Project 2: Basic particle system Constrained Particle System - - PowerPoint PPT Presentation

Project 2:

Constrained Particle System

Requirements

• Basic particle system
• Tinkertoys

Particle system

• Implement following components
• Particle structure
• Force structure
• ODE solver
• Particle system that has accesses to particles,

forces, and an instance of ODE solver

Requirements for particle system

• The particle system is attached to a node of your

hierarchical model other than the root node

• There are at least two distinctive forces acting on the

particle system. For example, gravity and spring forces

Skeleton code

• Provide high level particle system structure in

ParticleSystem class

• A Euler step is executed every time

ParticleSystem::computeForcesAndUpdateParticles() is called from ModelerView::draw()

• ODE solver is called from

computeForcesAndUpdateParticles()

ParticleSystem

• constructor, destructor, and etc.
• computeForcesAndUpdateParticles()
• drawParticles()
• startSimulation()
• stopSimulation()

Other structures

• Particle class
• Force class
• An elegant implementation would include a

generic force class and a variety of distinct forces that inherit from it

Other structures

• ODE solver
• Ideally, ODE solver should be independent from

the particle system

• Particle system instantiates an ODE solver and

keeps the pointer as a data member

• When an ODE solver is created, a void pointer

that points to the particle system is passed to the ODE constructor

Embedding in animation system

• Store particles as coordinates in world space
• Attach a particle emitter to a node in the model

hierarchy

• need to calculate the world coordinates of the

particle emitter every time a particle is spawned

• glGetFloatv(MODELVIEW_MATRIX, m)

Tinkertoy

• Extend the basic particle system with constraints
• Implement following two types of constraints
• Constraint that keeps the bead on the circle
• Constraint that keeps two particles at a fixed

distance apart from each other

Requirements for Tinkertoys

• Implement a particle that is constrained to move

along a circle

• Implement a second particle that is kept a fixed

distance apart from the particle on the circle

• Simulate the particles under the gravity and the

interactive force applied using the mouse

• Experiment the coefficients for the constraint

feedback

Skeleton code

• There is no skeleton code for this part of the

assignment

Where do you start?

• Draw a circle on the screen
• Rewrite robotarm.cpp by taking out all the

controls and drawing a 2D circle on the screen

• Define global structures in ParticleSystem
• Need to allocate space for structure such as

Jacobian matrix

Constraints

• Implement constraints in a similar way as forces
• Define a base class for constraints and inherit

from it when you implement each specific type of constraints

• Number your constraints and particles so you can

index them easily

Jacobian matrix

• 2D array
• VL matrix class
• Sparse matrix

n blocks m blocks xj xk Ci

Solving constraint forces

• Build a linear system
• Loop over each constraint to evaluate the

constraint function and its various derivatives

• Solve the final linear system by
• computing the inverse matrix
• using linear system solvers provided by VL

VL: Vector library

• VL provides a set of vector and matrix classes, as

well as a number of functions for performing arithmetic with them

• Most arithmetic operators and functions for vectors

and matrices are supported (+, -, *, /, dot(), len(), cross(), trans(), inv(), etc)

• VL also provides two linear system solvers:

SolveOverRelax() and SolveConjGrad()

• Include “VLd.h” in your code

Hooking up to basic particle system

• Constraint forces are calculated after ordinary forces

and before updating the derivative of the current state

• Everything happens in

computeForcesAndUpdateParticles()

Mouse interaction

• Each time the mouse button and the shift key are

pressed at the same time, find the particle closest to the mouse and apply the force directly on that particle

• Apply an attractive spring force between the particle

and the mouse until the button is released

• Add code in ModelerView::handle() to catch the

event when left button and the shift key are pushed

• Create and delete “mouse forces” on the fly

Experiments

• Add feedback term to the constraint acceleration
• Play with the coefficients ks and kd to find the
• ptimal values
• Do these experiments from the UI, instead of

recompiling the entire code every time you change the coefficients

¨ C = −ksC − kd ˙ C

Bells and whistles

• Implement additional types of constraints
• Constraints that output more than one scalar
• Initialize the velocity of particles
• Helicopter with a cannon launching packages out

Bells and whistles

• Realistic looking particles
• Billboard technique
• Alpha blending

Bells and whistles

• Implement a more sophisticated ODE solver
• Adaptive step size
• Midpoint method
• 4th order Runge-Kutta methd
• Implicit Euler’s method

Bells and whistles

• Implement collision detection
• Provide control of the restitution constant
• Allow particles to bounce off each other
• Create an interactive billboard game

Bells and whistles

• Add flocking behaviors to simulate creatures moving

in flocks, herds, or schools

• Simulate complicated interaction between the

character and the particles

• Design a set of tools to build arbitrary tinkertoys on

the fly

• building blocks: beads, rings, sticks, springs, etc.

Bells and whistles

• Create a chain reaction machine
• You might need to implement a rigid body

simulator

• Cloth simulation
• Read the literature in this area first

Introduce: monstrous bell Introduce: monstrous bell

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Demos