ViewDependent Simplification of Arbitrary Polygonal Environments

1
View-Dependent Simplification of Arbitrary
Polygonal Environments

• David Luebke
• Carl Erikson
• Presented by
• Aaron Wong-Sing

2
Hierarchical Dynamic Simplification

• Simplifying arbitrary polygonal environments
• Clustering vertices together in a hierarchical
  fashion

3
Polygonal Models in Interactive 3D Computer
Graphics

• Mathematically Simple
• Rapid Rendering of polygonal datasets
• Widely available polygon-rendering hardware

4
When Complexity of Polygonal Models Exceeds
Capability of Graphics Hardware

• Augment the raw polygonal data
• Gouraud Shading and texture mapping
• Cull away large portions which are occluded from
  current viewpoint
• Polygonal Simplification
• Simplify the polygonal geometry of small or
  distant objects
• Reduces rendering cost without a significant loss
  to the visual content of the scene

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Polygonal Simplification

• Simplifies the geometry of entire scene
  dynamically as the user moves around
• Algorithm criteria
• General- As few assumptions as possible about
  input model
• Deal robustly with degenerate and non-manifold
  models
• Completely Automatic
• Simplify scene adaptively
• Dynamically Adjustable
• Trade off performance with fidelity

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Hierarchical Dynamic Simplification

• Vertex Tree- single large data structure
• Hierarchy of vertices queried dynamically
• Information about the vertices and triangles of
  the model (not topology)
• Collapsing all the vertices within a node to a
  single representative vertex
• Triangles with collapsed corners become redundant
  and can be eliminated
• Node can be expanded by splitting the vertex into
  the representative vertices of the nodes children

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Hierarchical Dynamic Simplification

• Entire system is dynamic
• Nodes collapsed or expanded based on their screen
  size
• Screenspace of node is monitored
• Certain nodes in the vertex tree will fall below
  the size threshold
• Fold and unfold the nodes for each frame

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Active Triangle List

• Takes advantage of temporal coherence
• A sequence of visible triangles
• Expanding a node appends triangles onto active
  triangle list collapsing the node removes them
• Doubly linked list

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Active Triangle List

• struct Tri
• Node corners3
• Node proxies3
• Tri prev, next

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Vertex Tree

• Created during preprocessing stage
• Controls order vertices are collapsed
• Stores data necessary to collapse and uncollapse
  vertices quickly
• Unfolded nodes are labeled active folded nodes
  are labeled inactive
• Active nodes comprise a contiguous region the
  active tree with boundary nodes

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Vertex Tree

• struct Node
• BitVec id
• Byte depth
• NodeStatus label
• Coord repvert
• Coord center
• float radius
• Tri tris
• Tri subtris
• Node parent
• Byte numchildren
• Node children

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View-Dependent Simplification

• Screenspace Error Threshold
• Collapse nodes which occupy a small amount of the
  screen
• Error introduced by collapsing the vertices
• maximum distance a vertex can be shifted during
  the collapse operation
• length of the vector between the two farthest
  vertices in the cluster (screenspace error)

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View-Dependent Simplification

• Screenspace Error Threshold
• Unfold nodes whose screenspace error gt user
  specified threshold t
• No vertex shall move more than t pixels on the
  screen
• Determining Screenspace of a vertex
• Associate a bounding volume with each node in the
  vertex tree
• Use Bounding Spheres

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View-Dependent Simplification

• Silhouette Preservation
• Specify a cone of normals
• coneNormal, a vector
• coneAngle, a floating-point scalar
• Conservatively bounds all normals of all
  triangles in subtree rooted at node
• Viewing cone created at run time that originates
  from viewer and tightly encloses bounding sphere
  of node
• Any normal in the cone of normals orthogonal to
  any direction within the viewing cone, node is
  potentially on the silhouette
• Allocate more details to objects along
  silhouettes retain important visual cues for
  object recognition

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Triangle-Budget Simplification

• Allows user to specify number of triangles in the
  scene
• HDS minimizes the screenspace error of boundary
  nodes within this constraint
• Priority queue of boundary nodes
• Ordered by screenspace error
• Unfold node, remove from top of queue, insert
  children back into queue

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Optimization

• Exploiting Temporal Coherence
• firstActiveAncestor() stored as a field of N
• Culling the Active Triangle List
• Clump polygons together using a spatial hierarchy
• Distribute active triangles across the vertex
  tree
• Rendering top-down traversal of vertex tree
• Loses advantage of temporal coherence
• Hybrid

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Optimization

• Avoiding Irrelevant Nodes
• Invisible nodes may need to be examined
• Tris and subtris of node visible
• Irrelevant Nodes
• Expanding or collapsing the node cannot possibly
  affect the scene
• Does not contain a corner of any potentially
  visible triangle
• Add a container field to each node in the vertex
  tree
• Smallest node that contains every tri and subtri
  of the node and the nodes descendants

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Optimization

• Asynchronous Simplification
• SIMPLIFY task traverses the vertex tree folding
  and unfolding nodes
• RENDER task cycles over the active triangle list
  rendering each triangle
• Let SIMPLIFY and RENDER run asynchronously
• Avoid dropouts failure to maintain consistent
  database
• Simple locking schemes inadequate
• Use update queue all changes to active triangle
  list takes place as a batch before any triangles
  are rendered

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Simplification

• Spatial Subdivision
• Space-partition vertices of model using an octree
• Use local criteria to rank vertices
• Most important vertex in node is representative
  vertex
• Vertices clustered roughly according to proximity
• Unless uniformly distributed vertices, octree
  highly unbalanced
• Tight Octree
• Smallest axis-aligned cube which encloses
  relevant vertices before node is subdivided
• Efficient, easy to code, partitioning fast
• No knowledge of polygon mesh used

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Simplification

• Spatial Subdivision
• Space-partition vertices of model using an octree
• Use local criteria to rank vertices
• Most important vertex in node is representative
  vertex
• Vertices clustered roughly according to proximity
• Unless uniformly distributed vertices, octree
  highly unbalanced

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Simplification

• Simplification Envelopes
• Offset surfaces of a polygonal mesh to prevent
  self-interaction an a bounded to a distance ? of
  a mesh
• Preserves global topology that varies from the
  original surface no more than ?

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Simplification

• Progressive Meshes
• Stream of edge collapse records in a progressive
  mesh maps to HDS vertex tree
• Never collapses more than 2 vertices at a time
• Collapse vertices within a mesh separate meshes
  never merge
• Restricting edge collapses to those that preserve
  manifold topology limits possible simplification

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Simplification

• Hybrid Approach
• Combine simplification envelope and progressive
  mesh with top-down spatial subdivision
• Drastic simplification and merging of objects
• Result is a collection of vertex trees of the
  collection of objects
• Spatial subdivision unifies the vertex forest
  into a single tree

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Remarks

• Polygonal simplification is a process of
  approximation
• Recover original object when algorithm taken to
  the limit
• View-dependent simplification is immediate mode
• Current hardware favours retained-mode display
  lists

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Conclusion

• HDS is framework for dynamic view-dependent
  simplification of complex polygonal environments
• Framework is robust
• Any simplification method reducible to a series
  of vertex clustering operations can be used by
  HDS preprocessing
• Different criteria for expanding and collapsing
  vertices can be used by HDS
• Supports screenspace error tolerance, triangle
  budget, silhouette preservation
• Optimizations asynchronous simplification
  decouples rendering and simplification tasks

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Conclusion

• Future Work
• HDS currently limited to static scenes
• Fast spatial subdivision cannot keep up
• Incremental algorithm for creating and
  maintaining vertex tree allow for simplification
  of dynamic scenes
• More sophisticated run-time criteria
• Bounding spheres poor fit for vertices in a
  cluster more sophisticated bounding volumes, but
  complicate nodeSize()
• Nodes might be unfolded for more detail to
  regions containing specular highlights or
  perceptually important regions using
  gaze-directed heuristics.