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Transcript of Eurohaptics 2002 [email protected] © Interactive Haptic Display of Deformable Surfaces Based on the...
Eurohaptics 2002
Interactive Haptic Display of Deformable Surfaces Based
on the Medial Axis Transform
Jason J. Corso, Jatin Chhugani, Allison OkamuraThe Johns Hopkins University
Eurohaptics 2002
Eurohaptics 2002
Interaction
• Definition of interactive changes– Graphics: 15 – 30 Hz– Haptics: 1000 Hz
• Definition of rendering changes– Graphics: pixel-wise (NxN)– Haptics: single-point (typically)
• How do these differences affect algorithms?
Eurohaptics 2002
Talk Outline
• Overview and Related Work
• The Medial Axis Transform
• Object Modeling
• Object Interaction
• Implementation and Results
• Conclusions
Eurohaptics 2002
Overview Of Our Work
• Interactive deformation and haptic rendering of viscoelastic surfaces
• Medial Axis Transform
• Compact representation
• Efficient rendering with low memory usage
Eurohaptics 2002
Related Work
• Physically-Based Modeling
– Spectrum:
– ArtDefo uses BEM [Pai 99,00]
– Medical Simulations often use FEM/BEM
• D-NURBS – physics based generalization that is coupled with FEM [Terzopoulos 94]
Eurohaptics 2002
Related Work
• Graphics-Based Deformation– Free-Form [Coquillart 97]– Volumetric Approaches [Avila 96]– Adaptively Sampled Distance Fields
[Frisken 01]
• NURBS Surfaces for haptic rendering
– Surface-Surface Interaction [Cohen 98]
Eurohaptics 2002
Medial Axis Transform
• MAT proposed by Blum [67]• A multilocal,multiscale representation
for graphics [Pizer, UNC]• Automatically generate a volumetric
representation of a polygonal mesh [Gagvani]
• Okamura developed a robotic system to acquire MAT models of real rigid-body objects [01].
Eurohaptics 2002
Medial Axis Transform
• Foundation: shape skeletons• Geometric abstraction of curves• Skeleton called medial axis (2D)• Each point on skeleton is associated
with a locally maximal disk.• These medial points coupled with
their radii define the MAT.
Eurohaptics 2002
Object Modeling
• An object is comprised of– The discretized skeleton– Radii of circles centered along skeleton– Stiffness, mass, damping, etc
Eurohaptics 2002
Object Modeling
• Interpolate a spline through skeleton (SK) (include position, radius, etc).
• Interpolate an envelope spline (SC) through contour.
Eurohaptics 2002
Talk Outline
• Overview and Related Work
• The Medial Axis Transform
• Object Modeling
• Object Interaction
• Implementation and Results
• Conclusions
Eurohaptics 2002
Object Interaction
• Nearest Point Localization
• Collision Detection
• Force/Deformation Calculation
• Spline Deformation
• Perform Rendering
Eurohaptics 2002
Nearest Point Localization
• Perform a binary search over domain of the skeleton spline.
• Evaluates circle nearest Q
Eurohaptics 2002
Object Deformation
• D = Rintersect - ||PQ||
• SK and SC are deformed appropriately.
Eurohaptics 2002
Object Deformation
• D = Rintersect - ||PQ||
• SK and SC are deformed appropriately.
Eurohaptics 2002
Object Deformation
• D = Rintersect - ||PQ||
• SK and SC are deformed appropriately.
Eurohaptics 2002
Spline Deformation
• Given d, a deformation vector, deform the most influential control points.
Eurohaptics 2002
Haptic Rendering
• Interact with circles through springs and dampers.
• Shear forces incorporated
Eurohaptics 2002
Graphic Rendering
• View-dependent adaptive tessellation
• Tessellate with maximum screen-space deviation of 3 pixels.
• Contour splines must be re-tessellated every frame to reflect the deformation.
Eurohaptics 2002
Implementation - DeforMAT
• In C++ on 700MHz PIII with 384MB
• GeForce2 and OpenGL (with the GLU NURBS Tessellator) for graphics
• 2D – Immersion IE2000
• 3D – SensAble 3DOF Phantom
Eurohaptics 2002
Results
• The complexity of the environment being graphically rendered is on average 105 triangles independent of MAT complexity.
Eurohaptics 2002
Conclusions
• A new algorithm for interactively deforming viscoelastic bodies at haptic interactive rates; i.e. 1KHz
• Couples efficient computation for haptic feedback with view-dependent graphics
• Minimal memory footprint
Eurohaptics 2002
Future Work
• Incorporate bifurcation• Non-ordered Medial Axes/Surfaces• Analysis of Area/Volume preservation• Extension of graphical rendering
algorithms• Direct performance comparison• Analysis of parameter estimation
– Robot to gather data
Eurohaptics 2002
Acknowledgments
• Samuel Khor for starting the work on haptic rendering using shape skeletons at Hopkins
• Budi Purnomo for his many suggestions with respect to spline deformation