Difference between revisions of "Simplified and Abstracted Geometry for Forward Dynamics"

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(Introduction)
(Introduction)
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==Abstract==
 
==Abstract==
 
==Introduction==
 
==Introduction==
Geometric simplification has played an important role in the computer graphics field by allowing believable viewing of scenes too complex for timely computation.  However, the approaches used in computer graphics for geometric simplification have as their goal the realistic portrayal of a scene to a viewer, not the similarity between the simplified or abstracted system and the physical ground truth.  In physical simulations, the model does not need to look like the original.  If a robot's legs can be abstracted as a pair of oval wheels that hit contact points appropriately, this might be acceptable for a physical simulation.  However, it would be completely inappropriate for a graphical system.  This offers a freedom of abstraction and simplification that does not exist in the graphics world.  However, other constraints apply: in rigid-body simulations of robots and complex mechanisms, geometry plays a key role in determining where the contact points, and thus collision joints, occur; different simplification methods will lead to different simulated results.  The choice of simplification method can be the determining factor of whether a simulation is accurate enough.
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Geometric simplification has played an important role in the computer graphics field by allowing believable viewing of scenes too complex for timely computation.  However, the approaches used in computer graphics for geometric simplification have as their goal the realistic portrayal of a scene to a viewer, not the similarity between the simplified or abstracted system and the physical ground truth.  In physical simulations, the model does not need to look like the original.  If a robot's legs can be abstracted as a pair of oval wheels that hit contact points appropriately, this might be acceptable for a physical simulation.  However, it would be completely inappropriate for a graphical system.  This offers a freedom of abstraction and simplification that does not exist in the graphics world.  However, other constraints apply: in rigid-body dynamics simulations of robots and complex mechanisms, geometry plays a key role in determining where the contact points, and thus collision joints, occur; different simplification methods will lead to different simulated results.  The choice of simplification method can be the determining factor of whether a simulation is accurate enough.
  
 
==Background==
 
==Background==

Revision as of 21:58, 8 October 2006

Draft

Contents

Abstract

Introduction

Geometric simplification has played an important role in the computer graphics field by allowing believable viewing of scenes too complex for timely computation. However, the approaches used in computer graphics for geometric simplification have as their goal the realistic portrayal of a scene to a viewer, not the similarity between the simplified or abstracted system and the physical ground truth. In physical simulations, the model does not need to look like the original. If a robot's legs can be abstracted as a pair of oval wheels that hit contact points appropriately, this might be acceptable for a physical simulation. However, it would be completely inappropriate for a graphical system. This offers a freedom of abstraction and simplification that does not exist in the graphics world. However, other constraints apply: in rigid-body dynamics simulations of robots and complex mechanisms, geometry plays a key role in determining where the contact points, and thus collision joints, occur; different simplification methods will lead to different simulated results. The choice of simplification method can be the determining factor of whether a simulation is accurate enough.

Background

Example Problem

Approach

Empirical Results

Conclusions

References

Model Simplification(PDF)

Adaptive Dynamics(PDF)

Milling Machine Simplification(PDF)

Geometric Model Simplification for CAD(PDF)