ObjectSpace Visibility Culling Anthony Steed University College London

Object-Space Visibility Culling Anthony Steed University College London Based upon material presented by Claudio T. Silva at Eurographics 1999 Slides, and material for slides, have been provided by Satyan Coorg (MIT/IBM), Sigal Dahan and Dudu Sayag (Tel-Aviv)

Approximate Visibility Determination Develop algorithms that are output sensitive, that is, complexity depends on the number of visible polygons, not the total number of polygons. Drop the exact visibility requirement, and instead attempt to develop algorithms that estimate the triangles which have visible fragments In this talk, we will speak about algorithms that overestimate the visible fragments, the so called conservative visibility algorithms

Talk Summary • Cells and portals – Teller and Sequin, Siggraph 91 – Luebke and Georges, I 3 D 95 • Visibility culling with large occluders – Coorg and Teller, So. CG 96 and I 3 D 97 – Hudson et al, So. CG 97

The Cells-and-Portals Approach (1)Decompose space into convex cells (2) For each cell, identify its boundary edges into two sets: opaque or portal (3) Precompute visibility among cells (4) During viewing (eg, walkthrough phase), use the precomputed potentially visible polygon set (PVS) of each cell to speed-up rendering

Space Subdivision Input Scene: Convex subdivision: Generated by computing a k-d tree of the input faces

Determining Adjacent Information

Computing the PVS of a cell Linear programming problem: S • L 0, S • R 0, L L R R 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)

Eye-to-Cell Visibility The eye-to-cell visibility of any observer is a subset of the cell-to-cell visibility for the cell containing the observer

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

Results

Talk Summary • Cells and portals – Teller and Sequin, Siggraph 91 – Luebke and Georges, I 3 D 95 • Visibility culling with large occluders – Coorg and Teller, So. CG 96 and I 3 D 97 – Hudson et al, So. CG 97

Luebke and Georges, I 3 D 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

Luebke and Georges, I 3 D 95 28/10/2021 17

Luebke and Georges, I 3 D 95 28/10/2021 18

Talk Summary • Cells and portals – Teller and Sequin, Siggraph 91 – Luebke and Georges, I 3 D 95 • Visibility culling with large occluders – Coorg and Teller, So. CG 96 and I 3 D 97 – Hudson et al, So. CG 97

When does A occludes B ?

Convex Occluers A occludes B A B C A B is not occluded B

Important Events e v A A B B

Naïve Algorithm • For all combinations of edges and vertices find the corresponding plane – (n 2) planes • Partition space by these planes – (n 6) cells

Relevant Planes • Only a small selection of planes are actually relevant • For complete objects - consider the silhouettes B v e A Plane ve separates A and B All silhouette edges produce supporting planes

For Individual Polygons • Track Visibility Changes – Track all planes defined by E and vertices in edge from B that intersect E

For Individual Polygons • Non-edge cases Track planes – V 7, V 3, V 5 – V 7, V 5, V 6 – V 7, V 6, V 3 • Overall this is (n+m) for an object pair

For N Objects • Reduce complexity from (n 2) by using an octree structure

Hierarchical Tests

Optimising the Octree Traverse • Not feasible to compute visibility relationship for whole octree each time viewpoint moves • Re-use the idea of tracking the separating planes – Do this for each octree cell on boundary – Note that a cell visibility can only become visible if its parent is partially visible

Dynamic Plane Maintenance • First approach – find a sub-set of close planes and test only those if viewpoint does not move more than r

Dynamic Plane Maintenance • Second approach – keep the planes themselves in an octree – in each octree cell keep a list of intersecting planes – a cell-cell traversal through the octree goes via the LCA, adding and deleting planes • no possibility of repeating an add or delete, so this is strictly better than naïve recomputation with worst case being situations where LCA is root

Coorg and Teller, I 3 D 97 Added the capability to join the effect of connected occluders, that is, a form of occluder fusion re no d Ig A B Ignored T

Occluder Fusion

Fast Tangent Plane Computation

Fast Tangent Plane Computation Because this computation is fast, it is no longer necessary to keep fine-grain visibility events

Use Temporal Coherence to Cache Relevant Events

Choosing Occluders • Pick large occluders close to the viewpoint – Good for application to octree scene structure • Pick smaller occluder that are close to objects (detail occluders) – I. E. they occlude an object most of the time – Applied only to a specified object, not to the general scene octree

Detail Occluders

Metric for Comparing Occluder Quality Occluder quality: (-A (N * V)) / ||D||2 A : the occluder’s area N : normal V : viewing direction D : the distance between the viewpoint and the occluder center Large polygon have large area-angle.

Results

Results The percentage of polygons draw The culling and drawing times (in milliseconds)

Talk Summary • Cells and portals – Teller and Sequin, Siggraph 91 – Luebke and Georges, I 3 D 95 • Visibility culling with large occluders – Coorg and Teller, So. CG 96 and I 3 D 97 – Hudson et al, So. CG 97

Hudson et al, So. CG 97 Occluder A Viewpoint C B

Occluder Storage • Partition model into cells and store good occluders in the cells • Identify likely occluders for a cell – they subtend a large solid-angle (similar to Coorg and Teller) • Test likely occluders – use a sample of viewpoints and compute actual shadow volumes resulting

Occluder Usage • At run-time – form shadow volumes from likely occluders – do view-volume cull and shadow-volume occlusion test in one pass across the spatial subdivision of the scene – each cell of the sub-division is tested for inclusion in view-volume and non-inclusion in each shadow volume

Occluder Test • Overlap test (cell to shadow volume) is performed in 2 D – If the subdivision uses bounding boxes, then a very efficient overlap test is presented

Conclusions • 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”

Conclusions • Visibility culling with large occluders – Very good for outdoor (city) scenes where occluders are large and depth complexity can be very high – Not good for indoor scenes in general since there are many small occluders that would need to be fused