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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
