Interactive graphics enable users to manipulate visual content in real-time. This leads to better decision-making, enhanced learning, and more intuitive user experiences. They are crucial in simulations, CAD systems, games, and data visualization.
Computer graphics are used in a variety of fields:
Applications of computer graphics can be classified based on their function:
Modern computer graphics rely on advanced hardware and software:
The synergy between hardware and software determines the efficiency and quality of graphical applications.
The framework includes components such as:
Scan conversion refers to the process of converting geometric data into pixel data for raster displays.
The Bresenham's Line Algorithm is commonly used to draw straight lines efficiently on raster displays.
Example:
Draw line from (0,0) to (5,3) using Bresenham’s Algorithm.
Initial point: (0,0)
Next points: (1,1), (2,1), (3,2), (4,2), (5,3)
The Midpoint Circle Algorithm determines the points needed to draw a circle by calculating pixel positions along the circle’s circumference.
Example:
Center = (0,0), Radius = 5
Calculated pixels in one octant:
(0,5), (1,5), (2,4), (3,4), (4,3), (5,2)
The Midpoint Ellipse Algorithm is used for drawing ellipses, involving separate calculations for regions where x or y grows faster.
Example:
Center = (0,0), Rx = 6, Ry = 4
Points calculated in region 1 and 2 are plotted using symmetry.
Hardcopy devices produce permanent output of graphics. Common types include:
Display technologies form the visual interface of computer graphics. These include:
In raster-scan systems, the screen is refreshed line by line from top to bottom, storing the image in a frame buffer.
Example:
Each pixel is stored in memory and refreshed 60 times per second.
The video controller handles conversion of image data from memory to signals for the monitor. It synchronizes pixel refresh and coordinates the display timing.
Unlike raster systems, random-scan (vector display) directly draws lines and shapes using an electron beam, offering higher resolution for line drawings.
Input devices are essential for interacting with graphics systems:
Image scanners convert physical documents or images into digital form using light sensors. They are used in digitization and graphic input.
Practical tools used in multimedia and web graphics development:
Clipping restricts drawing to a specified region (viewport). Major algorithms include:
This algorithm checks if a line is completely inside, outside, or partially inside the clipping area and performs region codes to clip.
Example:
Line with endpoints (x1,y1) and (x2,y2) are tested with region codes and clipped accordingly.
Used for line clipping against convex polygonal window. It is a parametric algorithm based on dot product tests.
Example:
For convex window with normals and parametric t values, calculate entry and exit points of the line segment.
This is a recursive algorithm that divides the line at its midpoint until a trivially accepted or rejected segment is obtained.
Example:
Check midpoint of (x1,y1)-(x2,y2). If undecided, split and repeat for each half.
2D transformations change the position, size, and orientation of objects in a two-dimensional space. Basic types include:
To perform transformations using matrix multiplication, coordinates are represented in homogeneous form (x, y, 1).
Example:
Translation Matrix for Tx and Ty:
[ [1, 0, Tx],
[0, 1, Ty],
[0, 0, 1 ] ]
Scaling Matrix:
[ [Sx, 0, 0],
[0, Sy, 0],
[0, 0, 1] ]
Multiple transformations can be combined into a single transformation matrix by matrix multiplication.
Example:
First rotate, then translate:
Resultant Matrix = Translation × Rotation
This maps objects from a logical coordinate system (window) to the physical device coordinates (viewport).
The transformation involves scaling and translation:
Example:
Xv = Xvmin + (Xw - Xwmin) × (Xvmax - Xvmin)/(Xwmax - Xwmin)
Yv = Yvmin + (Yw - Ywmin) × (Yvmax - Yvmin)/(Ywmax - Ywmin)
In 3D, transformations involve x, y, and z axes. The homogeneous coordinate system is extended to (x, y, z, 1).
Example:
3D Translation Matrix:
[ [1, 0, 0, Tx],
[0, 1, 0, Ty],
[0, 0, 1, Tz],
[0, 0, 0, 1 ] ]
A polygon mesh is a collection of polygons, typically triangles or quadrilaterals, that form the surface of a 3D object. They are widely used in 3D modeling due to their simplicity and flexibility.
These curves are defined using mathematical functions based on a parameter, usually denoted as t. Common parametric curves include:
Cubic curves are polynomial curves of degree three and are commonly used in CAD systems. Bezier and Hermite curves are typical examples.
Example:
Cubic Bezier Curve Equation:
B(t) = (1−t)^3P0 + 3t(1−t)^2P1 + 3t^2(1−t)P2 + t^3P3
Quadric surfaces are second-degree algebraic surfaces such as spheres, cones, ellipsoids, and paraboloids, defined by equations like:
Example:
Sphere: x² + y² + z² = r²
Ellipsoid: x²/a² + y²/b² + z²/c² = 1
Solid modeling provides complete information about the volume and shape of 3D objects. Key methods include:
Boolean operations (union, intersection, difference) are applied to solids using regularized set theory to maintain validity of resulting shapes.
Example:
Union: A ∪ B
Intersection: A ∩ B
Difference: A − B
Uses predefined 3D shapes (cube, cylinder, sphere) called primitives, which can be scaled, rotated, and translated to form complex models.
Involves sweeping a 2D shape along a path (translation or rotation) to generate a 3D object, e.g., extrusion or revolution techniques.
Represents a solid by its enclosing surfaces, edges, and vertices. B-Rep is useful for high-resolution models in CAD.
Divides 3D space into non-overlapping regions (e.g., octrees, BSP trees) for efficient rendering and collision detection.
Builds complex objects by combining primitives using Boolean operations in a tree structure.
Boundary Representation: Good for visual rendering, harder for Boolean operations
CSG: Better for modeling and editing, less intuitive for display
Spatial Partitioning: Efficient for computation and rendering in complex environments
Multimedia refers to content that uses a combination of different forms such as text, audio, images, animations, video, and interactive content. It enhances communication and user engagement.
CD-ROM (Compact Disc Read-Only Memory) was one of the earliest storage devices for multimedia content. The multimedia highway refers to broadband networks and infrastructure that deliver multimedia services and applications over the internet.
Computer Animation involves creating moving images using computer graphics. It includes:
Example:
In 2D animation, a bouncing ball is created using keyframes and motion interpolation.
Multimedia is used extensively in:
The development process typically includes:
Various courses and certifications are available in animation, video editing, web design, game development, and digital storytelling from institutions and online platforms.
Multimedia engages multiple senses, increases retention, and facilitates interactive learning and communication, making it an essential tool in modern applications.