6 DOF Haptic Rendering Spatialized Normal Cone Search D' E' Johnson, P' Willemsen, and E' Cohen, "Si

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6 DOF Haptic Rendering - Spatialized Normal
Cone Search D. E. Johnson, P. Willemsen, and E.
Cohen, "Six Degree-of-Freedom Haptic Rendering
Using Spatilized Normal Cone Search," IEEE
Transactionson Visualization and Computer
Graphics, vol. 11, pp. 661-670, 2005.

• CSE 20065160
• ???(inux_at_postech.ac.kr)
• 2006.5.8

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Outline

• Spatialized Normal Cone Hierarchies (SNCH)
• Haptic Rendering Using SNCH Search
• Performance Tests
• An Accessibility Application
• Penetration Estimation Using SNCH Search
• Conclusion

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SNCH - Approach

• Distance between surfaces f(u,v) and g(s,t)
• To be a local minima, partials should be
  zeros.
• Normals of surfaces satisfy collinearity each
  other.

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SNCH - Concept

• Spatialized Normal Cone Hierarchies
• A cone is defined by an axis vector and a spread
  angle.
• A normal cone presents range of normals of each
  node in hierarchy.

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SNCH Building the Hierarchy

• SNCH uses a vertex-edge-face data structure with
  neighbor information for vertices and edges on
  top of the triangulated model.
• A hierarchy is constructed using the binary
  spatial splitting technique.
• A node have normals of vertices, edges and faces.

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SNCH Building the Hierarchy

• A cone axis vector is an average of the
  face, edge and vertex normals of node .
• Each node has a bounding sphere with center
  and radius .

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SNCH Searching the Hierarchy

• Top nodes of each models structure are connected
  as an active pair.
• Every active pair undergoes a series of tests
  that determine local minimum existence.
• If an active pair passes the tests, two sets of
  children nodes make four new active pairs.
• Tests are continued recursively.

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SNCH Searching the Hierarchy

• Naïve collinearity Test
• If true, the active pair is not collinear.
• If false, we need more comprehensive tests.
• A B Actually, A and B should have
  different forms from those shown in this figure.

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SNCH Searching the Hierarchy

• Solution line cone radius of each bounding
  sphere
• A half spread angle
• A central axis is the line that connects two
  bounding spheres centers.

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SNCH Searching the Hierarchy

• An active pair is tested for whether they are in
  the solution line cone or not.
• If the test fails, the pairs are pruned.

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SNCH Leaf Tests

• The first step is to find the closest points
  between leaf triangles TA and TB .
• The closest points can locate on the
• Triangle face
• Edge
• Vertex
• The closest points form a potential solution
  vector.
• We will test the collinearity of a potential
  solution vector with the normals of the location.

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SNCH Leaf Tests

• is the normalized solution vector
  
• Face test
• A face has an unique normal vector.

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SNCH Leaf Tests

• Edge test
• An edge has a range of vectors.
• So, we use average edge normal as a
  boundary.

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SNCH Leaf Tests

• Vertex test
• We add counterclockwise neighbor triangle face
  normal to the vertex average normal
  and the triangle face normal

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Haptic Rendering Using SNCH Search - LMD

• We want to prevent collisions by applying
  repulsive forces as models approach each other.
• We use local minimum distances (LMD) to calculate
  the repulsive forces.
• A local minimum point can represent a region.
• It can increase haptic stabillity.

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Haptic Rendering Using SNCH Search - Cutoff
Distance

• We do not need the local minima, having too far
  distance value.
• All active pairs further apart than the cutoff
  distance are pruned.
• It helps to reduce much of computation.

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Haptic Rendering Using SNCH Search - Acceleration
with Local Search

• We can divide the whole LMD search into the
  global search and the local search.
• The global search finds and passes new LMDs to
  the local search.
• The local search updates LMDs position and value.

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Haptic Rendering Using SNCH Search - Acceleration
with Local Search

• When the model is moved, the local search
  algorithm looks at the neighborhood triangles of
  each LMD points.
• And then, calculate distance to the other models
  neighborhood triangles.

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Haptic Rendering Using SNCH Search - Acceleration
with Local Search

• If the distance is smaller than the LMD,
  algorithm continues on those triangles
  neighborhood until the minimum distance
  converges.
• The points that form this new minimum distance
  are the updated LMD.

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Haptic Rendering Using SNCH Search - Search
Efficiency

• For models with low aspect side lengths, the
  number of checked triangles are roughly .
• The global search efficiency is dependent on the
  number of LMDs and the complexity of models.
• Single LMD with balanced complexityis the best
  case. (complexity of log n)
• Manifold solutions, like parallel planes is the
  worst case. (complexity of n log n)

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Performance Tests

• Tested on 6-DoF PHANTOM, Dual P4 2.4GHz CPU, 1GB
  ram and Geforce Ti4400.
• The local search thread occupies one processor
  and the global search and graphic thread another
  processor.

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Performance Tests

• Gear-Crank ( 6,300 45,000 triangles)

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Performance Tests

• Horse and Bunny

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An Accessibility Application

• Collision-Free Path
• Detecting Collisions
• Path Visualization

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Penetration Estimation Using SNCH Search

• We can use the solution line cone and the node
  normal cones.
• For extremal distance, the normal cones should
  point away each other.
• Switch the p and 0!

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Penetration Estimation Using SNCH Search

• We do not have appropriate leaf tests.
• Extra computation may not yield much additional
  pruning.
• The closest pairs of points on the triangles are
  used as the solution line.

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Penetration Estimation Using SNCH Search
Adaptive Cutoff Distance

• We can bound the maximum penetration depth.
• The new cutoff distance is set as (The maximum
  penetration depth from last time step)
  (relative movement of the models).
• When the penetration depth is small, much of
  computation is reduced by small cutoff distance.
• It allows unbounded penetration depth.

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Penetration Estimation Using SNCH Search - Results

• The penetration depth cannot handle as
  high-resolution models as the LMD approach.
• Because more active pairs are retained.

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Conclusion

• We can implement six DOF haptic rendering of
  arbitrary polygonal models with this algorithm.

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Reference

• D. E. Johnson, P. Willemsen, and E. Cohen, "Six
  Degree-of-Freedom Haptic Rendering Using
  Spatilized Normal Cone Search," IEEE
  Transactionson Visualization and Computer
  Graphics, vol. 11, pp. 661-670, 2005.