CS-378: Game TechnologyLecture #2.2: Clipping and

Hidden Surfaces

Prof. Okan ArikanUniversity of Texas, Austin

Thanks to James O’Brien, Steve Chenney, Zoran Popovic, Jessica HodginsV2005-06-1.1

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Today

Clipping Clipping to view volumeClipping arbitrary polygons

Hidden Surface RemovalZ-BufferBSP TreesOthers

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ClippingStuff outside view volume should not be drawn

Too close: obscures view

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ClippingStuff outside view volume should not be drawn

Too close: obscures viewToo far:

ComplexityZ-buffer problems

Too high/low/right/left:Memory errorsBroken algorithmsComplexity

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Clipping Line to Line/PlaneLine segment to be clipped

Line/plane that clips it

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Clipping Line to Line/PlaneLine segment to be clipped

Line/plane that clips it

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Clipping Line to Line/PlaneSegment may be on one side

Lines may be parallel

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Polygon Clip to Convex Domain

Convex domain defined by collection of planes (or lines or hyper-planes)Planes have outward pointing normalsClip against each plane in turnCheck for early/trivial rejection

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Polygon Clip to Convex Domain

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Polygon Clip to Convex Domain

Inside Outside

s

p

Output p

Inside Outside

sp

Output i

Inside Outside

s

p

No output

Inside Outside

sp

Output i and p

i

i

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Polygon Clip to Convex Domain

Sutherland-Hodgman algorithmBasically edge walking

Clipping done often... should be efficient

Liang-Barsky parametric space algorithmSee text for clipping in 4D homogenized coordiantes

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General Polygon Clipping

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Weiler AlgorithmDouble edges

General Polygon Clipping

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Hidden Surface RemovalTrue 3D to 2D projection would put every thing overlapping into the view plane.We need to determine what’s in front and display only that.

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Z-BuffersAdd extra depth channel to imageWrite Z values when writing pixelsTest Z values before writing

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Z-BuffersBenefits

Easy to implementWorks for most any geometric primitiveParallel operation in hardware

LimitationsQuantization and aliasing artifactsOverfillTransparency does not work well

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Z-BuffersTransparency requires partial sorting:

Partiallytransparent

Opaque

Opaque 1st

2nd

3rdFront

Good

Partiallytransparent

Opaque

Opaque 2nd

3rd

1st

Not Good

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Z-BuffersRecall depth-value distortions.

It’s a feature...More resolution near viewerBest use of limited precision

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A-BuffersStore sorted list of “fragments” at each pixelDraw all opaque stuff first then transparentStuff behind full opacity gets ignored

Nice for antialiasing...

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Scan-line AlgorithmAssume polygons don’t intersectEach time an edge is crossed determine who’s on top

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Painter’s AlgorithmSort Polygons Front-to-Back

Draw in orderBack-to-Front works also, but wasteful

How to sort quickly?Intersecting polygons?Cycles?

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BSP-TreesBinary Space Partition Trees

Split space along planesAllows fast queries of some spatial relations

Simple construction algorithmSelect a plane as sub-tree rootEverything on one side to one childEverything on the other side to other childUse random polygon for splitting plane

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BSP-Trees

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BSP-Trees

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BSP-Trees

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BSP-Trees

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BSP-Trees

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BSP-Trees

+ -

+ - + -

+ +

+

+ +

+

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Visibility TraversalVariation of in-order-traversal

Child oneSub-tree rootChild two

Select “child one” based on location of viewpoint

Child one on same side of sub-tree root as viewpoint

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BSP-Trees

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BSP-Trees

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Suggested Reading

Fundamentals of Computer Graphics by Pete Shirley

Chapter 7Clipping in chapter 11.1 and 11.2