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3D Hidden Surface Removal

2001.2.28

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Contents

Goal Motivation Approaches

- back face detection- depth buffer- A-buffer- Scan line- Depth sorting

- BSP-tree- Area subdivision- Ray casting

Conclusion

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Goal

A major consideration isidentifying those parts of a scene thatare visible from a chosen view position.

Represent realistic 3D display

Visual-surface detection methods

hidden-surface elimination methods

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Surfaces may be various of situationsaccording to view positions.

- surfaces may be back-facing

Motivation (1/4)

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Surface may be occluding

Motivation (2/4)

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Surfaces may be overlapping

Motivation (3/4)

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Surfaces may be intersecting

Motivation (4/4)

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Back-face detection Depth buffer

A-buffer

Scan line Depth sorting

BSP-tree

Area subdivision

Ray casting

Approaches

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Objectspace methods- Viewerobject,

- wire frame display

line display

Image-space methods- using most methods- projection planepixel positionpointvisibility

Classification

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Fast & simple object-space method Be based on Inside-outside test

- decide on the back face

P(x,y,z) on the polygonAx + By + Cz + D < 0 inside

back face

V N > 0 back faceV : Viewing direction vector(eye,camera)

N : Normal vector to a polygon surface

Back-face detection (1/2)

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Back-face detection (2/2)

VVzprojection coordinatesconvert

V = (0,0,Vz)Vz

Vx

Vy

V

V N = VzC ( C : variable)C(+ or -)back face

C 0 viewer

VN

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Image-space method Compare surface depths at each pixelposition on the projection plane.

Z-buffer method

Depth-Buffer Method (1/3)

Vz

Vx

Vy

S3S2 S1

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Step

- initialize the depth & refresh bufferdepth(x,y) = 0, refresh(x,y) = Ibackground

- compare depth values topreviously stored values in depth buffer Calculate the depth z for each (x,y)

position on the polygon if z > depth(x,y), then set

depth(x,y) = z, refresh(x,y) = Isurf(x,y)

Depth-Buffer Method (2/3)

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Comments- requires lots of memorya system with resolution 1024 by 1024= 1024 x 1024 x 24bits

- subject to aliasing(A-buffer)- commonly implemented in hardware

Depth-Buffer Method (3/3)

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Extension of the depth-buffer method Antialiased,

Area-averaged,

Accumulation-buffer method by Lucasfilm For implementation in the surface

rendering system

- REYES(Renders Everything You Ever Saw) Viewing for more than one surface

Antialiasing

A-Buffer Method (1/3)

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A-Buffer has two fields- depth field : store +,- real number- intensity field

Using Linked list

- d > 0 : single surface overlap

- d < 0 : multiple surface overlap

A-Buffer Method (2/3)

d > 0 I

Depth

field

Intensity

field

d < 0 Surf1

Depth

field

Intensity

field

Surf2

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Included data in the linked list- RGB intensity components- Opacity parameter(present of transparency- Depth- Persent of area coverage- surface identifier- other surface-rendering parameters

- pointer to next surface

A-Buffer Method (3/3)

background

opaque surface

foregroundtransparentsurface

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Image-space method Extension of the scan line algorithm Using Edge tables, polygon tables

Set up an active list of edgescross the current scan line Define a flag for each surface (on or off)

- to indicate whether inside or outside Take advantage of Coherence along scan

lines Commonly implemented in software

Scan-Line Method (1/2)

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Scan line 1 : no depth calculations

Scan line 2 : depth calculations

Scan line 3 : no depth calculations

- take advantage of coherence

Scan-Line Method (2/2)

C

A BED

FGScan line 1

Scan line 2

Scan line 3

S1 S2

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Both image-space and object-space method- sorting operation : both- scan conversion : image-space method

Painters algorithm : oil painting Sort surfaces in order of decreasing depth

No depth overlap

- Scan convert surfaces in order, startingwith the surface of greatest depth

Depth overlap

- need to additional reordering process

Depth Sorting Method (1/7)

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Depth Sorting Method (2/7)

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2.Surface S is completely behind the overlap-ping surface relative to the view position

3.Overlapping surface is completely in front

of S relative to the view position

Depth Sorting Method (5/7)

Vz

Vx

S

S

Vz

Vx

S

S

Test2 is not trueTest2,3 are true

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4.The projections of the two surfaces ontothe view plane do not overlap

Depth Sorting Method (6/7)

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When 4 tests failed,interchange surfaces in the sorted list

Depth Sorting Method (7/7)

Vz

Vx

S

S

In sorted listS,S S,S

Vz

Vx

S

S

In sorted listS,S,S S,S,S

S

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A kind of Depth-sorting Method Be useful when the view reference point

changes,but the objects are fixed position

Painting in the order back to front Commonly implemented in hardware

BSP-Tree Method (1/2)

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BSP-Tree Method (2/2)

A

B

C

D

P1

P2

frontfront

back

back P1

front back

P2 P2

front back

A C

front back

B D

Painting orderDBC A

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Image-space method- object-space method : depth ordering

Start with total view determine whether subdivision or not subdivision until a single surface orthe size of a single pixel

Similar to quad tree

Area-Subdivision Method (1/4)

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If one of conditions is true, no subdivision

1. All surfaces are outside2. Only one surface intersects in the area3. One surface occludes other surfaces

within area

Area-Subdivision Method (2/4)

Surroundingsurface

Overlappingsurface

insidesurface

outsidesurface

Boundary area

surface

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All surfaces are outside- check the bounding rectangles of allsurfaces against the area boundaries

Only one surface intersects in the area- bounding rectangles can be usedas initial check

- no intersection insideintersection need to additional checkwhether overlap,outside,surrounding

Area-Subdivision Method (3/4)

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One surface occludes other surfaceswithin area

- using 4 vertices method

the minimum depth ofall other surfacewithin the area

Area-Subdivision Method (4/4)

Vz

VxArea

Zmax(surrounding

surface)

maximum depth of

surrounding surface

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Cast ray from viewpoint through each pixelto find front-most surface

Ray Casting Method (1/2)

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Ray Casting Method (2/2)

Light-ray paths backward from the pixelsthrough the scene

More effective detection method

- Curved surface, particularly spheres a variation on the depth buffer method

Conceptually simple, but not generally used

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Hidden Surface Removal Algorithm- Back-face detection- Depth buffer

- A-buffer- Scan line- Depth sorting- BSP-tree

- Area subdivision- Ray casting

Summary