Visibility Preprocessing for Interactive Walkthroughs The Setting - - PowerPoint PPT Presentation

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Visibility Preprocessing for Interactive Walkthroughs The Setting - - PowerPoint PPT Presentation

Nov 29, 2023 231 likes •608 views

Visibility Preprocessing for Interactive Walkthroughs The Setting 1991 Second generation graphics hardware (SGI) Hardware transform, polygon rasterization, z- buffer Application Visibility Problem How do we ensure that the

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Visibility Preprocessing for Interactive Walkthroughs

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The Setting

  • 1991
  • Second generation graphics

hardware (SGI)

  • Hardware transform,

polygon rasterization, z- buffer

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Application

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Visibility Problem

  • How do we ensure that

the front-most polygon is used to shade the pixel?

  • For efficiency - how can

we shade as few fragments per pixel as possible (ideally only 1)?

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Precomputed Visibility

  • Many existing solutions for exact visibility
  • But can be complex, in terms of data and

implementation

  • BSPs - potentially O(n^2) new polygons
  • Quad-tree, Octree - common in raytracers,

not so great for interactive applications

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Precomputed Visibility

  • But we have a hardware Z-buffer now
  • Maybe we don’t have to be exact
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Precomputed Visibility

  • Existing visibility approximations
  • Quadtree/octree frustum culling
  • Portal shadow volumes
  • Discrete sampling
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Goals

  • Conservative
  • But not too conservative
  • Reasonable precomputation time
  • Reasonable precomputed data size
  • Allow further view frustum culling at runtime
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Outline of Approach

  • Precomputation
  • Spatial subdivision (cell and portal)
  • Conservative visibility (sightlines)
  • Runtime
  • View cone culling
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Assumptions

  • Axial faces - not necessary, but simplifies

implementation

  • 2D - extension to 3D described but not

tested

  • Ignore small/insignificant objects
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Spatial Subdivision

  • Requirements
  • Convex cells
  • Point location support
  • Portal enumeration
  • Neighbor finding
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Spatial Subdivision

  • Axis aligned faces and portals
  • k-D tree
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Spatial Subdivision

Disjoint

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Spatial Subdivision

Spanning

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Spatial Subdivision

Covering

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Spatial Subdivision

Incident

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Spatial Subdivision

Cleaving

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Spatial Subdivision

  • Recursively subdivide leaf nodes
  • If no incident or spanning faces, stop
  • If any spanning faces, split on median

spanning face

  • Else, split along median, sufficiently
  • bscured, minimum cleaving face
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Spatial Subdivision

  • Store (portal, neighbor) pairs at leaf nodes
  • Effectively have adjacency graph
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Finding Sightlines

  • Problem: Given set of portals forming path

from one portal to another, how do determine if there is a sightline that passes through all those portals.

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Finding Sightlines

  • Key insight: orient portals
  • All portal left end points must be on positive

side of the line

  • All portal right end points must be on

negative side of the line

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Finding Sightlines

  • Unknown line: S
  • Constraints:
  • S . L >= 0 for all portal left points
  • S . R <= 0 for all portal right points
  • This is a linear programming problem.
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Cell to Cell Visibility

  • Given a cell and the sightline algorithm, we

need to find, for each cell, all cells visible from it

  • Use adjacency lists to traverse graph depth

first

  • At each cell, recurse only if sightline test is

positive

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Cell to Cell Visibility

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Eye to Cell Visibility

  • Cell to cell visibility clearly a superset of eye

to cell visibility

  • So we can just cull based on the view frustum
  • A few methods are presented, increasing in

accuracy

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Eye to Cell Visibility

  • Disjoint cell
  • For each potentially

visible cell

  • Discard if cell

intersection with frustum is empty

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Eye to Cell Visibility

  • Connected Component
  • DFS on stab tree
  • Only recurse at cell if it

intersects with view frustum

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Eye to Cell Visibility

  • Incident Portals
  • DFS on stab tree
  • Recurse down edge if

portal intersects view frustum

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Eye to Cell Visibility

  • Exact
  • DFS traversal of stab

tree

  • For each additional

portal check for a sightline that

  • passes through the

portals

  • passes through the

eye

  • lies in half-spaces

defined by frustum

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Results

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Results

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Extension to 3D

  • Still assume axial faces
  • Portals can be non-convex
  • Bounding box - looser approximation of VS
  • Decompose - possible combinatorial

explosion

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Extension to 3D

  • Sightlines
  • Stab sequence of n axis-aligned quads
  • Another paper describes how to do this

in O(n lg n)

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Discussion

  • Does solve their problem, and easily in 2D.
  • Spatial subdivision relies on axial faces, but

rest of the algorithms don’t.

  • Not general.
  • No dynamic scenes.
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Discussion

  • Efficiency very data dependent.
  • Not thoroughly tested.
  • Long precomputation, potentially significant

storage.

  • Inefficient - no way to reuse paths
  • What about other types of portals? E.g.

mirrors?

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Discussion

  • Front-to-back BSP drawing developed soon

after

  • Cell to cell visibility used in Quake
  • Stab tree storage very expensive
  • Visibility set storage expensive, requires

compression

  • Simple bounding box cell-frustum culling
  • Expensive precomputation for 3D, even 5

years later

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Questions?