Computer Graphics Core Concepts: Display, Rendering, Algorithms

Posted on Sep 17, 2025 in Computers

Display Technologies: Beam Penetration vs. Shadow Mask

Graphics Rendering: Raster Scan vs. Vector Scan

Object Space vs. Image Space in Computer Graphics

Computer Graphics Fundamentals

What is a Computer?

A computer is an electronic device that accepts data as input, processes it according to instructions, and produces output.

Advantages of Computer Graphics

• Visual representation of data.
• Easy understanding of complex concepts.
• Interactive communication.
• Realistic image generation.

Application Areas of Computer Graphics

• CAD (Computer-Aided Design)
• Animation & Gaming
• Scientific Visualization
• Virtual Reality & Simulation
• Education & Training

Z-Buffer Algorithm

The Z-Buffer algorithm is a common technique for hidden surface removal in 3D computer graphics.

Step 1: Initialize

• Depth buffer: Set all values to Zmax (farthest possible depth).
• Frame buffer: Set all pixels to background color.

Step 2: Process Each Polygon

For each polygon in the scene:

• Project it onto the screen.
• For each pixel inside the polygon:
  • Calculate the polygon’s depth (Z) at that pixel.
  • Compare it with the depth buffer value at that pixel.
  • If closer:
    • Update the depth buffer with the new Z.
    • Update the frame buffer with the polygon’s color.

Step 3: Final Image

The frame buffer now contains the final visible image.

The Painter’s Algorithm

The Painter’s Algorithm is a simple hidden surface removal algorithm that renders polygons from back to front.

Step 1: Sort Polygons

Sort polygons based on their depth (e.g., average Z or farthest vertex Z).

Step 2: Render Polygons

For each polygon in sorted order:

• Project to the 2D screen.
• Fill the pixels in the frame buffer (overwriting previous colors if needed).

Step 3: Complete Image

The visible image is complete.

Scan-Line Algorithm

The Scan-Line algorithm is used for rendering polygons by processing them scan line by scan line.

Step 1: Sort Edges

Sort all polygon edges by their Y-coordinates.

Step 2: Process Each Scan Line

For each scan line (horizontal row of pixels):

• Find all polygon edges intersecting this scan line (Active Edge Table – AET).
• Determine intersection points with the scan line.
• Sort intersection points by X-coordinate.
• Fill the pixels between pairs of intersections with the polygon’s color.
• Update edges in the Active Edge Table for the next scan line.

Step 3: Repeat

Repeat until all scan lines are processed.

Back-Face Removal

Back-Face Removal is an object-space hidden surface removal technique.

Purpose

To skip rendering polygons that face away from the camera, because they can never be visible.

Mathematical Test

1. Let:
   • N = surface normal vector of polygon (in view space)
   • V = view vector from the eye (camera) to the polygon
2. Compute the dot product:

   D = N . V

3. If:
   • D > 0 → Polygon is facing the viewer → keep it.
   • D ≤ 0 → Polygon is facing away → discard it.

Light, Color, and Color Models

Light & Color Basics

• Light: Visible electromagnetic waves (380–780 nm).
• Color: Perception from light wavelengths reflected/emitted by objects.

Color Models

1. RGB (Additive)

   • Components: Red, Green, Blue.
   • Mix light: Black = (0,0,0), White = (255,255,255).
   • Used in: Monitors, TVs, cameras.

2. CMY (Subtractive)

   • Components: Cyan, Magenta, Yellow.
   • Mechanism: Inks subtract light colors.
   • Conversion: C=1−R, M=1−G, Y=1−B.
   • Used in: Printing.

3. YIQ

   • Components: Y (brightness), I (orange–cyan), Q (purple–green).
   • Application: Y for B/W TVs, I & Q for color information.
   • Used in: NTSC TV broadcast.

The 2D Graphics Pipeline

1. Modeling Transformation

   • Convert objects from model coordinates (local space) to world coordinates.
   • Example: Move a square from its local origin to a position in the scene.

2. World to Viewing Transformation

   • Map world coordinates to view coordinates (camera space).
   • Positions objects relative to the viewer’s window.

3. Clipping

   • Remove (clip) portions of objects outside the view window (viewport in world coordinates).
   • Saves processing by ignoring unseen parts.
   • Example: If part of a line lies outside the drawing area, only the visible part is kept.

4. Window-to-Viewport Transformation

   • Map the clipped coordinates from the world view window to the screen’s viewport.
   • Converts world units to device units (pixels).
   • Ensures the scene fits on the display.

5. Rasterization (Scan Conversion)

   • Convert vector data (lines, shapes) into pixel data.
   • Fills polygons, draws lines as discrete pixels.

6. Display

   • Send rasterized image to the frame buffer for display on the screen.