Boolean Operations on SurfelBounded Solids Using Programmable Graphics Hardware

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Boolean Operations onSurfel-Bounded Solids Using
Programmable Graphics Hardware

• Bart Adams Philip Dutré
• Katholieke Universiteit Leuven

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Goal CSG on the GPU
not rendering, but construction ? GPGPU
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Related Work

• Adams and Dutré 2003
• points, 3-color octree

• Pauly et al. 2003
• points and MLS, kd-tree

• Purcell et al. 2002
• ray tracing on the GPU

• Zwicker et al. 2004
• splatting clipped surfels

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Adams and Dutré 2003

• Space partitioned using 3-color octree

• Boundary cells partitioned using // planes

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Adams and Dutré 2003

• Classification of a surfel

• test against 3-color octree
• test against boundary planes
• test against nearest surfel
• NN query!

a
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CPU? GPU Problems

• Hierarchical algorithm
• solution
• use 3-color grid instead of octree
• only test surfels individually
• NN query for surfels close to the boundary
• solution
• avoid NN query
• use local distance fields

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Part 1 Inside-Outside Partitioning
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Partitioning Idea

• Partition space around solids
• Construct 3-color grid
• interior cells
• exterior cells
• boundary cells
• Partition boundary cells
• signed distance field

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Partitioning Boundary Cells

• Lay out cell corners in texture memory

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Partitioning Boundary Cells

• Lay out cell corners in texture memory

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Partitioning Boundary Cells

• Render each surfel as 3x3 glPoint with center
  corresponding to cell center

p10
p9
p11
p8
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Partitioning Boundary Cells

• Render each surfel as 3x3 glPoint with center
  corresponding to cell center

p10
p9
p11
p8
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Partitioning Boundary Cells

• Render each surfel as 3x3 glPoint with center
  corresponding to cell center

p10
p9
p11
p8
known as scatter easy in VP
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Partitioning Boundary Cells

• Fragment program computes signed distance between
  surfel and cell corner

p6
p10
p5
p9
ps
p7
p11
dist p4 ps sign (p4
ps)nsgt0?1-1 color dist sign depth
dist/diag
p4
p8
Set glDepthFunc to GL_LEQUAL
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Classifying Empty Cells

• Construct 3-color grid using distance values from
  boundary cell corners
• render textured quad
• each pixel corresponds
• to a cell

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Classifying Empty Cells

• First pass cells on the left from boundary cell
  are classified
• inside if ?di lt 0
• outside if ?di gt 0
• Easy in FP
• 4 texture fetches

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Classifying Empty Cells

• Next passes cells on the left from a classified
  empty cell are classified
• Easy in FP
• 1 texture fetch

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Classifying Empty Cells

• Next passes cells on the left from a classified
  empty cell are classified
• Easy in FP
• 1 texture fetch
• Iterate further

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Classifying Empty Cells

• Next passes cells on the left from a classified
  empty cell are classified
• Easy in FP
• 1 texture fetch
• Iterate further

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Classifying Empty Cells

• Next passes cells on the left from a classified
  empty cell are classified
• Easy in FP
• 1 texture fetch
• Iterate further

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Classifying Empty Cells

• Next passes cells on the left from a classified
  empty cell are classified
• Easy in FP
• 1 texture fetch
• Iterate further

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Classifying Empty Cells

• All non-classified cells are outside (assumption
  closed solid)

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Part 2 Inside-Outside Classification
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Classification Idea

• Test surfels against partitioning of other solid

• test against 3-color grid
• test against distance field
• ( compute clipping plane)

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Implementation First Pass

• Enable depth write
• Render quad textured with surfel positions
• Test each surfel against 3-color grid
• if surfel in empty cell
• surfel takes classification of empty cell
• write depth value z1
• if surfel in boundary cell
• write depth value z2 with z1 lt z2

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Implementation Second Pass

• Disable depth write
• Set glDepthFunc to GL_LEQUAL
• Render quad textured with surfel positions
• at depth z with z1 lt z lt z2
• Classify surfel using distance field
• 8 texture fetches, tri-linear reconstruction
• Only unclassified surfels pass
• fragments with z z2
• Early z culling!

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Clipping Plane

• Surfels close to other surface
• clipped
• resampled
• Clipping plane defined by
• distance field value
• distance field gradient

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Timings partitioning

• Distance field creation step ( surfels)

• 3-color grid creation step ( grid size)

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Timings CPU ? GPU
5
10
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Dragon - dragon
Each dragon surfels 650k grid
size 363 partitioning 700ms classification 12
2ms
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Discussion

• Limitations
• space wasted in distance field texture
• not adaptive (? ADFs)
• no hierarchy each surfel classified individually
• accuracy dependent on grid resolution
• Advantages
• 5 to 10 times faster