Computer Graphics Flashcards

Question 1

(a) Motion Capture

• Motion capture captures the motion of a real-life actor for use in a model.
• Markers are placed on the actor's body, typically at joints, to record motion in real-time.
• Multiple calibrated cameras track the markers.
• Triangulation is used to estimate joint positions.

(b) Rendering Pipeline in 3D Graphics

• The rendering pipeline includes modeling, transformation, lighting, rasterization, and pixel shading.
• It transforms 3D objects into a 2D image by projecting vertices onto the screen.
• It applies lighting and shading calculations.
• Rasterization converts the result 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.
• This enables rendering of transparent objects like glass, while 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:
  • Better texture quality at varying distances.
  • Enhanced performance.
  • Prevention of texture popping artifacts.
• It is particularly useful in real-time graphics and scenarios where consistent texture quality across distances is critical.

(e) Global Illumination 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: ray tracing, path tracing, and radiosity.

(f) Capabilities of Rendering Algorithms

• 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

• Lighting Calculations: Normals determine how light interacts with a surface, affecting its brightness and shading. Used to compute diffuse and specular reflections accurately.
• Bump Mapping and Displacement Mapping: Used to simulate fine surface details without altering the geometry by perturbing normals, creating the illusion of bumps and deformations.
• Surface Smoothing: Normals interpolated across vertices create the illusion of smooth shading in techniques like Gouraud and Phong 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 approximated as an ideal diffuse surface.
• Backward tracing stops at the surface point.
• A shadow ray is created from the surface point to the light source.
• The gemstone occludes the shadow ray, classifying the point as in shadow.
• The highlighted area is rendered as completely in shadow, without caustics.

Path Tracing

• Many rays are shot for every pixel and follow a random walk.
• Some rays are refracted within the gemstone and hit the light source.
• Aggregating contributions of random rays simulates complex interactions.
• The illumination on the cushion surface is very realistic and includes caustics.

Question 3

Specular Highlight Calculation

• Directional light source and a 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 $t$ gives: $b = -2$ and $d = 18$.

Question 4

Transforming Shape M into Shape N

• Origin is at the center of shape M.

• First Scale shape M with two in y direction

• Second Rotate it for 45 degrees around the z-axis

• Finally, translate with the vector (+2, -2, 0)

• 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

(a) Z-buffer Algorithm with alpha = 1

• Z-buffer handles occlusions by recording the depth of each rendered pixel and overwriting it if a closer surface is rendered.
  1. Render the yellow bar.
  2. Render the green bar.
  3. Render the red bar.

(b) Algorithm Choice with alpha = 0.4

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