BCA 4Sem Notes- Cyrus-Beck Algorithm

• 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

Cyrus-Beck Algorithm

Cyrus-Beck Line Clipping Algorithm

Cyrus Beck Line cutting calculation is really, a parametric line-cutting calculation. The term parametric implies that we require finding the estimation of the parameter t in the parametric portrayal of the line section for the point at that the fragment converges the cut-out edge

This algorithm is more efficient than the Cohen-Sutherland algorithm. It employs parametric line representation and simple dot products.

Parametric equation of line is −

P0P1:P(t) = P0 + t(P1 - P0)

Let Ni be the outward normal edge Ei. Now pick any arbitrary point PEi on edge Ei then the dot product Ni.[Pt$t$ – PEi] determines whether the point Pt$t$ is “inside the clip edge” or “outside” the clip edge or “on” the clip edge.

The point Pt$t$ is inside if Ni.[Pt$t$ – PEi] < 0

The point Pt$t$ is outside if Ni.[Pt$t$ – PEi] > 0

The point Pt$t$ is on the edge if Ni.[Pt$t$ – PEi] = 0 Intersectionpoint$Intersectionpoint$

Ni.[Pt$t$ – PEi] = 0

Ni.[ P0 + t(P1 - P0) – PEi] = 0 ReplacingP(t$ReplacingP(t$ with P0 + t(P1 - P0))

Ni.[P0 – PEi] + Ni.t[P1 - P0]      = 0

Ni.[P0 – PEi] + Ni∙tD      = 0 (substituting D for [P1 - P0])

Ni.[P0 – PEi]     = - Ni∙tD

The equation for t becomes,

t=Ni.[Po−PEi]−Ni.D$$t=\frac{N_i.[P_o-P_{Ei}]}{-N_i.D}$$

It is valid for the following conditions −

• Ni ≠ 0 errorcannothappen$errorcannothappen$
• D ≠ 0 (P1 ≠ P0)
• Ni∙D ≠ 0 (P0P1 not parallel to Ei)

Next TopicMidpoint Subdivision Algorithm

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