Computer Graphics Overview

1. Display Devices

Definition:
Display devices are output units used to present visual information to the user in text, graphics, or images form.

1. Cathode Ray Tube (CRT)

• Uses electron beams to excite phosphor dots on the screen.
• Components: Electron gun, focusing & deflection system, phosphor-coated screen.
• Types:
  • Raster Scan: Refreshes entire screen line by line (used in TVs, monitors).
  • Random Scan: Draws only lines/curves (used in vector displays, oscilloscopes).
• Advantages: High resolution, good color.
• Disadvantages: Bulky, high power consumption, limited portability.

2. Liquid Crystal Display (LCD)

• Uses liquid crystals that modulate light between polarizers.
• Each pixel controlled by an electric field.
• Types:
  • Passive Matrix LCD – slower response, cheaper.
  • Active Matrix (TFT LCD) – faster, better color and contrast.
• Advantages: Thin, lightweight, low power.
• Disadvantages: Limited viewing angles, slower refresh rates.

3. Light Emitting Diode (LED)

• Array of LEDs used as light source (backlight or direct emission).
• Better brightness, contrast, and energy efficiency than LCD.
• Variants: Edge-lit and full-array LED displays.

4. Plasma Display Panel (PDP)

• Uses small gas cells containing neon/xenon plasma that emit UV light to excite phosphors.
• Advantages: Wide viewing angle, high brightness.
• Disadvantages: Heavy, high power use, image burn-in.

5. Organic LED (OLED)

• Uses organic compounds that emit light when current passes.
• Self-emissive (no backlight needed).
• Advantages: Excellent contrast, thin, flexible, energy efficient.
• Disadvantages: Shorter lifespan, expensive manufacturing.

6. Digital Light Processing (DLP)

• Uses micromirrors on a semiconductor chip to reflect light.
• Common in projectors.
• Advantages: High contrast, good color accuracy.
• Disadvantages: Rainbow effect, complex optics.

7. Touch Screen Displays

• Detect user input via touch sensors.
• Technologies: Resistive, Capacitive, Infrared, Surface Acoustic Wave (SAW).
• Used in smartphones, ATMs, kiosks.

Summary Table:

Type	Technology	Key Feature	Example Use
CRT	Electron beam	High resolution	Old monitors
LCD	Liquid crystals	Thin, low power	Laptops
LED	LED backlight	Bright, efficient	TVs
PDP	Gas discharge	Large screens	Plasma TVs
OLED	Organic emitters	Flexible, high contrast	Smartphones
DLP	Micromirrors	Projection	Projectors
Touch Screen	Sensor-based	Interactive input	ATMs

---

2. Output Primitives

Output primitives are basic graphic elements used to construct complex images. They define how objects are represented on a display device.

2.1 Point

• Smallest visible unit on the display.
• Represented by pixel coordinates (x, y).
• To plot a point:

  putpixel(x, y, color);

• Transformation: Translation, Scaling, Rotation can be applied to points.

2. Line

• Connects two points (x1, y1) and (x2, y2).
• Line attributes: type (solid/dashed), color, thickness.
• Algorithms for line generation:
  • Digital Differential Analyzer (DDA)
  • Bresenham’s Line Algorithm
• Equation of a line: y = mx + c

3. Circle

• Set of points at a fixed distance (radius) from a center (xc, yc).
• Equation: (x – xc)² + (y – yc)² = r²
• Circle drawing algorithms:
  • Midpoint Circle Algorithm
  • Bresenham’s Circle Algorithm

4. Ellipse

• Equation: (x²/a²) + (y²/b²) = 1
  where a = semi-major axis, b = semi-minor axis.
• Algorithm: Midpoint Ellipse Algorithm.

5. Polygon

• Closed figure made of connected line segments.
• Specified by vertices (x1, y1), (x2, y2), …, (xn, yn).
• Types: Convex and Concave.
• Polygon filling algorithms:
  • Boundary-fill algorithm
  • Flood-fill algorithm
  • Scan-line fill algorithm

6. Character and Text

• Display of alphanumeric characters.
• Represented by stroke (vector) or bitmap.
• Attributes: font, size, color, orientation.

7. Attributes of Output Primitives

• Line Attributes: type, width, color.
• Curve Attributes: thickness, pattern.
• Color Attributes: RGB or indexed color.
• Area-fill Attributes: pattern, color, hatch.
• Character Attributes: font, size, spacing, style.

Summary Table:

Primitive	Basic Element	Example Algorithm
Point	Pixel	—
Line	2 endpoints	DDA, Bresenham
Circle	Center & Radius	Midpoint, Bresenham
Ellipse	Major/Minor Axes	Midpoint
Polygon	Set of vertices	Scan-line, Flood-fill
Text	Characters	Bitmap/Stroke representation

---

3. Geometric Modelling

Definition:
Geometric modelling is the mathematical representation of objects’ shapes and structures used for computer graphics and CAD applications. It defines how a 2D or 3D object is described and displayed.

1. Types of Geometric Models

(a) Wireframe Model

• Represents object using points, lines, and curves.
• Shows edges and vertices only.
• Advantages: Simple, low storage, fast rendering.
• Disadvantages: Ambiguous, lacks surface & volume information.

(b) Surface Model

• Describes surfaces (not volume) of objects using polygons or curved patches.
• Common formats: Polygon meshes, Bézier or B-spline surfaces.
• Advantages: Realistic appearance, used in visualization.
• Disadvantages: No interior details, complex shading.

(c) Solid Model

• Represents complete 3D volume of an object.
• Defines both exterior and interior properties.
• Techniques:
  • Constructive Solid Geometry (CSG): Combines primitives (cube, sphere, cylinder, etc.) using Boolean operations (Union, Intersection, Difference).
  • Boundary Representation (B-Rep): Describes object by its faces, edges, and vertices.
• Advantages: Complete and unambiguous.
• Disadvantages: Requires large storage and computation.

2. Geometric Transformation

Used to modify object’s position, orientation, and size.
Types:

• Translation – shifting by (tx, ty, tz).
• Scaling – resizing by factors (sx, sy, sz).
• Rotation – turning about an axis.
• Reflection – mirror about axis/plane.
• Shearing – slanting object shape.

3. Representation Schemes

• Parametric Representation: Curve defined by parameters (e.g., Bézier, B-spline).
• Implicit Representation: Equation form (e.g., x² + y² + z² – r² = 0).
• Explicit Representation: y = f(x) type equations.

4. Common 3D Geometric Primitives

• Cube, Cylinder, Sphere, Cone, Torus, Pyramid, etc.
• These can be combined to form complex objects using Boolean operations.

Summary Table:

Model Type	Description	Example	Information Provided
Wireframe	Lines & vertices	3D skeleton	Shape only
Surface	Faces & curves	Mesh model	Surface only
Solid	Volume representation	CSG, B-Rep	Full geometry

---

4. Two-Dimensional Viewing and 3-D Concepts

1. Two-Dimensional Viewing

Definition:
2D viewing defines how a part of a 2D world (world coordinate system) is displayed on a device (screen coordinate system).

(a) Window and Viewport Concepts

• Window: Portion of the world to be displayed. (world coordinates)
• Viewport: Area on the display device where window content is mapped. (device coordinates)
• Mapping ensures window fits into viewport.

Mapping Equation:

xv = xvmin + (xw - xwmin) * (xvmax - xvmin) / (xwmax - xwmin)
yv = yvmin + (yw - ywmin) * (yvmax - yvmin) / (ywmax - ywmin)

(b) Clipping

• Process of selecting visible portions of an image within a window.

• Types:

  • Point Clipping
  • Line Clipping (Algorithms: Cohen–Sutherland, Liang–Barsky)
  • Polygon Clipping (Sutherland–Hodgman)
  • Text Clipping

• Purpose: Remove objects outside the display region.

(c) Coordinate Systems

• World Coordinate System (WCS): Defined by user.
• Device Coordinate System (DCS): Actual display coordinates.
• Normalized Device Coordinates (NDC): Range 0–1 for mapping portability.

2. 3-D Concepts

3D graphics extends 2D by adding depth (z-axis) for realistic modeling and visualization.

(a) 3D Coordinate Systems

• Right-Handed System: +z comes out of screen.
• Left-Handed System: +z goes into screen.
• Coordinates: (x, y, z).

(b) 3D Transformations Used to manipulate 3D objects.

• Translation: Move by (tx, ty, tz)
• Scaling: Scale by (sx, sy, sz)
• Rotation: About x, y, or z axis
• Reflection: About coordinate planes
• Shearing: Slant shape

(c) Projections Convert 3D objects into 2D view for display.

• Parallel Projection: Projection lines parallel.
  • Orthographic: Projectors perpendicular to view plane.
  • Oblique: Projectors at an angle.
• Perspective Projection: Projectors converge to a point (gives depth).
  • Types: One-point, two-point, three-point perspective.

(d) 3D Viewing Pipeline

Steps to convert 3D scene to 2D display:

1. Modeling Transformations
2. Viewing Transformations
3. Clipping
4. Projection
5. Viewport Transformation

Summary Table:

Concept	Purpose	Key Algorithms/Methods
Window-Viewport	Map world to device	Mapping equations
Clipping	Remove outside objects	Cohen–Sutherland, Liang–Barsky
3D Transformations	Modify object geometry	Translation, Rotation, Scaling
Projection	Convert 3D → 2D	Parallel, Perspective

---

5. Visible Surface Detection Methods

Definition:
Visible Surface Detection (Hidden Surface Removal) determines which surfaces or parts of a 3D object are visible to the viewer and which are hidden behind others.

1. Classification

• Object-Space Methods: Compare objects and surfaces in 3D space to decide visibility (e.g., Back-Face Detection).

• Image-Space Methods: Determine visibility for each pixel on the projection plane (e.g., Z-Buffer).

2. Object-Space Methods

(a) Back-Face Detection

• Simple method based on surface orientation.
• For a polygon with normal vector N = (A, B, C) and view direction V,
  if N · V > 0, face is back face → not visible.
• Works for convex solid objects only.
• Fast and used for initial elimination.

(b) Depth-Sort (Painter’s Algorithm)

• Surfaces sorted by depth (z-value).
• Paint from farthest to nearest → nearer surfaces overwrite farther ones.
• Problems: Overlapping or intersecting surfaces.

3. Image-Space Methods

(a) Z-Buffer (Depth Buffer) Algorithm

• For each pixel, stores smallest depth (z) value.
• Steps:
  1. Initialize depth buffer with ∞ and frame buffer with background color.
  2. For each polygon, compute z for every pixel.
  3. If z < z-buffer(x, y), update pixel color and depth.
• Advantages: Simple, hardware-supported.
• Disadvantages: High memory use.

(b) Scan-Line Algorithm

• Processes one scan line at a time.
• For each line, determine visible polygon segments using depth comparison.
• More efficient than pixel-by-pixel methods.

(c) A-Buffer Algorithm

• Extension of Z-buffer supporting transparency and anti-aliasing.
• Stores intensity and depth for multiple surfaces per pixel.

4. Other Methods

(a) Ray Casting / Ray Tracing

• For each pixel, cast a ray from eye through the view plane into the scene.
• The nearest intersected surface determines visible pixel.
• Produces realistic images with shadows and reflections but computationally expensive.

(b) Binary Space Partitioning (BSP) Tree

• Divides scene recursively into front and back subspaces using planes.
• Used for efficient visibility determination in complex scenes.

5. Comparison Table

Method	Type	Technique	Advantages	Disadvantages
Back-Face	Object-space	Normal–view test	Fast	Only for solid objects
Depth-Sort	Object-space	Sort by z-depth	Simple	Overlap issues
Z-Buffer	Image-space	Depth buffer	Easy, hardware support	High memory
Scan-Line	Image-space	Line-by-line	Efficient	Complex to implement
A-Buffer	Image-space	Extended Z-buffer	Handles transparency	Memory heavy
Ray Tracing	Image-space	Ray intersection	High realism	Very slow
BSP Tree	Hybrid	Space partitioning	Efficient for scenes	Complex setup