Mass-Spring-System model for real time expressive

behaviour synthesis

Why and how to use Physical Model in Pure Data (pmpd)

Cyrille Henry (ch@chnry.net)

Abstract

Mass-spring-system (MSS) physical model (PM) are vastly documented in literature and

on internet. They where developed to imitate natural behaviours, specially for audio

synthesis but they can also be used to create natural behavious or even “plausible”

behaviours. This “plausible” behaviours are comportment that does not imitate any

specific real life behaviours, but - since basic real life physic are respected - looks

“natural”. This is specially useful for real time user interactions. Even if this “plausible”

behaviour can be use for any human / computer interface this document will mostly

focuses on artistic application.

After a quick overview of the equation used for this kind of simulation, this document will

list different strategies use in MSS (implementation, creation of a simulated system,

strategies for interaction and using data from this system). Finally the pmpd library for pure

data will be presented.

Introduction

In this document, we discuss the use of mass-spring-system physical model to create

expressive movement for real time interaction.

We are dealing with the production and the control of data flow aiming at the control of any

kind of software parameter : Sound synthesis, images synthesis, lighting or motor actuator

by example can be driven thanks to a physical model. This parameters can usually benefit

from an expressive control. We are using physical model to synthesize data flow and

control their behaviours.

MSS model can be use to imitate natural behaviours, but they can also be used to create

lot's of different behaviours. We did not focuses on real behaviours, but on “plausible”

behaviours : a movement that look natural, even if it did not imitate a specific real life

physics. MSS model can easily generate this “plausible” behaviours since it respect basic

real life physics. Moreover this kind of physical models allow a wild range of user

interaction for real time control of the movement.

Using this models can lead to control of different media with data flow and to control

correlation between this data, thus having sound and images by example that does not

represent the same data, but express the same underling process.

This document aim is to give key to a deep understanding of process involved in MSS

model. After a quick overview of the equation used for this kind of simulation, we will

present different approach to create topologies of mass / link network. Then it will list

different strategies used to interact with this MSS simulation. Latter, we will list few

approach to use the generated data flow for both sound synthesis control and images

synthesis control. It should not be seen as exhaustive, but as a summarized of the author

experience in developing PM for many different artistic applications. Latter, we will have a

look at pmpd : a specific implementation of MSS system for the Pure Data software.

Index
Abstract.................................................................................................................................................1
Introduction..........................................................................................................................................1
Index.....................................................................................................................................................2
Motivations...........................................................................................................................................4
Real motion......................................................................................................................................4
Movement using a simple interpolation...........................................................................................5
Mass Spring System.........................................................................................................................5
Physical Model.....................................................................................................................................7
Basic equation..................................................................................................................................7
Implementation................................................................................................................................8
Units.................................................................................................................................................8
Basic oscillating system...................................................................................................................8
Topologies........................................................................................................................................9
Regular structures.......................................................................................................................9
Random structures.....................................................................................................................10
Collection of independent simple structures.............................................................................11
Shape morphing.........................................................................................................................11
Modal synthesis.........................................................................................................................12
Real time interaction strategies......................................................................................................12
Moving fixed masses................................................................................................................12
Sending force to masses............................................................................................................12
Changing physical parameter....................................................................................................13
Using data created by a MSS.........................................................................................................13
Sound synthesis.........................................................................................................................14
Direct audio simulation........................................................................................................14
Scanned synthesis.................................................................................................................14
“Many element synthesis”....................................................................................................15
Visual synthesis.........................................................................................................................15
Complex system.............................................................................................................................17
Non linearity.............................................................................................................................17
Space limitation of links.......................................................................................................17
Non linear rigidity................................................................................................................17
Non linear damping..............................................................................................................18
More interactions......................................................................................................................18
Motion damping...................................................................................................................18
Creep of a link......................................................................................................................18
Plastic link............................................................................................................................19
Breaking link........................................................................................................................19
Link elongation computation error...........................................................................................19
MSS simulation and emergent phenomena...............................................................................20
Instabilities................................................................................................................................21
Controlling instabilities.............................................................................................................21
Example : chdh – emergence....................................................................................................23
MSS and Pure Data: the pmpd library................................................................................................26
Installation.....................................................................................................................................26
Generality.......................................................................................................................................26
Masses............................................................................................................................................26
Link................................................................................................................................................26
Metronome.....................................................................................................................................27
Interactor........................................................................................................................................27

Test.................................................................................................................................................27
pmpd* objects................................................................................................................................27
System creation.........................................................................................................................28
Interacting with the system.......................................................................................................28
Getting data from a system.......................................................................................................28
Pmpd*~ objects..............................................................................................................................29
website...........................................................................................................................................29
Sources...........................................................................................................................................29
Installation.....................................................................................................................................29
Conclusion..........................................................................................................................................29
Annexes..............................................................................................................................................30
References......................................................................................................................................30
pmpd objects list............................................................................................................................31

Motivations

Real motion

Since a movement is initiated thanks to a force, looking at the speed and acceleration (that

are linked to force, as we will see latter), is a good way to analyses a movement, and gives

more details than only looking only at the position over time. Figure 1 represent position,

velocity and acceleration over time for 6 different recording of a hand motion moving a

cursor from 2 different points 10 cm approximatively apart.

Even for simple movement with relatively similar position vs. time curve, lot's of variety can

appears in real life motion. When looking at the acceleration curve : minimum and

maximum acceleration and position of this extreme can be relatively different. The human

brain have been trained to analyse and understand this differences. Being able to

reproduce such diversity is the first step toward generating expressive behaviours.

Figure 1: 6 recording of a simple hand movement, and there corresponding velocity and

acceleration over time.

Movement using a simple interpolation

Using Pure data to move a parameter is usually done with the [line] object. This object

perform a linear interpolation between two points (see figure 2). This is not a kind of

movement that can easily be find in the nature. Using this to move a fader result in a very

different movement than what would be performed by a human, mainly because it did not

respect the world physics. The linear interpolation imply a constant speed of the

parameter, and no velocity before and after the transition. This result in an infinite

acceleration at the beginning and at the end of the movement.

Such movement is easily identifiable as artificial.

Mass Spring System

Fdili Alaoui and Al explain motivation using a MSS in an article published in the IJPADM

revue (REF 1). Here is an extract :

MSS present various properties that make them attractive to use in the performing arts

(Hsieh 2007; Jacquemin 2008; Johnston 2009; Fdili Alaoui 2012). They have the ability to

produce physically plausible behaviours because they are governed by the laws of physics

and hence have an evocative representation of real-world dynamics. We describe the

behaviour of a physical model as physically plausible when it generates realistically

perceived dynamics that are created autonomously to evoke real-world dynamics, without

imitating real-world mechanics.

MSS provide a wide range of controllable parameters in real-time (such as the parameters

of the forces applied to the masses) that govern its behaviours, and thus offer rich

possibilities of interaction. The MSS can be controlled through the mapping between the

MSS physical parameters and the features of the analysed movement. The resulting

interaction would create a relationship between the performer’s movement and the

associated MSS behaviours. This relationship follows pre-defined rules or interaction

scenarios.

figure 2: movement generated by a linear interpolation