Computer Graphics Exam Notes

Motion Capture

• Motion capture aims to capture the motion of a model from a real-life actor.
• Procedure:
  • Place markers on the actor’s body, typically at joints, to record motion in real time.
  • Track markers using multiple calibrated cameras.
  • Estimate joint positions using triangulation.

Rendering Pipeline in 3D Graphics

• Stages: modeling, transformation, lighting, rasterization, and pixel shading.
• Process: Transforms 3D objects into a 2D image by:
  • Projecting vertices onto the screen.
  • Applying lighting and shading calculations.
  • Rasterizing 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 artifacts.
• 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

• Scene: A gemstone placed on a velvet cushion with a light source.
• Caustic Effects: Consider the area where strong caustics would appear in the real world.
  • Phong Model
    • Only considers local geometry and the direction of incoming light.
    • Estimates a reflection intensity not affected by the gemstone.
    • The colors of the velvet surface are represented without any shadows or caustics.
  • Whitted Ray Tracing
    • Approximates the velvet surface as an ideal diffuse surface.
    • Backward tracing of the corresponding ray stops at the surface.
    • A shadow ray (aka light ray) is created from this point to the light source.
    • The gemstone occludes the path of this shadow ray, classifying the point as being in the shadow.
    • The highlighted area is rendered as being completely in the shadow, without any caustics.
  • Path Tracing
    • For every pixel on the cushion surface, many rays are shot, each following a random walk.
    • Some rays are refracted within the gemstone, hitting the light source in bright caustic regions.
    • Aggregating the contributions of all random rays simulates complex interactions between light and objects realistically.
    • The illumination on the cushion surface is very realistic and includes the caustics.

Calculation of Specular Highlight Peak

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

Matrix Transformation Sequence

• Transform shape $M$ into shape $N$.
• Origin is located at the center of shape $M$.
• Steps:
  • Scale shape $M$ by 2 in the y direction.
  • Rotate it by 45 degrees around the z-axis.
  • Translate with the vector $(+2, -2, 0)$.
• The transformation matrix applied to shape $M$ is:
  $\begin{bmatrix} 1 & 0 & 0 & 2\ 0 & 1 & 0 & -2\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix}$
  $\begin{bmatrix} \frac{\sqrt{1}}{2} & - \frac{\sqrt{1}}{2} & 0 & 0\ \frac{\sqrt{1}}{2} & \frac{\sqrt{1}}{2} & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix}$
  $\begin{bmatrix} 1 & 0 & 0 & 0\ 0 & 2 & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix}$

Z-buffer Algorithm

• Handles occlusions by recording the depth of each rendered pixel and overwriting it if a new, closer surface is rendered on the same location.
• Steps (with alpha = 1):
  1. Render the yellow bar.
  2. Render the green bar.
  3. Render the red bar.

Algorithm Choice for Translucency

• If $alpha = 0.4$, Painters is a better choice than Z-buffer.
• Reason:
  • Z-buffer cannot easily handle translucency 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 instead of overwriting it.