Computer Graphics Algorithms and Animation Principles

Digital Differential Analyzer (DDA) Algorithm

• Input: The starting point (x1, y1) and ending point (x2, y2).
• Calculate:
  • dx = x2 - x1
  • dy = y2 - y1
• Find:
  • Steps = max(|dx|, |dy|)
• Compute:
  • xinc = dx / Steps
  • yinc = dy / Steps
• Plot: The initial point.
• Iterate: Add xinc and yinc repeatedly until the endpoint is reached.

Bresenham's Line Drawing Algorithm

• Calculate dx and dy.
• Initialize the decision parameter.
• Plot the starting pixel.
• According to the decision parameter, choose the next pixel.
• Update the decision parameter.
• Repeat until the endpoint is reached.

Midpoint Circle Drawing Algorithm

• If P < 0, choose the East pixel.
• If P ≥ 0, choose the South-East pixel.
• Update the decision parameter.
• Continue until x > y.
• Use 8-way symmetry to complete the circle.

Sutherland-Hodgman Polygon Clipping

Definition

This algorithm is used to clip polygons against a rectangular clipping window.

Algorithm Steps

Process each polygon edge against every clipping boundary. There are four cases:

1. Inside → Inside: Output the second vertex.
2. Inside → Outside: Output the intersection point.
3. Outside → Inside: Output the intersection point and the second vertex.
4. Outside → Outside: Output nothing.

Flood Fill Algorithm

Fills connected pixels that have the same interior color.

Steps

1. Start from a seed point.
2. Replace the interior color.
3. Move to neighboring pixels.

Boundary Fill Algorithm

Fills pixels until a specific boundary color is reached.

Steps

1. Start inside the object.
2. Fill pixels until the boundary color appears.

Graphical Kernel System (GKS)

Features

• Device independent: Works across different hardware.
• Portable: Easy to move between systems.
• Standard graphics functions: Provides a consistent API.
• Easy application development: Simplifies the coding process.

GKS Primitives

1. Polyline
2. Polymarker
3. Fill Area
4. Text

Applications

• Computer-Aided Design (CAD)
• Scientific visualization
• Graphics software development

Principles and Types of Animation

Animation is the process of displaying a sequence of images (frames) rapidly to create the illusion of continuous motion. In computer graphics, animation is used to make objects move, change shape, or simulate real-world motion.

Basic Principles of Animation

The basic principles of animation improve the realism and quality of animated objects:

• 1. Squash and Stretch: Gives flexibility and weight to objects. Example: A bouncing ball squashes when it hits the ground and stretches while moving upward.
• 2. Timing: Controls the speed and duration of movement.
• 3. Anticipation: Prepares the viewer for an upcoming action.
• 4. Follow Through: Parts of an object continue moving after the main object stops.

Types of Animation Systems

1. Scripting Animation: Animation is controlled using scripts or programming languages, providing flexibility and automation.
2. Procedural Animation: Motion is generated automatically using mathematical formulas or algorithms.
3. Representational Animation: Objects are represented using mathematical or geometric models.
4. Stochastic Animation: Uses random values and probability to generate natural-looking motion.