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

Sep 19, 2023 •278 likes •930 views

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

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 Pictures 2007]
Motivation
Motivation [Manson et al. 2008]
Marching Cubes [Wyvill et al. 1986] [Lorensen and Cline 1987]
Marching Cubes Perfect Sphere MC
Related Work [Mor et al. 1996] [Wu and Sullivan 2003] [Reitinger et al. 2005]
Related Work [Gibson and Frisken 1998] [Chica et al. 2007]
Gaussian Blur Poseidon
Gaussian Blur MC
Gaussian Blur Blur size 3
Gaussian Blur Blur size 7
Gaussian Blur Ours MC Blur
Gaussian Blur Ours MC
Contributions • Simple and easy to implement modification to the MC algorithm – Replaces the linear interpolant in MC • Computationally inexpensive • Greatly reduces surface contouring artifacts
Contouring
DIF
Dual Grid
Dual Grid
2D MC change t 0 1
2D MC change a 1 a 2
Side - Side a 1 a 2
Bottom - Top a 1 a 2
Bottom - Side a 1 a 2
Side- Top a 1 a 2
Parameter Space 1 a 2 .5 0 .5 a 1
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space 1 a 2 .5 0 .5 a 1
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Parameter Space
Difference from Linear Interp.
Linear functions
Linear functions
Linear functions
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D
Expanding to 3D MC
Expanding to 3D Ours
Expanding to 3D MC Ours
Perfect Sphere
MC
Ours
MC Ours
Sphere Normal Error 70 60 50 Degrees 40 MC Max MC Avg 30 Our Max Our Avg 20 10 0 0 5 10 15 20 25 30 Radius in Cells
MC
Ours
MC
Ours
Limitations?
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.

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