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Functions Jason Smith, Josiah Manson, and Scott Schaefer Texas - - PowerPoint PPT Presentation

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Contouring Discrete Indicator Functions Jason Smith, Josiah Manson, and Scott Schaefer Texas A&M University Indicator Functions Discrete Indicator Functions (DIF) Extracted Surface Motivation [Green 2007] Motivation [Warner Bros

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SLIDE 1

Contouring Discrete Indicator Functions

Jason Smith, Josiah Manson, and Scott Schaefer Texas A&M University

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Indicator Functions

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SLIDE 3

Discrete Indicator Functions (DIF)

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SLIDE 4

Extracted Surface

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Motivation

[Green 2007]

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Motivation

[Warner Bros Pictures 2007]

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SLIDE 7

Motivation

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SLIDE 8

Motivation

[Manson et al. 2008]

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SLIDE 9

Marching Cubes

[Wyvill et al. 1986] [Lorensen and Cline 1987]

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SLIDE 10

Marching Cubes

MC Perfect Sphere

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SLIDE 11

Related Work

[Mor et al. 1996] [Wu and Sullivan 2003] [Reitinger et al. 2005]

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SLIDE 12

Related Work

[Gibson and Frisken 1998] [Chica et al. 2007]

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SLIDE 13

Gaussian Blur

Poseidon

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SLIDE 14

Gaussian Blur

MC

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SLIDE 15

Gaussian Blur

Blur size 3

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SLIDE 16

Gaussian Blur

Blur size 7

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SLIDE 17

Gaussian Blur

Ours MC Blur

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SLIDE 18

Gaussian Blur

Ours MC

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Contributions

  • Simple and easy to implement modification to

the MC algorithm

– Replaces the linear interpolant in MC

  • Computationally inexpensive
  • Greatly reduces surface contouring artifacts
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SLIDE 20

Contouring

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SLIDE 21

DIF

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Dual Grid

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SLIDE 23

Dual Grid

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2D MC change

1

t

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SLIDE 25

2D MC change

a1 a2

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SLIDE 26

Side - Side

a1 a2

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SLIDE 27

Bottom - Top

a1 a2

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SLIDE 28

Bottom - Side

a1 a2

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SLIDE 29

Side- Top

a1 a2

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SLIDE 30

Parameter Space

a1 a2

.5 .5 1

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Parameter Space

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SLIDE 32

Parameter Space

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SLIDE 33

Parameter Space

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Parameter Space

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SLIDE 35

Parameter Space

a1 a2

.5 .5 1

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Parameter Space

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SLIDE 37

Parameter Space

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SLIDE 38

Parameter Space

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SLIDE 39

Parameter Space

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SLIDE 40

Parameter Space

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SLIDE 41

Parameter Space

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Difference from Linear Interp.

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Linear functions

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Linear functions

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Linear functions

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Expanding to 3D

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SLIDE 47

Expanding to 3D

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SLIDE 48

Expanding to 3D

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SLIDE 49

Expanding to 3D

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SLIDE 50

Expanding to 3D

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SLIDE 51

Expanding to 3D

MC

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Expanding to 3D

Ours

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SLIDE 53

Expanding to 3D

MC Ours

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SLIDE 54

Perfect Sphere

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SLIDE 55

MC

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SLIDE 56

Ours

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SLIDE 57

Ours MC

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SLIDE 58

Sphere Normal Error

10 20 30 40 50 60 70 5 10 15 20 25 30

Degrees Radius in Cells

MC Max MC Avg Our Max Our Avg

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SLIDE 59

MC

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Ours

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MC

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Ours

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Limitations?

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Conclusion

  • Replaced Linear Interpolation of Marching Cubes.
  • Oscillation artifacts removed from surface contours while

preserving details.

  • Inexpensive method not requiring any pre processing of

function values, or post processing of output mesh.