Sun-Jeong Kim

2D Viewing

11th Week, 2008

Computer Graphics2

Two-Dimensional Viewing

The procedures for displaying views of a two-dimensional picture on an output device

To specify which part of a defined picture is to be displayed and where that part is to be placed on the display device

Computer Graphics3

2D Viewing Pipeline (1)

Clipping windowClipping windowA section of a 2D scene that is selected for display

World windowWorld window or viewing windowviewing window

ViewportViewportThe placement within the display window

Clipping WindowClipping Window ViewportViewport

What we want to see Where to be viewed on the output device

Computer Graphics4

2D Viewing Pipeline (2)

The mapping of a 2D, world-coordinate scene description to device coordinates

Computer Graphics5

Normalization and ViewportTransformations (1)

[Case 1] mapping the clipping window into a normalized viewport (0~1)

Scale translate

Computer Graphics6

Normalization and ViewportTransformations (2)

[Case 2] mapping the clipping window into a normalized square (–1~+1)

Scale translate scale translate

Computer Graphics7

Clipping Algorithms

Procedures that eliminate those portions of a picture that are either inside or outside of a specified region of space

Point clipping

Line clipping (straight-line segments)

Fill-area clipping (polygons)

Curve clipping

Text clipping

Computer Graphics8

2D Point Clipping

A 2D point P=(x, y) is inside the clipping window, if the following inequalities are satisfied:

If any one of these four inequalities is not satisfied, the point is clipped

maxmin

maxmin

ywyyw

xwxxw

≤≤≤≤

Computer Graphics9

2D Line Clipping

Clipping straight-line segments using a standard rectangular clipping window

Computer Graphics10

Cohen-Sutherland Line Clipping (1)

Every line endpoint in a picture is assigned a four-digit binary value

Region codeRegion code

True (or 1) – endpoint is outside of that window border

Computer Graphics11

Cohen-Sutherland Line Clipping (2)

The nine binary region codes

Computer Graphics12

Cohen-Sutherland Line Clipping (3)

Classifying some lines quickly by AND of region codes of two endpoints (must be 0)

P10

P5

P6

P9

1000P7

P8

1010

0010

01100100

0000

0101

0001

P1

P2

1001

P4

P3

Computer Graphics13

Cohen-Sutherland Line Clipping (4)

To clip a line segment, several intersection calculations might be necessary

P6

1000 1010

0010

01100100

0000

0101

0001

1001

P4

P3

P’5

P’7

P’8

Computer Graphics14

Polygon Fill-Area Clipping

Processing a polygon fill area against successive clipping-window boundaries (left, right, bottom, and top)

Computer Graphics15

Sutherland-Hodgman Polygon Clipping

Sending the polygon vertices through each clipping stage

A single clipped vertex can be immediately passed to the next stage