Computer Graphics Exam Notes

Motion Capture

• Motion capture aims to capture the motion of a model from a real-life actor.
• This is done by placing markers on the actor’s body, typically at joints, to record motion in real-time.
• The markers are tracked using multiple calibrated cameras.
• Joint position is estimated using triangulation.

Rendering Pipeline in 3D Graphics

The rendering pipeline includes stages like:

• Modelling
• Transformation
• Lighting
• Rasterisation
• Pixel shading

It 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

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

MIP Mapping in OpenGL

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

• Global illumination in computer graphics simulates how light interacts with surfaces and scatters throughout a scene, considering specular and diffuse lighting.
• It differs from local illumination models, which do not consider object-to-object interactions.

Examples of global illumination techniques:

• Ray tracing
• Path tracing
• Radiosity

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).

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 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.

Rendering Methods and Caustic Effects

Phong Model:

• The Phong model only takes into account the local geometry and the direction of incoming light.
• It would estimate a reflection intensity that would not be affected by the presence of the gemstone at all.
• 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.
• Then, 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.
• In conclusion, the highlighted area would be rendered as being completely in the shadow, without any caustics.

Path Tracing:

• In this case, 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. In conclusion, 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 defined by $r = 2(n \cdot L)n - L$, where L is the light direction and n is the normal vector.

• 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 $d = 18$.

Transformation Matrices

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.

Steps:

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

Rendering with Translucency

• If alpha = 0.4, Painters algorithm is a better choice to render this scene, Z-buffer cannot deal with translucency easily as it requires to store multiple depths in the depth buffer.
• While Painters can render the yellow bar by blending the pixel’s colour with the previous colour using the appropriate alpha instead of overwriting it.