unit-iii - wordpress.com › 2015 › 01 › unit-3-11.pdfcourse contents • two-dimensional...

UNIT-III

4/8/2015 @Copyrights UNIT-3|Abhishek Khare| http://abhishekkharecloud.wordpress.com

By: Abhishek KhareSVIM Indore

Email Id: abhishekkhare@rocketmail.comWebsite: http://abhishekkharecloud.wordpress.com

Computer Graphics & Multimedia

4/8/2015 @Copyrights UNIT-3|Abhishek Khare| http://abhishekkharecloud.wordpress.com 2

• Viewing coordinates, Window, view port,clipping, Window to view port transformation,line clipping

• Algorithm; Cohen Sutherland, polygon clipping;Sutherland hodgman algorithm, 3D clipping :Normalized view volumes, view port clipping,clipping in homogeneous coordinates.

• Illumination model: Light sources, diffusereflection specular reflection, reflected light,intensity levels,

• Surface shading; phong shading groundshading, color models like RGB, YIQ, CMY, HSVetc.

Course Contents

• Two-Dimensional Viewing and Clipping• Three-Dimensional Clipping• Illumination Model and Surface Rendering

Methods• Color Models

Windowing and Clipping

• Typically a graphics package allows us tospecify which part of a defined picture is tobe displayed.

• Use of Scaling, translation and rotationtechnique.

The process of selecting and viewingthe picture with different views is calledwindowing.

A process which divides each elementof the picture into its visible and invisibleportions, allowing the invisible portion tobe discarded is called clipping.

Viewing Transformation• World Co-ordinate System (WCS)

– The picture is stored in the computer memory using any convenient Cartesian co-ordinate system.

• Physical Device Co-ordinate System(PDCS)– When picture is displayed on the display device it is

measured in pdcs.

Mapping: WCS PDCS= Viewing Transformation

Displaying an image of a picture involvesmapping the co-ordinates of the co-ordinatesof the points and lines that form the picture intothe appropriate physical device co-ordinatewhere the image is to be displayed. Thismapping of co-ordinates is achieved with theuse of co-ordinate transformation known asViewing Transformation.

How to achieve Viewing Transformation

– Normalization Transformation(N)

– Workstation Transformation(W)

Normalization Transformation(N)

• Different display devices may have different screen sizes as measured in pixels.

Less Resolution

MoreResolution

Contd.

• To avoid this and to make out programs to be device independent-

Normalized device co-ordinates

(1,1)(0,1)

(0,0)(1,0)

(0.5,0.5)

InterpreterNormalized device co-ordinate to the Actual device

coordinate• Formula

X = Xn * Xw

Y = Yn * Yh

WhereX : Actual device x co-ordinateY : Actual device y co-ordinateXn : Normalized x co-ordinate Yn : Normalized y co-ordinateXw : Width of actual screen in pixelsYh : Height of actual screen in pixels

The transformation which maps the world co-ordinate to normalized device co-ordinate is called normalization transformation.

It involves scaling of x and y thus it is also refereed to as scaling transformation.

Workstation Transformation(W)

The transformation which maps the normalizeddevice co-ordinate to physical device co-ordinate is called workstation transformation.

Viewing transformation = Normalization transformation * Workstation transformation

V = N*W

Two dimensional viewing transformation

Workstation Transformation[ Translation Scaling Translation]

Device co-ordinate(DC)

Normalization Transformation

Normalized coordinate(NC)

World co-ordinate(WC)

Window and Viewport

World co-ordinate system(WCS) is infinite Device display area is finite.

To perform a viewing transformation we select a finite world co-ordinate area for display called a window

An area on a device to which a window is mapped is called a viewport.

• The window define what is to be viewed• The viewport defines where it is to be

displayed.

How to achieve workstation transformation

W = T.S.T-1

Sx 0 0

0 Sy 0

Xvmin-Xwmin.Sx Yvmin-Ywmin.Sy 1

Sx = Xvmax – Xvmin/Xwmax - Xwmin

Sy = Yvmax – Yvmin/Ywmax - Ywmin

Numerical

Q1. Find the normalization transformationwindow to viewpoint, with window lower leftcorner at (1,1) and upper right corner at (3,5)onto a viewpoint with lower left corner at(0,0) and upper right corner at (1/2,1/2).

Sx = 0.25Sy= 0.125

0.25 0 0

0 0.125 0

-0.25 -0.125 1

PPTsIntroduction to multimedia, multimedia components,(UNIT-5)

Roll No- 1 to 5 (25/26 March)

multimedia ha(UNIT-5)rdware, SCSI, IDE, MCI

Roll No- 6 to 10 (6/7 April)

Multimediadata and file formats, RTF, TIFF, MIDI, JPEG, DIB, MPEG(UNIT-5)

Multimedia tools, presentations tools,Authoring tools, presentations. (UNIT-5)

Illumination model: Light sources, diffuse reflection specular reflection(UNIT-3)

Reflected light, intensity levels, (UNIT-3) Roll No- 28 to 30 (20/22 April)

Surface shading; phong shading ground shading(UNIT-3)

Color models like RGB, YIQ, CMY, HSV etc(UNIT-3)

Roll No- 36 to Last (27/28/29/30 April)

Numerical

Q2. Find the normalization transformationwindow to viewpoint, with window lower leftcorner at (1,1) and upper right corner at (3,5)onto a viewpoint for entire normalized devicescreen.

Sx = 1/2Sy= 1/4

0.5 0 0

0 0.25 0

-0.5 -0.25 1

Numerical

Q3. Find the normalization transformationwindow to viewpoint, with window lower leftcorner at (0,0) and upper right corner at (4,3)onto the normalized device screen so thatthe aspect ratio is preserved.

Sx = 1/4Sy= 1/4

1/4 0 0

0 1/4 0

View port (0.0) (1,3/4)

Window(0.0) (4,3)

Aspect ratio• A property of video monitors is aspect ratio.• This number gives the ratio of vertical points

to horizontal points necessary to produceequal-length lines in both directions on thescreen.

• An aspect ratio of 3/4 means that a verticalline plotted with three points has the samelength as a horizontal line plotted with fourpoints.

Clipping

A procedure which identifies the part of apicture that are either inside or outside of thespecified region of the space.

Before mapping the window onto viewport the partof the picture outside the window is to be discarded .This process of discarding is called “clipping”.

Line Clipping

Four-bit codes for nine regions

Sutherland and Cohen Subdivision Line Clipping Algorithm

• This algorithm uses a four digit (Bit) code toindicate which of nine regions contain the endpoint on line.

• The four bit codes are called region codes orout codes.

• These codes identify the location of the pointrelative to the boundaries of the clippingrectangle.

Contd.

• Set Bit 1- if the end point is to the left of thewindow.

• Set Bit 2- if the end point is to the right of thewindow.

• Set Bit 3- if the end point is to the below ofthe window.

• Set Bit 4- if the end point is to the above ofthe window.

• Otherwise, the bit set to zero

Algorithm: Steps

P1(x1,y1)

P2(x2,y2)

(Wx1 , Wy1)

(Wx2 , Wy2)

P1(0,2)

P2(5,7)

(2 , 5)

(7 , 0)

1. Read two end point of the line say P1(x1,y1) and P2(x2,y2).

2. Read two corners (left-top and right-bottom) of the window say (Wx1,Wy1) and (Wx2,Wy2).

3. Assign the region codes for two endpoints P1 and P2 using following steps:– Set Bit 1 – if (x < Wx1)– Set Bit 2 – if (x > Wx2)– Set Bit 3 – if (y < Wy2)– Set Bit 4 – if (y > Wy1)

4. Check for visibility of line P1P2a) If region codes for both endpoints P1 and P2

are zero then the line is completely visible.Hence draw the line and go to step 9.

b) If region codes for endpoints are not zero andthe logical ANDing of them is also nonzerothen the line is completely invisible, so rejectthe line and go to step 9.

c) If region codes for two endpoint do notsatisfy the conditions in 4(a) and 4(b) the lineis partially visible.

5. Determine the intersecting edge of theclipping window by inspecting the region codeof two endpoints.a) If region codes for both the end points are

non-zero, find intersection points P1’ and P2’with boundary edges of clipping window withrespect to point P1 and point P2 respectively.

b) If region code for any one end point is nonzero then find intersection point P1’ or P2’with the boundary edge of the clippingwindow with respect to it.

6. Divide the line segments considering intersection points.

7. Reject the line segment if any one end point of it appears outsides the clipping window.

8. Draw the remaining line segments.9. Stop.

unit-iii - wordpress.com › 2015 › 01 › unit-3-11.pdfcourse contents • two-dimensional...

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