2D and 3D clipping.pdf

7/27/2019 2D and 3D clipping.pdf

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Clipping


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When?


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2D clipping


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2D clipping

? Part of the primitive is inside the window

defined in WCS

Remark: clipping is done to avoid the cost of

future transformations on those parts of the

primitives that are not visible in the image


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Methods

1. Analytic

2. During the scan conversion

3. Copy pixels from one memory region to

another memory region

Remark: Met 1 for lines and polygons, Met 2 for

other primitives


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Point clipping

Suppose a rectangular window with the

corners (xmin,ymin) and (xmax,ymax)

P(x,y) is visible

xmin


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Simple alg. for line segments

Suppose F=rectangular window; ? PQ/F


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Acceptance / rejection tests

Accept if both ends of the segment are visible

Reject if both ends of the segment are un the

same part of the window (left, right, top,

bottom)

Simple alg + tests = efficient alg when the no.

of interior or exterior segments is big


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Acceptance/rejection tests and coding


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Examples


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Cohen-Sutherland alg.


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Example


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Examples


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Examples


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Examples


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Bisection algorithm

Principle: if the tests for acceptance or

rejection fail on PQ then PQ is divided in twosegments, PR, RQ, R=(P+Q)/2

? PR, PQ accepted/rejected

Remark: segments are accepted or rejected

at most after log2 N steps, where N is the

dimension in pixels of the discretized version

of the segment PQ


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Parametric line clipping algorithm

(Cyrus-Beck algorithm)

Suppose:

trigonometric sense

An edge of the window is inside the window

The normal N to an edge E is oriented towards

window exterior

The support line for a given segment P1P0 is

P(t)=P0+(P1-P0)t, t in R.

Suppose x0


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Cyrus-Beck algorithm


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CB alg - computations


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Simplifying the computations


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Nicholl-Lee-Nicholl algorithm


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Code of NLN algorithm


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Weiler-Atherton alg.


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Polygon clipping


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Polygon clipping


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Polygon clipping

Tests for acceptance/rejection: method of

bounded aria by finding the smallest rectaglethat surrounds the polygon

Sutherland-Hodgman algorithm:

Divide-et-impera strategy

No. stages = no. edges of the clipping polygon

I: list of initial vertex

O: list of final vertex


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Bounded aria method


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SH algorithm


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SH Algorithm


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SH Algorithm


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SH algorithm


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SH algorithm


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SH algorithm


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Liang Barsky algorithm

Suppose F=rectangle, vertex {P1,P2,Pn}

numbered in trigonometric order ? {P1,P2,Pn} defining the clipped polygon

Interior region 2 = corner region

Interior region 3 = edge region

Remark: an edge is entering in a corner

region => the corner is added to the outputlist


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LB alg


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LB alg: passing through a corner region


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LB alg


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LB alg


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3d Clipping


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3d clipping


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3d clipping

With respect to the viewing volume

Methods: generalization from 2d->3d: Cohen-Sutherland, bisection, Cyrus-Beck

Cohen-Sutherlang alg: using the canonic volume


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3d clipping, perspective


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CS Alg - codes

Bit Canonic vol./ Canonic vol./

parallel proj. perspective proj.


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3d clipping

l


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CS alg - computations

C B k l


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Cyrus-Beck alg.

CB l d


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CB alg - code

Documents

2D and 3D clipping.pdf