Unit 5: VSD & Animation

5.1 Visible Surface Detection (VSD)

Also called "Hidden Surface Removal". The goal is to draw only what the camera sees.

1. Back-Face Detection

Concept: Check if a polygon is facing away from the camera.

The Test: Calculate Dot Product of View Vector ($V$) and Surface Normal ($N$).
If $V \cdot N > 0$, it is a Back-Face (Hidden). Don't draw it.

2. Z-Buffer Algorithm (Depth Buffer)

Analogy: The Painter's Canvas.
For every dot you paint, you write down its "distance". If you try to paint another dot at the same spot, check the distance.
If the new dot is Closer, paint over it.
If the new dot is Father, ignore it.

Pros: Simple, hardware friendly.
Cons: Uses lots of memory, cannot handle transparency well.
Logic: Test $Z_{new} < Z_{buffer}$.

3. A-Buffer (Accumulation Buffer)

Concept: An upgrade to Z-Buffer. Instead of storing 1 value per pixel, it stores a List of values.

Stores: Depth, Color, Opacity (Transparency), Coverage.
Why? Allows for Transparent objects (glass) and Anti-Aliasing.

4. Scan-Line Algorithm (Image Space)

Concept: Process the image line-by-line using Edge Tables to decide what is visible.

The 5-Step Logic:

Scan Line: Draw an imaginary horizontal line across the scene.
Intersection: Find all points where this line cuts polygon edges.
Sort: Sort these points by X-coordinate.
Fill: Color pixels between pairs of points (Interval Coherence).
Depth Check: If polygons overlap, check Z-depth at that interval to see which wins.

Key Structures:

Global Edge Table (GET): Stores all edges sorted by Y-min.
Active Edge Table (AET): Stores edges intersecting the current scan-line.

5. The Plane Equation (For Depth)

How do we find $z$ for a random pixel?

$$Ax + By + Cz + D = 0$$ $$z = \frac{-(Ax + By + D)}{C}$$

This formula allows the Z-Buffer to calculate depth quickly.

mindmap
  root((Hidden Surfaces))
    Math Check
      Back-Face Det
      Dot Product
      V dot N > 0
    Pixel Check
      Z-Buffer
      Compare Depth
      Close wins
    List Check
      A-Buffer
      Transparency
      Anti-Aliasing
    Line Check
      Scan-Line
      Intervals
      Edge Tables

5.2 Animation Concepts

Definition: Illusion of motion by showing a sequence of frames (>24 FPS).

Key Techniques

Keyframing: The artist draws the "Key" poses (Start/End). The computer fills in the rest.
Tweening (In-Betweening): The computer's job. Interpolating position, size, rotation, or color between keyframes.
Morphing: Transforming one shape into another (e.g., Man $\to$ Wolf).
Panning: Moving the camera horizontally across a scene.
Onion Skinning: Making previous frames translucent so the animator can see the motion trail while drawing.

Types of Animation Logic

Procedural: Code-driven (Fire, Smoke, Water). Uses math/physics.
Behavioral: Rule-driven (Flocking birds, Traffic). Objects have "brains".
Kinematics: Moving joints/limbs.
- Inverse Kinematics (IK): You pull the hand, the elbow and shoulder move automatically.
Dynamics: Physics simulation (Gravity, Collisions, Cloth).
Motion Capture (MoCap): Recording real actors.

mindmap
  root((Motion Logic))
    The Basics
      Keyframing (Poses)
      Tweening (In-Between)
    Techniques
      Morphing (Shape Change)
      Onion Skin (Trails)
    Physics
      Kinematics (Joints)
      Dynamics (Gravity)