Hybrid Computational Voxelization using the Graphics Pipeline - - PowerPoint PPT Presentation

SLIDE 1

Hybrid Computational Voxelization using the Graphics Pipeline

Randall Rauwendaal Michael J. Bailey

Sunday, April 6, 14

SLIDE 2

Mar 14, 2014

Voxelization

• Conversion of input geometry (triangles) into a

regular 3D discretized representation (voxels)

• Analogous to rasterization in 3D

2

Original Image

Sunday, April 6, 14

SLIDE 3

Mar 14, 2014

Motivation

• Voxels are useful in many applications (global

illumination, collision detection, fluid sim, etc...)

• Voxelization can enable these efgects for traditional

triangle based scenes

• Fast voxelization can enable these efgects for

dynamic scenes

3

Sunday, April 6, 14

SLIDE 4

Mar 14, 2014

Triangle vs Fragment Parallel

Triangle Parallel

• Threads per triangle
• Can sufger from uneven triangle size distributions

Fragment Parallel

• Threads per triangle fragment
• Can sufger from oversubscription and poor thread

utilization

4

Sunday, April 6, 14

SLIDE 5

Mar 14, 2014

Triangle-Parallel Performance

5

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SLIDE 6

Mar 14, 2014

Triangle-Parallel Analysis

• Performs well on scenes with many small evenly

sized triangles

• Performs poorly on any scene with large triangles
• Performance degrades as voxel resolution increases

6

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SLIDE 7

Mar 14, 2014

Fragment-Parallel Performance

7

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SLIDE 8

Mar 14, 2014

Fragment-Parallel Analysis

• Performs well on scenes with large triangles
• Performs poorly on scenes with many small triangles
• Performance degrades as voxel resolution decreases
• Poor “quad-utilization” on small triangles

8

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SLIDE 9

Mar 14, 2014

Fragment vs Triangle parallel @2563

9

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SLIDE 10

Mar 14, 2014

Hybrid Voxelization

• Introduce a hybrid pipeline that splits the workload

between “small” and “large” triangles

10

• Sunday, April 6, 14

SLIDE 11

Mar 14, 2014

Details

• Creates a “two-pass” approach
• Avoids poor thread utilization and oversubscription

caused by rasterizing small triangles

• Avoids idle threads waiting on large triangles
• Efgectively classified scenes take longer

11

Sunday, April 6, 14

SLIDE 12

Mar 14, 2014

Optimized Hybrid Voxelization

• Immediately voxelize small triangles, defer only large

triangles

12

• Sunday, April 6, 14

SLIDE 13

Mar 14, 2014

Benefits

• Less overhead for small triangle voxelization
• Reduce under-utilized threads
• Reduces output of classification stage
• More of a “just over one-pass” approach, as typically
• nly a small subset of triangles are processed twice

13

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SLIDE 14

Mar 14, 2014

“Small” vs “Large” Triangles

• Classify triangles based on the maximal 2D projected

area of triangle in voxel units

• Triangles are classified as large or small according to

a cutofg value

14

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SLIDE 15

• Mar 14, 2014

Hybrid Performance (Sponza)

15

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SLIDE 16

• Mar 14, 2014

Hybrid Performance (zoomed)

16

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SLIDE 17

Mar 14, 2014

Implementation Details

• Surface Voxelization
• OpenGL 4.2
• Computational Intersection

17

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SLIDE 18

Mar 14, 2014

Surface Voxelization

• Conservative voxelization (26-separable)
• Thin voxelization (6-separable)

18

Thin Conservative

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SLIDE 19

Mar 14, 2014

Triangle/Voxel Overlap

• Reduce the set of potential voxel intersections to
• nly those that overlap the axis-aligned bounding

volume of the triangle

• Iterate over this reduced set of voxels and discard

any that do not intersect the triangle's plane

• If the triangle plane divides the voxels test all three
• f its 2D planar projections to confirm overlap

19

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SLIDE 20

Mar 14, 2014

3D Voxel Overlap

20

• Thin

Conservative

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SLIDE 21

Mar 14, 2014

2D Box Overlap

21

• Thin

Conservative

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SLIDE 22

Mar 14, 2014

Optimization

• Pre-compute all per-triangle variables
• Determine the dominant normal direction
• select the orthogonal plane of maximal projection (XY, YZ, or ZX)
• iterate over the component axes
• Test the 2D projected overlap with the orthogonal

plane of maximal projection first

• Depth intersection test to determine the minimal

necessary range to iterate over

• Test the remaining two planar projections for
• verlap

22

Sunday, April 6, 14

SLIDE 23

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 24

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

Precompute Variables

Sunday, April 6, 14

SLIDE 25

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 26

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

Iterate over maximal plane

Sunday, April 6, 14

SLIDE 27

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 28

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

maximal plane test

Sunday, April 6, 14

SLIDE 29

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 30

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

Z-range calc and iterate

Sunday, April 6, 14

SLIDE 31

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 32

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

remaining plane tests

Sunday, April 6, 14

SLIDE 33

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 34

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

unswizzle and store

Sunday, April 6, 14

SLIDE 35

Mar 14, 2014

Pseudocode

23

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 36

Mar 14, 2014

Fragment-Parallel Voxelization

• Improve parallelism by breaking up large triangles
• Use the existing rasterization based pipeline to

accomplish this

• 2 potential problems to overcome

1) Gaps within triangles caused by an overly oblique camera angle 2) Gaps between triangles caused OpenGL’s rasterization rules

24

Sunday, April 6, 14

SLIDE 37

Mar 14, 2014

(1) Projection

• Can solve the first problem by projecting the input

geometry onto the dominant plane

25

• Sunday, April 6, 14

SLIDE 38

Mar 14, 2014

3D Projection

• The appropriate projection plane is selected by the

dominant normal direction

26

• Sunday, April 6, 14

SLIDE 39

Mar 14, 2014

(2) Conservative Rasterization

27

• Can solve the second problem with “conservative

rasterization”

• Hasselgren (A)

Hasselgren (B) Hertel et al.

Sunday, April 6, 14

SLIDE 40

Mar 14, 2014

Conservative Rasterization

• Conservative rasterization dilates the input triangles

such that if any part of a pixel is covered by the

• riginal triangle the pixel center is covered by the

dilated triangle

28

v0

i = vi + l

✓ ei1 ei1 · nei + ei ei · nei−1 ◆

Sunday, April 6, 14

SLIDE 41

Mar 14, 2014

Quad Utilization

• Pixels actually processed in batches of 2x2 “quads”

to provide derivative information

• A sub-voxel sized triangle may utilize only 25% of

threads allocated

• Worse when triangle dilation is taken into account

29

Sunday, April 6, 14

SLIDE 42

Mar 14, 2014

Dilated Triangle Utilization

• This triangle exhibits only 8.33% thread utilization

30

Sunday, April 6, 14

SLIDE 43

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 44

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

Geometry Shader flat -> fragment shader

Sunday, April 6, 14

SLIDE 45

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 46

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

handled implicitly

Sunday, April 6, 14

SLIDE 47

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 48

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true

fragment shader

Sunday, April 6, 14

SLIDE 49

Mar 14, 2014

Pseudocode

31

(v0, v1, v2, bmin, bmax, unswizzle) ei v(i+1)mod3 vi n cross (e0, e1) nXY

ei

sign (nz) · (ei,y, ei,x)T nYZ

ei sign (nx) · (ei,z, ei,y)T

nZX

ei sign (ny) · (ei,x, ei,z)T

dXY

ei

⌦ nXY

ei , vi,xy

↵

+ max 0, nXY

ei,x

• + max

0, nXY

ei,y

• dYZ

ei ⌦

nYZ

ei , vi,yz

↵

+ max 0, nYZ

ei,x

• + max

0, nYZ

ei,y

• dZX

ei ⌦

nZX

ei , vi,zx

↵

+ max 0, nZX

ei,x

• + max

0, nZX

ei,y

• n sign (nz) · n

zmin < zmax dmin hn, v0i max(0, nx) max(0, ny) dmax hn, v0i min(0, nx) min(0, ny) px bmin,x, . . . , bmax,x py bmin,y, . . . , bmax,y 82

i=0

⌦

nXY

ei , pxy

↵

+ dXY

ei

zmin max bmin,z,⌅ ( hnxy, pxyi + dmin)

1 nz

⇧

zmax min bmax,z,⌃ ( hnxy, pxyi + dmax)

1 nz

⌥

pz zmin, . . . , zmax 82

i=0

⌦

nYZ

ei , pxy

↵

+ dYZ

ei 0 ^ ⌦

nZX

ei , pxy

↵

+ dZX

ei 0

V [unswizzle · p] true Sunday, April 6, 14

SLIDE 50

Mar 14, 2014

Computational v. Raster Intersection

• Triangle dilation can produce overly conservative

results leading to false positives during voxelization

• Maintaining a computational intersection test

eliminates false positives

32

Sunday, April 6, 14

SLIDE 51

Mar 14, 2014

Computational v. Raster Intersection

• Red voxels indicate false positives

33

Sunday, April 6, 14

SLIDE 52

Mar 14, 2014

Full Pipeline

34

Sunday, April 6, 14

SLIDE 53

Mar 14, 2014

Attribute Interpolation

• Calculate barycentric coordinates of dilated triangle
• Apply to the attributes of the original triangle to

calculate dilated attributes

35

λi (v0

i) = area (v0 i, vi+1, vi+2)

area (v0, v1, v2) a0

i = λ0 (v0 i) a0 + λ1 (v0 i) a1 + λ2 (v0 i) a2

Sunday, April 6, 14

SLIDE 54

Mar 14, 2014

Color Voxelization (Sponza)

36

Original Image

Sunday, April 6, 14

SLIDE 55

Mar 14, 2014

Results

37

Sunday, April 6, 14

SLIDE 56

Mar 14, 2014

Results

38

Sunday, April 6, 14

SLIDE 57

Mar 14, 2014

Conclusion

• Fastest available voxelization, even on less than state
• f the art hardware
• Easy to implement in current graphics APIs, avoids

complex tiling assignments, sorting stages, and work/load balancing schemes

• Does not sacrifice quality of the voxelization in order

to utilize the graphics pipeline, i.e. maintains robust computational intersection at all stages

39

Sunday, April 6, 14

SLIDE 58

Mar 14, 2014

Questions?

40

Sunday, April 6, 14

SLIDE 59

Mar 14, 2014

Results

41

@voxels2 1283 2563 5123 1283 2563 5123 1283 2563 5123 1283 2563 5123 1283 2563 5123 1283 2563 5123 1283 2563 5123 Sunday, April 6, 14