Computer Graphics 2 Lecture 8: Visibility Benjamin Mora 1 University of Wales Swansea Pr. Min Chen...

Computer Graphics 2Lecture 8:Visibility

Benjamin Mora 1University of Wales

Swansea

Pr. Min ChenDr. Benjamin Mora

Main techniques for visibility

2Benjamin MoraUniversity of Wales

Swansea

• Historical Techniques.

• Z-buffer techniques.– Used Much.– Basis for current hardware-accelerated

Technologies.

• Ray-Tracing.– See Next Lecture!

Content


Swansea

• Painter & Priority Lists Algorithms.• Cells and Portals.• Area subdivision algorithms.

– Warnock and Weiler Atherton algorithms.

• Scan line algorithms.• The z-buffer algorithm.• Extensions.

– Culling.– Hidden Surface Removal

• Hierarchical Occlusion maps.• Hierarchical z.

– Depth peeling.– Soft Shadows.– Shadow mapping.

Old Techniques


Swansea

Painter’s Algorithm


Swansea

• Painter’s Algorithm: – Only if graphics primitives can be separated by planes.

• Primitive can be projected from the farthest one to the closest (Back-to-Front) without any need to find the closest intersection.

• All the primitives being on the same side of the viewpoint (A) will be intersected first, so a Front-to-back analysis is more efficient.

(A)

(B)

Priority List/BSP Trees (Fuch)


Swansea

1

12

2

3

55

3

44

Priority List/BSP Trees (Fuch)


Swansea

• Proposed by Henry Fuch (1980).

• By preprocessing the scene and creating a binary space subdivision, primitives can then be projected in a visibility order.

• Handles Transparency correctly.

• In practice, constructing a Binary Space Partitioning tree is difficult!

Cells and Portals


Swansea

• In architectural scenes, rooms are usually not visible from other rooms.

• Used in 3D games (with Z-buffering).

• A visibility graph is usually associated to the scene.

A

B F

C E

D

A

E

B

CD

F

Cells and Portals


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• However:– Do not work with scenes like forest, clouds,…– Needs to pre-compute the graph.

• Dynamic scenes are an issue.

– Sorting out visibility inside the cells is still required.

• Sometime a method that can compute visibility in real-time (on-the-fly) is needed.– Z-Buffer/Hierarchical Z-buffer.– Hierarchical Occlusions Maps.– Occlusion queries.

Area Subdivision Algorithms


Swansea

• Warnock Algorithm (1969).– Not really used anymore.– Hierarchical method.– Quadtree structure.– Assumes no overlapping– Visibility is computed

on a per-block basis.

http://www.evl.uic.edu/aej/488/diagrams/areasub.gif



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• Weiler-Atherton algorithm– Kevin Weiler, Peter Atherton, “Hidden surface

removal using polygon area sorting”, Siggraph 1977.

– Works on 3D primitives instead of using screen space subdivisions.

– Maintains a list of clipped (visible) polygons.• Every time a new polygon is processed, clipping with

all the (visible) polygons is performed and a new list of polygons is generated.

• Once all the polygons processed, the clipped parts can be used for the final image.



Swansea

• Weiler Atherton algorithm.– Provides a general clipping algorithm for

concave polygons.

– Other algorithm for clipping: Sutherland-Hodgman algorithm.

Subject Polygon

Clip Polygon

Scanline (Watkins 70)


Swansea

• Watkins, G.S. A real-time visible surface algorithm. UTEC-CSc-70-101, Computer Science Dept., Univ. of Utah, June 1970.

• Principles similar to Weiler Atherton algorithm, but uses 1D clipping (line) only.– Maintains a list of clipped lines for every row.

• Scan-line term used for rasterization algorithms.

Scanline (Watkins 70)


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Image

p1 p2

Triangle #1

p1 p2

p1 p3

p3 p4

p4 p2p3 p4

Triangle #2

Scan Line y

Primitive list

Row y

Possible Issues with these algorithms


Swansea

• Could be too complex (e.g., 2D clipping).– Lead to several cases and bugs in

implementations.

• Not fast enough.– E.g. clipping.

• Hardly parallelizable.– Not suitable to hardware acceleration.

The Z-Buffer


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Z-Buffer test


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• Example:

Final image Final z-buffer

http://www.linux-magazin.de/Artikel/ausgabe/2000/07/VirtuelleWelten/render.jpg

http://www.linux-magazin.de/Artikel/ausgabe/2000/07/VirtuelleWelten/render_zbuffer.jpg

Z-Buffer test


Swansea

• Used by current hardware technology. • Primitives can be sent to the graphics hardware in any

order, thanks to the z-buffer test that will keep the closest fragments.

• A z value is stored for every pixel (z-buffer).• Algorithm for a given pixel:

If the rasterized z-value is less than the current z-value

Then replace the previous color and z-value by the new ones

Z-Buffer test


Swansea

• A scan line algorithm can be used to find all the pixels on the projection of a single triangle.

• Lines are filled with colors if the pixels pass the z-test.

Row yRow y+1

Row y+2

Extensions to these techniques


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Culling


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• Why ?– To avoid processing geometry that does not need to be

processed.– Useful when having millions (or billions) of triangles.– Can be done at the triangle or pixel level.

• View Frustum Culling.

• Back Face Culling.

• Occlusion Culling.

Culling


Swansea

• View Frustum Culling.– Primitives outside of the view frustum discarded.– Implemented on graphics cards.

Viewpoint

Viewing pyramid

Visible Triangle

Culled triangles

Culling


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• Can be accelerated (software) by grouping triangle and computing the frustum intersection only for the bounding box.

Don’t need to process these triangles.

Frustum

Bounding Box

Culling


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• Back Face Culling.

– If the viewpoint is fronting the backface, then the triangle is not processed.

– Hardware accelerated

– Can be enabled/disabled.

– Orientation given by the order of projected vertices.

Projected Triangle

(Visible)

#1

#2#3

#1

#3#2Wrong vertex order

(Triangle is culled)

Occlusion Culling


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• A set of algorithms to avoid processing hidden geometry/surfaces

– Hierarchical Occlusion Maps.

– Hierarchical z-buffer.

– Occlusion queries.

Hierarchical Occlusion Maps


Swansea

Hansong Zhang, Dinesh Manocha, Tom Hudson Kenneth E. Hoff III. Visibility Culling using Hierarchical Occlusion Maps. Siggraph 1997.

• Proposed by Zhang et al.

• Similar to Hierarchical z.• Only occlusion is stored here.

Hierarchical Occlusion Maps


Swansea

• Triangles are initially grouped into separate regions of space such as bounding boxes, grids or trees.

• This data structure is traversed in a front to back order.– The visibility of the region is given by the HOM.– If region is visible, then its content (i.e., triangles) must

be projected. – During projection, the content of the different maps is

updated every time a pixel becomes opaque.

• Not used by current hardware.– Hierarchical-z instead

Hierarchical Z-buffer


Swansea

• Proposed by Greene et al.

• A hierarchical z-max pyramid is constructed above the z-buffer.

• Every time a z value is updated, the hierarchy is updated.

Ned Greene, Michael Kass and Gavin Miller. Hierarchical Z-Buffer Visibility. Siggraph 1993.

6542

3576

2542

9132

67

94

9

88

8

Hierarchical Z-buffer


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• Current ATI and NVidia graphics card implement a limited z-hierarchy.

• Efficient when objects are projected in a front-to-back way.

• ATI Hyper-Z III:

http://graphics.tomshardware.com/graphic/20020718/radeon9700-08.html

Occlusion Queries


Swansea

• New Graphics Hardware allows counting the number of fragments that pass the z-test.

• 3 steps:– Lock the z-buffer and frame buffer (impossible to

modify the content of these buffers).– Render a bounding box.

• If no pixel has passed the z-test, then the region inside the BB is not visible.

– Unlock the Z-buffer and Frame-Buffer.

Occlusion Queries


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• Can take advantage of fast z tests.

• Efficient only if the BB contains many primitives.

• Must wait for the answer.

– The program should do something before testing the answer.

– Occlusions should be chained in order to avoid an empty graphics pipeline.

Depth Peeling


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FromInteractive Order-Independent TransparencyCass EverittNVIDIA OpenGL Applications Engineering

Depth Peeling


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• Z-buffer based visibility only allows finding the nearest elements of the scene.– Transparency cannot correctly be handled.

• Solution: use a multipass algorithm to find the second nearest surface, third nearest surface, and etc… for every pixel– At the end, combine the different images in a

front-to-back-order.

Computer Graphics 2 Lecture 8: Visibility Benjamin Mora 1 University of Wales Swansea Pr. Min Chen...

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