Interactive Ray Tracing for Isosurface Rendering

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Interactive Ray Tracing for Isosurface Rendering

• Graphics Lab.
• ???

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Introduction

• Isosurface Rendering
• display isosurfaces ?(x, y, z) ?iso
• by extracting explicit polygonal representation
  (Marching cube)
• by ray tracing

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Introduction

• Ray Tracing
• conventionally slower than hardware z-buffer
• competitive when rendering a large dataset
• for n?n?n volume
• Marching cube O(n2) ? Rendering O(n2)
• Ray tracing O(n) ? multiprocessor O(n/p)
• with large time constant

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Algorithm

• Three phase
• 1. traverse a ray through cells which do not
  contain an isosurface
• 2. analytically compute the isosurface
• 3. shade the resulting intersection point
• Benefit
• parallelization is straightforward
• adding incremental features has only incremental
  cost

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Ray-Isosurface Intersection

• Ray traverses cells
• If the ray finds a cell containing an isosurface,
  solve for the ray parameter t

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Ray-Isosurface Intersection

• ? is approximated with a trilinear interpolation
• Equation is expanded to a cubic polynomial in t
• For multiple roots, smallest t is used
• It is possible that a ray misses the isosurface
  in a cell

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Optimization

• Traversing cell is the computational bottleneck
• First optimization
• improves data cache locality
• organizes the volume into bricks

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Optimization

• Second optimization
• multi-level spatial hierarchy
• accelerate the traversal of empty cells
• cells are grouped divided into macrocell
• macrocell contains the minimum and maximum value
  for its children cells
• empirically tri-level hierarchy is efficient

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Optimization

• Multiprocessor load balancing
• cannot predict a priory complexity of extracting
  isosurface from a screen pixel
• use dynamic load balancing
• put assignments in a queue
• each processor pulls a assignment from a queue
  and performs the assigned work and returns to a
  queue

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Discussion

• Result using marching cube
• 10M polygons for full dataset
• about 1000 sec to extract surfaces
• Architecture of the parallel machine
• the dataset must be available to each processor
• high locality in the dataset for any particular
  processor
• ? shared memory or distributed shared memory
  system is suitable

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Future work and Conclusions

• All computation is performed in software
• Future work
• using an associated color value as a 3D texture
  map
• other hierarchical method
• isosurfacing of tetrahedral and hexahedral
  element grids
• high-order interpolation
• combination with other scalar/vector
  visualization tool

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(x1, y1)
(0, 0)
u1
(1, 1)
v0
b0
b1
b
v1
a0
a1
a
(x0, y0)
(0, 0)
(1, 1)
u0
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For m?m?m bricks of n?n?n cells, offset q into
the data array is given
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For faster calculation q, tabulate Fx, Fy, Fz and
lookup each table