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Computer Graphics - A World of Advances

• Computer graphics is the branch of computer science focused on image synthesis using computers
• Display screens have information in both text and graphics
• Computer graphics are prevalent in movies, video games, and commercials
• The book is designed as both a standalone textbook and a valuable study aid for understanding computer graphics principles
• The book emphasizes mathematics and algorithms for computerized image synthesis and contains worked examples
• Prerequisites include knowledge of a computer system, data structures, algorithms, linear algebra, and analytical geometry

Rapid Changes

• Computer graphics hardware has a short lifespan
• Industry standards often become obsolete before finalization
• Programming languages for graphics applications may become outdated quickly
• The book focuses on lasting concepts and relationships to avoid equipment or environment-specific details
• Discussions are framed within overall computer graphics, emphasizing mathematical and algorithmic solutions
• Algorithms use pseudo-code instead of specific programming languages
• Examples are adaptable for various computer systems

Diverse Benefits

• Serves as a general introduction to computer graphics with a focus on technical substance without implementation burden
• Can be used as a resource to supplement primary texts for instructors and students
• Acts as a stepping stone for practitioners seeking clear explanations beyond programmer's manuals
• The current version is a revision of an original edition, with updated topics
• The book aims to be stimulating and rewarding

Introduction to Key Concepts

• Computer graphics is about creating images with computers, from simple outlines to complex scenes
• Key topics include:
  • Geometric representation: Efficiently defining objects like triangles using coordinate systems
  • Transformation: Using matrices to position, orient, and scale objects in image space
  • Scan conversion: Converting continuous figures into discrete pixel approximations
  • Aliasing effect: Distortions from converting continuous space to discrete pixels
  • Anti-aliasing: Techniques to reduce negative impacts of the aliasing effect

The Graphics Pipeline

• Simplified graphics pipeline: Primitive objects -> Transformation -> Scan Conversion
• "World Coordinate System" places transformed objects to compose a picture
• Application programs call library subroutines for graphics tasks

3D Graphics and Realism

• 3D graphics distinguish the object and resulting picture
• Drawings represent 3D object projections onto a 2D display
• Computer graphics covers projection methods and requires hidden surface removal
• Photo-realistic images require understanding how cameras and nature create snapshots
• Local illumination models mimic optical phenomena
• Global illumination models account for comprehensive light transport
• Surface textures add realism, and incorporate shadows computationally

Image Processing and Computer-Human Interaction

• Image processing vs. computer graphics: Image processing starts with images in the image space and performs pixel operations
• Image processing produces new images with desired features
• Computer-human interaction focuses on effective communication between humans and machines
• User-friendly interactive protocols need effective use of devices and graphics

What's Ahead

• Each chapter includes background information and a summary.
• Inter-subject continuity are in the presentations and examples are used to elaborate abstract concepts
• Basic definitions and implementation protocols are available with broad coverage
• Applications are introduced early for usefulness
• Algorithms and programming examples are given in C style pseudo-code
• There are problems at the end of each chapter to reinforce the theoretical discussion.

Image Composition

• A digital image is composed of pixels arranged in rows and columns, forming a raster
• The total number of pixels depend on image size and resolution
  • Resolution: Pixels per unit length
  • Dimensions: total number of horizonal by vertical pixels
• Aspect ratio is the ratio of width to height, measured in length or pixels
• Individual pixels are referenced by coordinates
• Image creation involves setting pixel values, and colors giving distinct visual

Color Specification

• RGB color model uses Red, Green, and Blue primaries
  • Each has an intensity value from 0 (off) to 1 (on)
  • A linear combination produces a cube-shaped RGB color space
  • The RGB corner is at coordinate system origin to black, the opposite corner represents white
• Color specification with RGB is an additive process
• CMY model is a complementary model using Cyan, Magenta, and Yellow
  • Uses the color values from a subtractive process
  • Varies the amount of Cyan, the complement of Red , etc
  • Cube corner at (0, 0, 0) corresponds to white, whereas (1, 1, 1) is black
  • Can be converted with equations

Direct Coding

• Direct coding is the method of image values that uses an amount of storage space to code each pixel
• 3 bits per pixel, where with one bit for each primary color
  • Allows primaries to independently vary between two intensity levels: 0 (off) or 1 (on)
    • Each pixel can be one of the eight corners of the RGB color cube
• An industry standard is 3 bytes (24 bits) per pixel, with one byte for each primary color
  • Allows each primary color have 256 different intensity levels
  • Pixel can take on a color from 256 x 256 x 256 (16.7 million) possible choices
    • Known as true color representation, since the difference from differing by one intensity level is virtually undetectable.
  • Special case is black-and-white and gray-scale, where three primaries always have the same value and need not be coded separately.
    • Black-and-white image requires only one bit per pixel, with bit value 0 representing black and 1 representing white.
    • Gray-scale coded with 8 bits per pixel allows a total of 256 intensity or gray levels.
  • High storage demands for 24 bit, for example, a 1000 x 1000 true color images 3 million bytes despite their only being 1 million colors.

Lookup Tables

• A lookup table bridges low storage and sufficient color
• Image values do not directly code colors, pixel values are addresses or indices linking to a table of color values
• The color of a pixel is determined by the table value it references
• each entry containing a 24-bit RGB color value. Entries have addresses 0 through 255. Pixel values are now quantities of 1-byte, or 8-bits quantities.
• This 24-bit 256-entry lookup table representation often referred to as the 8-bit format, reduces the storage requirement of a 1000 x 1000 images to 1 mb plus 768 bytes and allows 256 colors chosen from 16.7 million.
• Image is defined by its pixel values, and also by its color values
• The latter form color map image

Display Monitors

• Display or video monitor is an image presentational output device that converts digitally represented images into perceivable pictures
• includes a monochromatic CRT, which mainly entails a cathode ray tube (CRT) and related control circuits
• CRT is a vacuum glass tube with the display screen at one end and connectors to the control circuits at the other
• inside the display screen has coating of phosphor, which emits light for short time when hit by a beam of electrons
• The light emitted by the phosphor coating is a function of intensity and the control shuts off the beam during retracing
• Displayed Image stored a dedicated system memory commonly called the frame buffer or refresh buffer
• The content of the frame buffer sent to the display called the refresh frame, refreshing approximately 60 times per second to avoid flicker due to slow response of the human eye
• Some monitors use interlacing to double the refresh rate of display and sweep across top to bottom

Color display monitor

• Moving on to color displays there are now three electron guns instead of one inside the CRT
• The phosphor coating on the display consists of dot patterns of three different types of phosphors to emit red, green, and blue light, respectively
• A thin screen shadow mask thin to constrain the electron beam and the light emitted by the phosphors blends together

The Printer

• The printer deposited color pigments onto a a print media by managing the light reflected onto its surface
• Given that print media is pieces of white paper:
  • We can in principle utilize three types of pigments (cyan, magenta, and yellow) to regulate the amount of red, green, and blue
  • However, in practice an additional black pigment is cost effective
• Some pigment blends and many cases the various color pigments remain separate, where techniques can achieve the effect of multiple pigment intensity levels.

Halftoning

• Halftoning uses variably sized pigment dots that creates impression of varying intensity
• A image produced from this technique is halftone that ranges from 60 to 80 dot newspaper 120 to 200 for book and magazine

Halftone Approximation

• The halftone is approximated by pixel grid patterns, wehre increased size can increase pixel intensity
• These halftone grid patterns dither patterns, and can pixel intensification from growth-of the grid center to mimic dot growth. There are symmetry considerations, to not have streaks.
• A dither matrix is useable here, e,g, 3x3s for bilevel reproduction that is a total of 19 levels.
• Another technique is dithering reduces, where intensity values are adjusted from d structures
• Another is error diffusion that sacrifies sacrifice resolution, where pixel is printed and the error term propagated
• All of these techniques are for devices with limited color

Image Files

• Digital images are often binary files for transmissions, and includes formats such as BMP, JPEG, and TIFF, that differ technically and share similarity
• The structure of an image is organized as format description, dimensions, image type, compression type, and pixel values
• header and image data sections that may compress with algorithms such as RLE/ "Run Length Encoding"

Pixel Attributes

• Setting individual pixel attributes is the most primitive graphics operations performed into a frame buffer
• These attributes specify data to system library calls and use aggregate data structures,
• Protocols have coordinate and color simultaneous and exist in two forms, one in direct pixel, or using lookup table, but all set by the systems recently specified current color in the operation
• Lookup tables and values in the read can accessed through such an operation, there to also rectangular pixel blocks

Mandelbrot

• An example of image construction is from pixel setting the color attributes for direct application is the Mandelbrot set
• it proceeds with an equation xi=++² were X and z are complex numbers and their arithmetic following the complex arithmetic form. The points are evaluated as non divergence

Scan Conversion

• Scan conversion is conversion is the conversion of a geometric definition such as a point into as set of pixel within an image
• This encompasses points, lines, circles, ellipses, filled regions and help differentiate the differences and reduce distortion in its process.

Scan-converting a Point

• A (mathematical) coordinate point is a point with x and y that are need to be scan-converted
• The process involves determining its closest integer approximation and coordinate and use second approach
• This system aligns integer values of coordinate system with integer pixel to its nearest coordinate value

Scan Converting a Lines

• A computer graphics line refer to what is technically a line segment that extend between end point y = mx + b and has many algorithms and method that increase graphic efficiency
• Direct Use of the Line use two converted values P₁ and P₂ to pixel coordinated, then set m = (2-4)/(x-x1) and by mx. where many floating points can increase computational complexity
• The DDA Algorithm or Digital differential analyzer increments calculations at each step following proceeding with previous step, and is an incremental scan.

Bresenham's Line Algorithm

• Bresenham's line algorithm is an effective integer based method for scan-converting lines and a simple arithmetic shift or multiplication by 2
• One have to choose if which axis is the greatest to determine S and T pixels, and the process is iterative over x and y

Scan-Converting a Circle

• Scan Converting a circle have use of symmetrical figures, such as point being calculated in quarter sector to achieve point by reflection along x and y axis
• Defining a Circle happens mathematically via order polynomial equations where efficiency depends on power calculation, and it is the same for trigonometric algorithm that involves angle.

Scan Conversion - Ellipse

• Is similar to scan conversion circle with four way symmetry and equations involve ratios to squares
• Midpoint ellipse Algorithm has more direct evaluation

Scan conversion - Arcs and Sectors

• In Arcs and Sectors a and used in conjunction with trigonometry, the starting value set to be equal angle start and ending where trigonometric is also an option

Regions and other conversions

• Scan Converting a Rectangle requires specification of vertices to then be converted into an algorithm

• Region Filling a matter are in terms

• Boundary definitions of pixel of image space and is associated between images. There 4 an 8 way

• A boundary fill algorithm is recursive to that effect.

• A Flood fill Algorithm share similarities in its operating principle and used often when area has in a uniform boundary. It's use is limited by algorithm type

A Scan Ling Algorithm

• Scan line Algorithm have algorithm handles polygonal positions that vertex coordinate. A scan line is drawn each point on line has vertices between the current can are arranged so the order of pixels has minimal difference

Character Scans

• Character is scan converts with lettters are scan conversions and uses raster or bitmap font or vector/outline font
• The latter have has lines, and curves

Anti-Aliasing

• Is the effort to "smooth out" distortions in the image called Aliasing, where distortion called conversion. In the architecture
• Four main factor is:
  • Stacase the jagged appearance
  • Unequal brightness of lines, where constant light shows different contrast,
  • Other issue that happen is the picket fence of not all image align and there issue with isolated "on pixels"
  • Solution often to have better dithering and matrix

Error Propagation and Diffusion

• Error is distributed with formula, often through a matrix, and it can work to eliminate visual artifacts

Dithering and Mitigation

• Alleviation is a focus and simplified graphics pipeline, with a simplified architecture that represents object and performs scans while or without anti- aliasing

Introduction

• The main goal of geometrical transformation is to emulate the manipulation of spaces like rotation and displacement. Geometric transformations transform the objects to remain stationary Two dimensional and three dimensional transformations exist and have various matrix and mathematical implementations.

Geometric Tranformations

• Basic Geometric operations include translations, rotation and scaling operation that will accomplish via sequences and steps.

Coordinates

• Let us impose a coordinate system on the plane objects in the space. Every point will include a corresponding set of xy coordinates and coordinates from 3d space

Translation

• An object can be displaced a given distance and direction from its original origin.
• Displacements are vector with I and J notation to dictate direction.

Rotation

• Object rotate 0° over an origin and a positive angle and then counterClockwise notation is noted.

Scaling

• The Dimension on the object can be compressed and the transformation for the shape given by ratio to origin

Two Dimensional Transformations

• In two dimensional geometry, the coordinates of the point can be specified relative to set axis I and rotated J axis.
• The scaling in the form of units as with the original data that is a key addition the description of its space

Geometric Manipulation with matrices

• Various tools and transformation are encoded in each coordinate system and with direct codiing various processes, we may set it an arbitrary direction within space.

Composites

• We describe the transformation that rotates with the help of coordinate geometry

• We are able to take various complex 4D vectors , compute to get their result

Transformation Matrices

• If the object is created and inscribed within space, we can measure from the point a space dimensioned from axis. They are to - To scale the point and make the location proportional to it:

Color and Shading Models - Light:

• Light source is located somewhere from the centre and and the camear, where the mathematic formulas optical is model of a local illumination

Imageing

Image have processing such as the monitor, which does require bit and that is not be cooded for the value and function of an array in ram

Mathematics for 3D image

• The basis is the number, line segment the vector that are all described and used by the 3d

Ray Tracing

• Ray tracing is global illumination model that counts for transport of light energy. Ray tracing makes computing ray surface intersections