BCA 4th Sem Notes-Homogeneous Coordinates and Matrix Representation of 2D 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

Homogeneous Coordinates and Matrix Representation of 2DTransformations

Homogeneous Coordinates

The revolution of a point, straight line or a whole picture on the screen, about a point other than the root, is accomplished by first moving the picture until the purpose of turn possesses the birthplace, the performing pivot, at that point, at last, moving the picture to its unique position. 

The moving of a picture starting with one spot then onto the next in an orderly fashion is known as an interpretation. An interpretation might be finished by adding or subtracting to each point, the sum, by which picture is required to be moved. 

Interpretation of point by the difference in arrangement can't be joined with different changes by utilizing straightforward grid applications. Such a mix is basic in the event that we wish to turn a picture about a point other than beginning by interpretation, pivot again interpretation. 

To join these three changes into a solitary change, homogeneous directions are utilized. Inhomogeneous organize frameworks, two-dimensional facilitate positions (x, y) is spoken to by triple-arranges.

Homogeneous coordinates are generally used in design and construction applications. Here we perform translations, rotations, scaling to fit the picture into proper position.

Example of representing coordinates into a homogeneous coordinate system: For a two-dimensional geometric change, we can pick homogeneous parameter h to any non-zero worth. For our benefit accept it as one. Every two-dimensional position is then spoken to with homogeneous directions (x, y, 1).

the matrix for two-dimensional transformation in homogeneous coordinate:

Matrix Representation of 2D Transformations

Next Topiccomposition of 2D Transformations

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