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From-Point Occlusion From-Point Occlusion CullingCulling

Chapter 23Chapter 23

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Talk Outline

• Image space methods– Hierarchical Z-Buffer– Hierarchical occlusion maps– Some other methods

• Object space methods– General methods

• Shadow frusta, BSP trees, temporal coherent visibility

– Cells and portals

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What Methods are Called Image-Space?

• Those where the decision to cull or render is done after projection (in image space)

View volume

Object space hierarchy

Decision to cull

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Ingredients of an Image Space Method

• An object space data structure that allows fast queries to the complex geometry

Space partitioning Hierarchical bounding volumes

Regular grid

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An Image Space Representation of the Occlusion Information

• Discrete– Z-hierarchy– Occlusion map hierarchy

• Continuous – BSP tree– Image space extends

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General Outline of Image Space Methods

• During the in-order traversal of the scene hierarchy do:– compare each node against the view

volume– if not culled, test node for occlusion – if still not culled, render objects/occluders

augmenting the image space occlusion• Most often done in 2 passes

– render occluders – create occlusion structure

– traverse hierarchy and classify/render

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Testing a Node for Occlusion

• If the box representing a node is not visible then nothing in it is either

• The faces of the box are projected onto the image plane and tested for occlusion

occluder

hierarchicalrepresentation

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Testing a Node for Occlusion

• If the box representing a node is not visible then nothing in it is either

• The faces of the box are projected onto the image plane and tested for occlusion

occluder

hierarchicalrepresentation

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Hierarchical Test

O

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Differences of Algorithms

• The most important differences between the various approaches are: – the representation of the

(augmented) occlusion in image space and,

– the method of testing the hierarchy for occlusion

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Hierarchical Z-Buffer (HZB) (Greene and Kass, SIG 93)

• An extension of the Z-buffer VSD algorithm

• It follows the outline described above• Scene is arranged into an octree which is

traversed top-to-bottom and front-to-back• During rendering the Z-pyramid (the

occlusion representation) is incrementally built

• Octree nodes are compared against the Z-pyramid for occlusion

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The Z-Pyramid

• The content of the Z-buffer is the finest level in the pyramid

• Coarser levels are created by grouping together four neighbouring pixels and keeping the largest z-value

• The coarsest level is just one value corresponding to overall max z

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The Z-PyramidObjects arerendered

Depth takenfrom the z-buffer

Construct pyramid by taking max of each 4

= furthest

= closer

= closest

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Using The Z-Pyramid= furthest

= closer

= closest

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Maintaining the Z-Pyramid

• Ideally every time an object is rendered causing a change in the Z-buffer, this change is propagated through the pyramid

• However this is not a practical approach

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More Realistic Implementation

• Make use of frame to frame coherence– at start of each frame render the

nodes that were visible in previous frame

– read the z-buffer and construct the z-pyramid

– now traverse the octree using the z-pyramid for occlusion but without updating it

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HZB: Discussion

• It provides good acceleration in very dense scenes

• Getting the necessary information from the Z-buffer is costly

• A hardware modification was proposed for making it real-time

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Hierarchical Occlusion Maps (Zhang et al, SIG 97)

• Similar idea to HZB but– they separate the coverage

information from the depth information, two data structures• hierarchical occlusion maps• depth (several proposals for this)

• Two passes– render occluders and build HOM– render scene hierarchy using HOM to

cull

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What is the Occlusion Map Pyramid?

• A hierarchy of occlusion maps (HOM)• At the finest level it’s just a bit map with

– 1 where it is transparent and – 0 where it is opaque (ie occluded)

• Higher levels are half the size in each dimension and store gray-scale values

• Records average opacities for blocks of pixels

• Represents occlusion at multiple resolutions

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Occlusion Map Pyramid

64 x 64 32 x 32 16 x 16

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How is the HOM Computed?

• Clear the buffer to black• Render the occluders in pure white (no

lighting, textures etc)• The contents of the buffer form the

finest level of the HOM• Higher levels are created by recursive

averaging (low-pass filtering) • Construction accelerated by hardware -

bilinear interpolation or texture maps / mipmaps

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Occlusion Map Pyramid

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Overlap Tests

• To test if the projection of a polygon is occluded– find the finest-level of the pyramid

whose pixel covers the image-space box of the polygon

– if fully covered then continue with depth test

– else descend down the pyramid until a decision can be made

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Resolving Depth

The point with nearest depth

Occluders

Viewing direction

This object passes the depth test

The plane

A

Imageplane

Bounding Bounding rectangle at rectangle at nearest nearest depthdepth

D. E. D. E. B.B.

OccludersOccluders

AA

Viewing Viewing directiondirection

Transformed view-frustumTransformed view-frustum

Bounding rectangle Bounding rectangle at farthest depthat farthest depth

BB

ImageImageplane plane

Either: a single plane at furthest point of occluders

Or: uniform subdivision of image with separate depth at each partition

Or even: just the Z-buffercontent

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Aggressive Approximate Culling

0 1 2 3 4

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HP Hardware implementation

• Before rendering an object, scan-convert its bounding box

• Special purpose hardware are used to determine if any of the covered pixels passed the z-test

• If not the object is occluded

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Simplified Occlusion Map

• Read top half of the buffer to use as an occlusion map

• Project top of cell to image space• Simplify projection to a line• Test if any pixel

along line is visible

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Discussion on Image Space

• Advantages (not for all methods)– hardware acceleration– generality (anything that can be

rendered can be used as an occluder)– robustness, ease of programming– option of approximate culling

• Disadvantages– hardware requirements– overheads

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Object Space Methods

• Visibility culling with large occluders– Hudson et al, SoCG 97– Bittner et al, CGI 98– Coorg and Teller, SoCG 96 and I3D 97

• Cells and portals – Teller and Sequin, Siggraph 91– Luebke and Georges, I3D 95

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Occlusion Using Shadow Frusta(Hudson et al, SoCG 97)

CB

AViewpoint

Occluder

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Assuming we can Find Good Occluders

• For each frame– form shadow volumes from likely

occluders– do view-volume cull and shadow-

volume occlusion test in one pass across the spatial sub-division of the scene

– each cell of the sub-division is tested for inclusion in view-volume and non-inclusion in each shadow volume

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Occluder Test

• Traverse the scene hierarchy top down

• Overlap test (cell to shadow volume) is performed in 2D– when the hierarchy uses an axis-

aligned scheme (eg kd-trees, bounding boxes etc) then a very efficient overlap test is presented

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Occlusion Trees (Bittner et al, CGI 98)

• Just as before– scene represented by a hierarchy (kd-

tree)– for each viewpoint

• select a set of potential occluders• compare the scene hierarchy for occlusion

• However, unlike the previous method– the occlusion is accumulated into a

binary tree– the scene hierarchy is compared for

occlusion against the tree

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Create shadow volume of occluder 1

Viewpoint

O1

O3

O2

Tree1

2

O1

IN

out

out

out

1

2

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Insert occluder 2 and augment tree with its shadow volume

Viewpoint

O1

O3

O2

Tree1

2

O1

IN

out

out3

4

O2

IN

out

out

out

1

23

4

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And so on until all occluders are added

Viewpoint

O1

O3

O2

Tree1

2

O1

INout

3

4

O2

IN

out

out

out

1

23

4

5

6

O3

IN

out

out

out

O4

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Check occlusion of objects T1 and T2 by inserting them in tree

Viewpoint

O1

O3

O2

Tree1

2

O1

INout

3

4

O2

IN

out

out

out

1

23

4

5

6

O3

IN

out

out

outT1

T2

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Occluder selection

• This is a big issue relevant to most occlusion culling algorithms but particularly to the last two

• At pre-processing – Identify likely occluders for a cell

• they subtend a large solid-angle

– Test likely occluders • use a sample of viewpoints and compute actual

shadow volumes resulting

• At run time– locate the viewpoint in the hierarchy and use

the occluders associated with that node

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Metric for Comparing Occluder Quality

Occluder quality: (-A *(N • V)) / ||D||2 A : the occluder’s areaN : normal

V : viewing directionD : the distance between the viewpoint and the occluder center

VA

N

DO

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Cells and Portals(Teller and Sequin, SIG 91)

• Decompose space into convex cells• For each cell, identify its boundary

edges into two sets: opaque or portal

• Precompute visibility among cells• During viewing (eg, walkthrough

phase), use the precomputed potentially visible polygon set (PVS) of each cell to speed-up rendering

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Determining Adjacent Information

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For Each Cell Find Stabbing Tree

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Compute Cell Visible From Each Cell

S•L 0, L LS•R 0, R RLinear programming problem:

Find_Visible_Cells(cell C, portal sequence P, visible cell set V) V=V C for each neighbor N of C for each portal p connecting C and N orient p from C to N P’ = P concatenate p if Stabbing_Line(P’) exists then Find_Visible_Cells (N, P’, V)

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Eye-to-Cell Visibility

• A cell is visible if– cell is in VV– all cells along stab

tree are in VV– all portals along

stab tree are in VV– sightline within VV

exists through portals

• The eye-to-cell visibility of any observer is a subset of the cell-to-cell visibility for the cell containing the observer

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Image Space Cells and Portals (Luebke and Georges, I3D 95)

• Instead of pre-processing all the PVS calculation, it is possible to use image-space portals to

make the computation easier

• Can be used in a dynamic setting

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Top View Showing the Recursive Clipping of the View Volume

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Discussion on Object Space

• Visibility culling with large occluders– good for outdoor urban scenes where occluders

are large and depth complexity can be very high– not good for general scenes with small

occluders

• Cells and portals – gives excellent results IF you can find the cells

and portals– good for interior scenes– identifying cells and portals is often done by

hand • General polygons models “leak”

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Conclusion

• There is a very large number of point-visibility algorithms

• Image space are becoming more and more attractive

• Specialised algorithms should be preferred if speed is most important factor