Raster graphics

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Raster graphics Line Drawing Algorithms
Kaushik.S VIT
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Raster

• The word "raster" has its origins in the Latin
  rastrum (a rake), which is derived from radere
  (to scrape), and was originally used in the
  raster scan of cathode ray tubes (CRT), which
  paint the image line by line it is used for a
  grid of pixels by generalization.

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Raster graphics- An Introduction

• In computer graphics, a raster graphics image or
  bitmap is a data structure representing a
  generally rectangular grid of pixels, or points
  of color, viewable via a monitor, paper, or other
  display medium.
• Raster images are stored in image files with
  varying formats.

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Bitmap

• A bitmap corresponds bit-for-bit with an image
  displayed on a screen, generally in the same
  format used for storage in the display's video
  memory, or maybe as a device-independent bitmap.
• A bitmap is technically characterized by the
  width and height of the image in pixels and by
  the number of bits per pixel (a color depth,
  which determines the number of colors it can
  represent).

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• Imagine the smiley face in the top left corner as
  an RGB bitmap image. When enlarged, it might look
  like the big smiley face to the right.
• Every square represents a pixel. Zooming in
  further, the individual pixels can be analyzed,
  with their colors constructed by adding the
  values for red, green and blue.

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Resolution

• Raster graphics are resolution dependent. They
  cannot scale up to an arbitrary resolution
  without loss of apparent quality.
• This property contrasts with the capabilities of
  vector graphics, which easily scale up to the
  quality of the device rendering them.
• Raster graphics deal more practically than
  vector graphics with photographs and
  photo-realistic images, while vector graphics
  often serve better for typesetting or for graphic
  design.

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• Modern computer-monitors typically display about
  72 to 130 pixels per inch (PPI), and some modern
  consumer printers can resolve 2400 dots per inch
  (DPI) or more
• Typically, a resolution of 150 to 300 pixel per
  inch works well for 4-color process (CMYK)
  printing.

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Raster-based image editors

• Raster-based image editors, such as Photoshop, MS
  Paint, and GIMP, revolve around editing pixels,
• unlike vector-based image editors, such as
  CorelDRAW, Adobe Illustrator, or Inkscape, which
  revolve around editing lines and shapes
  (vectors).

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Raster-based image editors

• When an image is rendered in a raster-based image
  editor, the image is composed of millions of
  pixels. At its core, a raster image editor works
  by manipulating each individual pixel.
• Most pixel-based image editors work using the RGB
  color model, but some also allow the use of other
  color models such as the CMYK color model.

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File formats

• Bitmap
• A bitmap or pixmap is pixel data storage
  structure employed by the majority of raster
  graphics file formats such as PNG.
• OpenRaster
• OpenRaster is a file format being developed under
  the auspices of the Create Project to give free
  software graphics editors a common raster
  graphics interchange format, that maintains as
  much of the working information that the
  applications use.
• .ico
• ICO file format is an image file format for icons
  in Microsoft Windows. .ico files contain one or
  more small images at multiple sizes and color
  depths.

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Programming in the Simple Raster Graphics Package
(SRGP)

• Cartesian coordinates
• A coordinate system base on two perpendicular
  axes, with positive coordinates to the right of
  the origin and above the origin.
• OR mode
• A graphic write mode in which each pixel bit
  becomes 1 if the current display bit is 1 or if
  the bit being written is 1.
• arc
• A section of an ellipse.
• canvas
• An area of memory which is used as a buffer
  between graphics software and graphics hardware.
• clipping
• The restriction of rendering to a designated
  area.

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SRGP (cont)

• exclusive or mode
• A graphic write mode in which each pixel bit
  becomes 1 only if the current display bit and the
  bit being written are different. font
• A set of character glyphs, usually consistent
• line
• A one dimensional geometric figure defined by two
  points.
• point
• A geometric figure with location only.
• replace mode
• A graphic write mode which is not affected by the
  previous contents of the display.
• screen coordinates
• A coordinate system based on the pixels of the PC
  BIOS, with the origin being at the upper left of
  the screen, and pixel rows being numbered
  downward.

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Graphics Hardware

• Its worth taking a little look at how graphics
  hardware works before we go any further
• How do things end up on the screen?

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Architecture Of A Graphics System
Display Processor Memory
Frame Buffer
Video Controller
Monitor
Monitor
CPU
Display Processor
System Memory
System Bus
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Output Devices

• There are a range of output devices currently
  available
• Printers/plotters
• Cathode ray tube displays
• Plasma displays
• LCD displays
• 3 dimensional viewers
• Virtual/augmented reality headsets
• We will look briefly at some of the more common
  display devices

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Basic Cathode Ray Tube (CRT)

• Fire an electron beam at a phosphor coated screen

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Raster Scan Systems

• Draw one line at a time

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Colour CRT

• An electron gun for each colour red, green and
  blue

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Plasma-Panel Displays

• Applying voltages to crossing pairs of conductors
  causes the gas (usually a mixture including neon)
  to break down into a glowing plasma of electrons
  and ions

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Liquid Crystal Displays

• Light passing through the liquid crystal is
  twisted so it gets through the polarizer
• A voltage is applied using the crisscrossing
  conductors to stop the twisting and turn pixels
  off

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2D Line Drawing AlgorithmThe Problem Of Scan
Conversion

• A line segment in a scene is defined by the
  coordinate positions of the line end-points

(7, 5)
(2, 2)
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The Problem (cont)

• But what happens when we try to draw this on a
  pixel based display?

• How do we choose which pixels to turn on?

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Considerations

• Considerations to keep in mind
• The line has to look good
• Avoid jaggies
• It has to be lightening fast!
• How many lines need to be drawn in a typical
  scene?
• This is going to come back to bite us again and
  again

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Line Equations

• Lets quickly review the equations involved in
  drawing lines

• Slope-intercept line equation

• where

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Lines Slopes

• The slope of a line (m) is defined by its start
  and end coordinates
• The diagram below shows some examples of lines
  and their slopes

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A Very Simple Solution

• We could simply work out the corresponding y
  coordinate for each unit x coordinate
• Lets consider the following example

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A Very Simple Solution (cont)
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A Very Simple Solution (cont)

• First work out m and b

• Now for each x value work out the y value

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A Very Simple Solution (cont)

• Now just round off the results and turn on these
  pixels to draw our line

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A Very Simple Solution (cont)

• However, this approach is just way too slow
• In particular look out for
• The equation y mx b requires the
  multiplication of m by x
• Rounding off the resulting y coordinates
• We need a faster solution

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A Quick Note About Slopes

• In the previous example we chose to solve the
  parametric line equation to give us the y
  coordinate for each unit x coordinate
• What if we had done it the other way around?
• So this gives us
• where and

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A Quick Note About Slopes (cont)

• Leaving out the details this gives us
• We can see easily that this line doesnt
  lookvery good!
• We choose which way to work out the line pixels
  based on the slope of the line

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A Quick Note About Slopes (cont)

• If the slope of a line is between -1 and 1 then
  we work out the y coordinates for a line based on
  its unit x coordinates
• Otherwise we do the opposite x coordinates are
  computed based on unit y coordinates

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A Quick Note About Slopes (cont)
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The DDA Algorithm

• The digital differential analyzer (DDA) algorithm
  takes an incremental approach in order to speed
  up scan conversion
• Simply calculate yk1 based on yk

The original differential analyzer was a physical
machine developed by Vannevar Bush at MIT in the
1930s in order to solve ordinary differential
equations. .
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The DDA Algorithm (cont)

• Consider the list of points that we determined
  for the line in our previous example
• (2, 2), (3, 23/5), (4, 31/5), (5, 34/5), (6,
  42/5), (7, 5)
• Notice that as the x coordinates go up by one,
  the y coordinates simply go up by the slope of
  the line
• This is the key insight in the DDA algorithm

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The DDA Algorithm (cont)

• When the slope of the line is between -1 and 1
  begin at the first point in the line and, by
  incrementing the x coordinate by 1, calculate the
  corresponding y coordinates as follows
• When the slope is outside these limits, increment
  the y coordinate by 1 and calculate the
  corresponding x coordinates as follows

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The DDA Algorithm (cont)

• Again the values calculated by the equations used
  by the DDA algorithm must be rounded to match
  pixel values

(round(xk 1/m), yk1)
(xk1, round(ykm))
(xk, yk)
(xk 1/m, yk1)
(xk, yk)
(xk1, ykm)
(round(xk), yk)
(xk, round(yk))
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DDA Algorithm Example

• Lets try out the following examples

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DDA Algorithm Example (cont)
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The DDA Algorithm Summary

• The DDA algorithm is much faster than our
  previous attempt
• In particular, there are no longer any
  multiplications involved
• However, there are still two big issues
• Accumulation of round-off errors can make the
  pixelated line drift away from what was intended
• The rounding operations and floating point
  arithmetic involved are time consuming

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Any Doubts???