Physical Simulation
Jeff M Phillips
Simulated Knot Tying
Summary
Deformable modeling is often necessary in areas of graphics and
simulation. Applications such as surgical simulation
require real-time and robust models for deformables. This projects
describes a model for a physics-based rope simulation which can tie
knots. The rope model requires realistic physics, numerical
stability, complete collision detection, and computational
efficiency. Knot tying presents a tough case for such a model
because of the high expressiveness and contact in the
relatively small portion of rope which is in the knot.
The model uses a spline of linear springs with the mass pushed to the
control points to represent the rope. The volume used for collision
detection is represented by a sphere on each control point. An
impulse model is used to handle collisions. We chose
this model for its simplicity and expressiveness.
Allowing for accurate physics and expressiveness while maintaining
complete collision detection required adaptive insertion and removal
of control points within the
spline by subdividing and joining springs.
This required handling each
control point as representing two separate sections of the rope (the
left half of the right spring and the right half of the left spring)
in order to avoid numerical, computational, and symmetry errors.
A discrete event simulation is used to handle all collisions (as well
as insertion and removal events) correctly. At every time step, we
calculate the order of all
events which will occur. They are then handled in order, at the exact
simulation time. After each event is handled, stale events are
dequeued and secondary events are queued.
We tested our model by tying overhand knots and reef knots. We start
with just a handful of control points and the structure subdivides
until the rope has a continuous volume.
Visuals
Movies of rope simulations:
reef.mpg
overhand.mpg
gravity.mpg
Powerpoint slides from ICRA 2002:
icra-rope.pps
Simulated Suturing
Summary
Deformable modeling is often necessary in areas of graphics and
simulation. Applications such as surgical simulation
require real-time and robust models for deformables.
This project models a piece of tissue for use in suturing in surgical
simulations which deforms in real-time.
The structure for the tissue is a lattice of control
points connected with physical springs. Two and three dimensional
lattices were implemented.
The springs react under Hooke's Law.
The tissue model deforms to minimize the energy of the spring
network. The energy minimizer moves the control points along the
energy gradient determined by the springs. When the global energy is
within some tolerance, the control points are relocated to the new
low energy position. As sections of the mesh are manipulated, only
local sections of the structure are deformed, avoiding expensive global
calculations.
Suturing control is governed by user input through mouse and keyboard.
As sections of the structure are manipulated, the nearby network
deforms to the low energy positions in real-time.
Stiff springs link locations on the tissue model when a suture is set.
Visuals
Publication
Simulated Knot Tying.
Jeff M. Phillips, Andrew M. Ladd, Lydia E. Kavraki.
IEEE International Conference on Robotics and Automation. May 2002.
jeff's home page