BCA 4th Sem Notes-The Window-to-Viewport Transformations

• UNIT-I 

~The Advantages of Interactive Graphics
~Representative Uses of Computer Graphics 
~Classification of Application Development of Hardware and software for computer Graphics
~Overview, Scan:
~Converting Lines
~Scan Converting Circles
~Scan Converting Ellipses

UNIT-II 

~Hardcopy Technologies
~Display Technologies
~Raster-Scan Display System
~Video Controller
~Random-Scan Display processor
~Input Devices for Operator Interaction
~Image Scanners
~Working exposure on graphics tools like Dream Weaver, 3D Effects etc
~Clipping
~Southland- Cohen Algorithm
~Cyrus-Beck Algorithm
~Midpoint Subdivision Algorithm

UNIT-III 

~Geometrical Transformation
~2D Transformation
~Homogeneous Coordinates and Matrix Representation of 2DTransformations 
~composition of 2D Transformations
~The Window-to-Viewport
Transformations

~Introduction to 3D Transformations Matrix

UNIT-IV 

Representing Curves & Surfaces----

Polygon meshes parametric

Cubic Curves

Quadric Surface

Solid Modeling   Representing Solids

Regularized Boolean Set Operation primitive Instancing Sweep   Representation
Boundary Representations
Spatial Partitioning Representations
Constructive Solid Geometry Comparison of Representations

UNIT-V                           

~Multimedia Definition
~CD-ROM and the multimedia highway
~Computer Animation
(Design, types of animation, using different functions)

UNIT-VI  

~Uses of Multimedia
~Introduction to making multimedia –
~The stage of Project
~hardware & software requirements to make good multimedia skills
~Training opportunities in Multimedia Motivation for Multimedia usage

The Window-to-Viewport  

Transformations

Once object descriptions have been transferred to the viewing reference frame, we choose

the window extents in viewing coordinates and select the viewport limits in normalized

coordinates. Object descriptions are then transferred to normalized device coordinates.

We do this using a transformation that maintains the same relative placement of objects

in normalized space as they had in viewing coordinates. If a coordinate position is at the center of the viewing window, for instance, it will be displayed at the center of the

viewport

A point at position (xw, yw) in the window is mapped into position (xv, yv) in the associated view-port. To maintain the same relative placement in the viewport as in the window, we require that

• World coordinate – It is the Cartesian coordinate w.r.t which we define the diagram, like Xwmin, Xwmax, Ywmin, Ywmax
• Device Coordinate –It is the screen coordinate where the objects is to be displayed, like Xvmin, Xvmax, Yvmin, Yvmax
• Window –It is the area on the world coordinate selected for display.
• ViewPort –It is the area on the device coordinate where graphics is to be displayed.

             Solving these impressions for the viewport position (xv, yv), we have
                 xv=xv_min+(xw-xw_min)sx
                 yv=yv_min+(yw-yw_min)sy ...........equation 2

        Where scaling factors are

Above equations can also be derived with a set of transformations that converts the window area into the viewport area. This conversion is performed with the following sequence of transformations:

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.

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 the output device.

Next TopicIntroduction to 3D Transformations Matrix

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