Computer Graphics - Exam Notes

Motion Capture

• Motion capture aims at capturing the motion of a model from a real-life actor.
• Procedure:
  • Placing markers on the actor’s body (typically at joints) to record motion in real-time.
  • Markers are tracked using multiple calibrated cameras.
  • Joint position is estimated using triangulation.

Rendering Pipeline in 3D Graphics

• Stages: modelling, transformation, lighting, rasterisation, and pixel shading.
• Process: Transforms 3D objects into a 2D image by:
  • Projecting vertices onto the screen.
  • Applying lighting and shading calculations.
  • Rasterising the result into pixels for display.

Alpha Channel in Texture Mapping

• Represents transparency.
• Allows textures to have varying levels of opacity.
• Enables rendering of transparent objects like glass, while maintaining realistic interactions with other objects.

MIP Mapping in OpenGL

• Improves texture rendering by creating a series of prefiltered texture images at different resolutions.
• Advantages:
  • Better texture quality at varying distances.
  • Enhanced performance.
  • Prevention of texture popping artefacts.
• Particularly useful in real-time graphics and scenarios where consistent texture quality across distances is critical for a visually pleasing and efficient rendering process.

Global Illumination

• Simulates how light interacts with surfaces and scatters throughout a scene, considering specular and diffuse lighting.
• Differs from local illumination models, which do not consider object-to-object interactions.
• Examples: ray tracing, path tracing, and radiosity.

Rendering Capabilities Characterization

• 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).

Primary Uses of Normals in Computer Graphics

• 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 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.

Rendering Methods and Caustic Effects on Velvet

• Phong model:
  • Only considers the local geometry and the direction of incoming light.
  • Would estimate a reflection intensity that would not be affected by the presence of the gemstone.
  • The colors of the velvet surface would be represented without any shadows or caustics.
• Whitted ray tracing:
  • Since the velvet surface is approximated as an ideal diffuse surface, for any point on the surface, the backward tracing of the corresponding ray would stop there.
  • A shadow ray (aka light ray) from this point to the light source would be created.
  • Since the gemstone occludes the path of this shadow ray from the point to the light source, the point would be classified as being in the shadow.
  • The highlighted area would be rendered as being completely in the shadow, without any caustics.
• Path tracing:
  • For every pixel on the cushion surface, many rays would be shot, and each one of them would follow a random walk.
  • Some of them would be refracted within the gemstone and, for the bright regions of the caustics, would eventually hit the light source.
  • Aggregating the contributions of all random rays, path tracing would simulate in a very realistic way the complex interactions between the light and the objects in the scene.
  • The illumination on the cushion surface would be very realistic and would include the caustics.

Specular Highlight Peak Calculation

• The reflection direction r is $(3, −1, −6)$. This is easy to see if you understand how the reflection direction is defined which is defined by $r = 2(n · L)n − L$, where $L$ is the light direction and $n$ is the normal vector.
• We first consider the ray from the reflection point to the eye:
  • $(4, 2, 6) = (b, 4, d) + t(3, −1, −6)$
• Use the y coordinate to solve for t gives $t = 2$.
• Substituting gives $b = -2$ and $d = 18$.

Matrix Transformation

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}

Z-buffer Algorithm

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

Rendering Order (alpha = 1)

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

Algorithm Choice (alpha = 0.4)

• Painters is a better choice.
• Z-buffer cannot deal with translucency easily as it requires to store 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 instead of overwriting it.