiple specular reflections).
• Radiosity method: $LD^*E$ (multiple diffuse reflections).

(g) Primary Uses of Normals

• Normals in computer graphics serve several essential purposes:
• Lighting Calculations: Normals determine how light interacts with a surface, affecting its brightness and shading. Different lighting models use normals to compute diffuse and specular reflections accurately.
• Bump Mapping and Displacement Mapping: Normals are employed in bump mapping and displacement mapping to simulate fine surface details without altering the geometry. By perturbing normals, these techniques create the illusion of bumps and deformations
• Surface Smoothing: Normals play a role in creating smooth surfaces. In techniques like Gouraud and Phong shading, normals are interpolated across vertices to create the illusion of smooth shading.

Question 2

Caustic Effects on Velvet Surface

• Scene: Gemstone on velvet cushion, with a light source.

Phong Model

• Only considers local geometry and incoming light direction.
• Reflection intensity is not affected by the gemstone.
• Velvet surface colors are represented without shadows or caustics.

Whitted Ray Tracing

• Velvet surface is approximated as an ideal diffuse surface.
• Backward tracing of the ray stops at the surface point.
• A shadow ray is created from the point to the light source.
• The gemstone occludes the shadow ray, so the point is classified as being in shadow.
• Result: Highlighted area is rendered as completely in shadow, without caustics.

Path Tracing

• Many rays are shot for every pixel on the cushion surface, following a random walk.
• Some rays are refracted within the gemstone and hit the light source.
• Aggregating contributions of all random rays simulates complex interactions.
• Result: Realistic illumination on the cushion surface, including caustics.

Question 3

Specular Highlight Calculation

• Directional light source and reflective ground plane at $x = 4$.
• Light source direction: $(3, 1, 6)$.
• Camera location: $(b, 4, d)$.
• Specular highlight peak at point: $(4, 2, 6)$.
• Reflection direction $r = (3, -1, -6)$.
• Reflection direction formula: $r = 2(n \cdot L)n - L$, where $L$ is the light direction and $n$ is the normal vector.
• Ray from reflection point to the eye: $(4, 2, 6) = (b, 4, d) + t(3, -1, -6)$.
• Solve for $t$ using the y-coordinate: $t = 2$.
• Substituting $t = 2$ gives:
  • $b = -2$
  • $d = 18$

Question 4

Transformation Matrix Sequence

• Transform shape M to shape N.
• Origin is at the center of shape M.

Steps

1. Scale shape M by 2 in the y direction.
2. Rotate it by 45 degrees around the z-axis.
3. Translate it with the vector $(+2, -2, 0)$.

Matrix

• The matrix applied to shape M is then:
  $\begin{bmatrix} 1 & 0 & 0 & 2 \ 0 & 1 & 0 & -2 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix}$
  $\begin{bmatrix} \frac{\sqrt{1}}{2} & - \frac{\sqrt{1}}{2} & 0 & 0 \ \frac{\sqrt{-1}}{2} & \frac{\sqrt{1}}{2} & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix}$
  $\begin{bmatrix} 1 & 0 & 0 & 0 \ 0 & 2 & 0 & 0 \ 0 & 0 & 1 & 0 \ 0 & 0 & 0 & 1 \end{bmatrix}$

Question 5

Z-buffer and Painter's Algorithm

(a) Z-buffer with Alpha = 1

• The Z-buffer handles occlusions by recording the depth of each rendered pixel.
• It overwrites the depth if a new, closer surface is rendered on the same location.

Rendering Order

1. Render the yellow bar.
2. Render the green bar.
3. Render the red bar.

(b) Algorithm Choice with Alpha = 0.4

• Painter's algorithm is a better choice.
• Z-buffer cannot easily deal with translucency, as it requires storing multiple depths in the depth buffer.
• Painter's algorithm can render the yellow bar by blending the pixel's color with the previous color using the appropriate alpha instead of overwriting it.