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Introduction to Computer Graphics

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Title: Introduction to Computer Graphics Author: Siva Kumar Description: ll product. Last modified by: masyura Created Date: 2/24/2000 11:52:41 AM Document ... – PowerPoint PPT presentation

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Title: Introduction to Computer Graphics


1
Introduction to Computer Graphics
  • Chapter 6 2D Viewing Pt 1

2
Two-Dimensional Viewing
  • Co-ordinate Systems.
  • Cartesian offsets along the x and y axis from
    (0.0)
  • Polar rotation around the angle ?.
  • Graphic libraries mostly using Cartesian
    co-ordinates
  • Any polar co-ordinates must be converted to
    Cartesian co-ordinates
  • Four Cartesian co-ordinates systems in computer
    Graphics.
  • 1. Modeling co-ordinates
  • 2. World co-ordinates
  • 3. Normalized device co-ordinates
  • 4. Device co-ordinates

3
Modeling Coordinates
  • Also known as local coordinate.
  • Ex where individual object in a scene within
    separate coordinate reference frames.
  • Each object has an origin (0,0)
  • So the part of the objects are placed with
    reference to the objects origin.
  • In term of scale it is user defined, so,
    coordinate values can be any size.

4
World Co-ordinates.
  • The world coordinate system describes the
    relative positions and orientations of every
    generated objects.
  • The scene has an origin (0,0).
  • The object in the scene are placed with reference
    to the scenes origin.
  • World co-ordinate scale may be the same as the
    modeling co-ordinate scale or it may be
    different.
  • However, the coordinates values can be any size
    (similar to MC)

5
Normalized Device Co-ordinates
  • Output devices have their own co-ordinates.
  • Co-ordinates values
  • The x and y axis range from 0 to 1
  • All the x and y co-ordinates are floating point
    numbers in the range of 0 to 1
  • This makes the system independent of the various
    devices coordinates.
  • This is handled internally by graphic system
    without user awareness.

6
Device Co-ordinates
  • Specific co-ordinates used by a device.
  • Pixels on a monitor
  • Points on a laser printer.
  • mm on a plotter.
  • The transformation based on the individual device
    is handled by computer system without user
    concern.

7
Two-Dimensional Viewing
  • Example
  • Graphic program which draw an entire building by
    an architect but we only interested on the ground
    floor
  • Map of sales for entire region but we only like
    to know from certain region of the country.

8
Two-Dimensional Viewing
  • When we interested to display certain portion of
    the drawing, enlarge the portion, windowing
    technique is used
  • Technique for not showing the part of the drawing
    which one is not interested is called clipping
  • An area on the device (ex. Screen) onto which the
    window will be mapped is called viewport.
  • Window defines what to be displayed.
  • A viewport defines where it is to be displayed.
  • Most of the time, windows and viewports are
    usually rectangles in standard position(i.e
    aligned with the x and y axes). In some
    application, others such as general polygon shape
    and circles are also available
  • However, other than rectangle will take longer
    time to process.

9
Viewing Transformation
  • Viewing transformation is the mapping of a part
    of a world-coordinate scene to device
    coordinates.
  • In 2D (two dimensional) viewing transformation is
    simply referred as the window-to-viewport
    transformation or the windowing transformation.
  • Mapping a window onto a viewport involves
    converting from one coordinate system to another.
  • If the window and viewport are in standard
    position, this just
  • involves translation and scaling.
  • if the window and/or viewport are not in
    standard, then extra transformation which is
    rotation is required.

10
Viewing Transformation
y-world
y-view
window
window
1
x-view
0
1
x-world
world
Normalised device
11
Window-To-Viewport Coordinate Transformation
Window-to-Viewport transformation
12
Window-To-Viewport Coordinate Transformation
YWmax
YVmax
xw,yw
xv,yv
YWmin
YVmin
XVmax
XVmin
XWmin
XWmax
13
Window-To-Viewport Coordinate Transformation
xv - xvmin xw - xwmin xvmax -
xvmin xwmax - xwmin   yv
yvmin yw - ywmin yvmax yvmin
ywmax - ywmin   From these two equations
we derived xv xvmin (xw xwmin)sx yv
yvmin (yw ywmin)sy where the scaling factors
are   sx xvmax xvmin sy yvmax -
yvmin xwmax xwmin
ywmax - ywmin  
14
Window-To-Viewport Coordinate Transformation
The sequence of transformations are 1. Perform
a scaling transformation using a fixed-point
position of (xwmin,ywmin) that scales the window
area to the size of the viewport. 2. Translate
the scaled window area to the position of the
viewport.
15
Window-To-Viewport Coordinate Transformation
  • Relative proportions of objects are maintained if
    the scaling factors are the same (sx sy).
    Otherwise, world objects will be stretched or
    contracted in either x or y direction when
    displayed on output device.
  • How about character strings when map to viewport?
  • maintains a constant character size (apply when
    standard character fonts cannot be changed).
  • If character size can be changed, then windowed
    will be applied like other primitives.
  • For characters formed with line segments, the
    mapping to viewport is carried through sequence
    of line transformations .

16
Viewport-to-Normalized Device Coordinate
Transformation
  • From normalized coordinates, object descriptions
    can be mapped to the various display devices
  • When mapping window-to-viewport transformation is
  • done to different devices from one normalized
    space, it is
  • called workstation transformation.

17
The Viewing Pipeline
18
OpenGL 2D Viewing Functions
  • To transform from world coordinate to screen
    coordinates, the appropriate matrix mode must be
    chosen
  • glMatrixMode (GL_PROJECTION)
  • glLoadIdentity( )
  • To define a 2D clipping window, we use OpenGL
    Utility function
  • gluOrtho2D( xwmin, xwmax, ywmin, ywmax)
  • This function also perform normalization (NDC)

19
OpenGL 2D Viewing Functions
  • To specify the viewport parameters in OpenGL, we
    use function
  • glViewport(xvmin, yvmin, vpWidth, vpHeight)
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