20072cgraphics-unit 8b 2d clipping v2

8/6/2019 20072CGraphics-Unit 8B 2D Clipping v2

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1

Computer Graphics

311321


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2

CHAPTER SIX

Two-DimensionalClipping


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Clipping

For the image below consider which points shouldbe kept and which ones should be clipped

wymax

wymin

wxmin wxmax

Window

P1

P2

P3P6

P5P7

P10

P9

P4

P8


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Point Clipping

Easy - a point (x,y) is not clipped if: wxmin x wxmax AND wymin y wymaxotherwise it is clipped

wymax

wymin

wxmin wxmax

Window

P1

P2

P5

P7

P10

P9

P4

P8

Clipped

Points Within the Window

are Not Clipped

Clipped

Clipped

Clipped


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5

Two-Dimensional Point Clipping

For a clipping rectangle in standard position, we save a two-

dimensional point P = (x,y) for display if the following inequalities

are satisfied:

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

(not saved for display).

Point clipping is useful in applications when pictures are modeledwithparticle systems. For example, scenes involving clouds and

smoke.

12)-(6maxmin

maxmin

ywyyw

xwxxw


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Point Clipping

6

Exercise: P1 = (10, 20), P2 = (30, 50), P3 = (60, 90), and

P4 = (130, 150). Suppose that the coordinates of the two

opposite corners of the clip window are

(xwmin, ywmin) = (30, 30) and (xwmax, ywmax) = (130, 110).Which of the above points will be clipped?


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7

Two-Dimensional Line Clipping

Figure 6-11 illustrates possible positions for straight-line segments

in relationship to a standard clipping window.

A line-clipping algorithm processes each line in a scene through a

series of tests and intersection calculations to determine whether

the entire line or any part of it is to be saved for display.


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Line Clipping

8


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Sutherland: Line Clipping

9

- One of the oldest and most popular line-clipping

procedures.

- The method speeds up the processing of line

segments by performing initial tests that reduce thenumber of intersections that must be calculated.

- Efficient method of accepting or rejecting lines that

dont intersect the window edges.


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10

Lines that cross a boundary of the window, are clipped

by computing the coordinates of the new boundary

endpoint of the line where it crosses the edge of the window.

Assign a binary 4 bit code to each vertex by comparing

it to clip coordinates:

Bit 1 (left): the sign bit ofxxwmin.

Bit 2 (right): the sign bit ofxwmaxx.

Bit 3 (below): the sign bit ofy - ywmin

Bit 4 (above): the sign bit ofywmaxy.


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Sutherland: World Division

11


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Sutherland: Labelling

Every end-point is labelled with theappropriate region code

wymax

wymin

wxmin wxmax

Window

P3 [0001]P6 [0000]

P5 [0000]

P7 [0001]

P10 [0100]

P9 [0000]

P4 [1000]

P8 [0010]

P12 [0010]

P11 [1010]

P13 [0101] P14 [0110]


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Sutherland: Lines In The Window

Lines completely contained within the windowboundaries have region code [0000] for both

end-points so are not clipped

wymax

wymin

wxmin wxmax

Window

P3 [0001]P6 [0000]

P5 [0000]

P7 [0001]

P10 [0100]

P9 [0000]

P4 [1000]

P8 [0010]

P12 [0010]

P11 [1010]

P13 [0101] P14 [0110]


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Sutherland: Lines Outside The Window

Any lines with a common set bit in the regioncodes of both end-points can be clipped

The AND operation can efficiently check this

wymax

wymin

wxmin wxmax

Window

P3 [0001]P6 [0000]

P5 [0000]

P7 [0001]

P10 [0100]

P9 [0000]

P4 [1000]

P8 [0010]

P12 [0010]

P11 [1010]

P13 [0101] P14 [0110]


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Sutherland: Other Lines

Lines that cannot be identified ascompletely inside or outside the window mayor may not cross the window interior

These lines are processed as follows: Compare an end-point outside the window to a

boundary (choose any order in which toconsider boundaries e.g. left, right, bottom, top)

and determine how much can be discarded

If the remainder of the line is entirely inside oroutside the window, retain it or clip itrespectively


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Sutherland: Other Lines (cont)

Otherwise, compare the remainder of the lineagainst the other window boundaries

Continue until the line is either discarded or a

segment inside the window is foundWe can use the region codes to determinewhich window boundaries should beconsidered for intersection

To check if a line crosses a particularboundary we compare the appropriate bits inthe region codes of its end-points

If one of these is a 1 and the other is a 0 thenthe line crosses the boundary


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Sutherland Examples (cont)

Consider the line P3 to P4 below

Start at P4 From the region codes

of the two end-pointswe know the linecrosses the left

boundary so calculatethe intersection point togenerate P4

The line P3 to P4 is completely outside the

window so is clipped

wymax

wymin

wxmin wxmax

WindowP4 [1001]

P3 [0001]

P4 [1000]

P3 [0001]


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Compute the end point Outcodes of A and B;

if (A == 0000 && B == 0000)

the whole line is visible (accept it);

Else if (A AND B != 0000) the whole line is outside of window (reject it);

else repeat the following {

compute intersection;

clip outside part;

test again;

}

22


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Sutherland Example

25


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Sutherland Example

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Calculating Line Intersections (cont)

The x-coordinate of an intersection with ahorizontal window boundary can be calculatedusing:

x = x1 + (yboundary - y1) /mwhereyboundary can be set to either wymin orwymax

m is the slope of the line in question and canbe calculated as m = (y2 - y1) / (x2 - x1)


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To clip the polygon, we need to keep the fill area as an

entity as it is processed through the clipping stages as

shown in the following Figure:


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Shutherland-Hodgman Polygon Clipping

v1

v2

v3'

v4

v5

v6

Left border:v1 v2both inside v1 v2v2 v3both inside v2 v3..... ........

v1,v2,v3,v4v5,v6,v1 Bottom Border:

v1 v2both inside v1 v2v2 v3v2 i, v3 o v2 v3'v3 v4 both outside nonev4 v5 both outside none

v5 v6v5 o, v6 i v5' v6v6 v1both inside v6 v1v1,v2,v3',v5',v6,v1

v3

v5'


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Shutherland-Hodgman Polygon Clipping

v1

v2

v3

v4

v5

v6

v1,v2,v3',v5',v6,v1

Right border:v1 v2 v1 i, v2 o v1 v2'v2 v3 v2 o, v3'i v2'' v3'v3' v5 both inside v3' v5'v5' v6 both inside v5' v6v6 v1 both inside v6 v1

v1,v2',v2'',v3',v5',v6,v1 Top Border:

v1 v2' both outside nonev2' v2'' v2' o, v2'' i v2''' v2''v2'' v3' both inside v2'' v3'v3' v5' both inside v3' v5'

v5' v6 both inside v5' v6v6 v1 v6 i, v1 o v6 v1'v2''',v2'',v3',v5',v6,v1'

v3'

v5'

v2'

v2''

v2'''

v1'


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20072cgraphics-unit 8b 2d clipping v2

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