Computer Graphics Notes

Motion Capture

• Motion capture aims at capturing 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.
• Markers are tracked using multiple calibrated cameras.
• Joint position is estimated using triangulation.

Rendering Pipeline in 3D Graphics

• Stages include modelling, transformation, lighting, rasterisation, and pixel shading.
• Transforms 3D objects into a 2D image by projecting vertices onto the screen.
• Applies lighting and shading calculations.
• Rasterises 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.

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.

Caustic Effects Rendering Comparison

• Phong Model:
  • Only considers local geometry and incoming light direction.
  • Would estimate a reflection intensity unaffected by the gemstone.
  • Velvet surface colors would be represented without shadows or caustics.
• Ray Tracing:
  • Approximates the velvet surface as an ideal diffuse surface.
  • Backward tracing of the ray would stop at the surface.
  • A shadow ray from the point to the light source would be created.
  • Gemstone occludes the shadow ray, classifying the point as in shadow.
  • Highlighted area rendered as completely in shadow, without caustics.
• Path Tracing:
  • Shoots many rays for every pixel on the cushion surface, each following a random walk.
  • Some rays are refracted within the gemstone and hit the light source for bright caustic regions.
  • Aggregating the contributions of all random rays simulates complex interactions.
  • Illumination on the cushion surface includes realistic caustics.

Specular Highlight Peak Calculation

• Reflection direction r is (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 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 gives b = −2 and d = 18.

Shape Transformation Matrix Sequence

• Scale shape M with two in y direction.

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

• Translate with the vector (+2,-2,0).

• The matrix applied to shape M is then:

  $\begin{bmatrix} 1 & 0 & 0 & 2\ 0 & 1 & 0 & -2\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} \frac{\sqrt{1}}{2} & \frac{-\sqrt{1}}{2} & 0 & 0\ \frac{\sqrt{1}}{2} & \frac{\sqrt{1}}{2} & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 0 & 0\ 0 & 2 & 0 & 0\ 0 & 0 & 1 & 0\ 0 & 0 & 0 & 1 \end{bmatrix}$

Z-Buffer Algorithm

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

Translucency Rendering

• If alpha = 0.4, Painters algorithm is a better choice than Z-buffer.
• Z-buffer cannot easily deal with 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.